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gauss doctoral thesis

Carl Friedrich Gauss and the Gauss Society: a brief overview

Axel d. wittmann.

Carl Friedrich Gauss (1777–1855) was one of the most eminent scientists of all time. He was born in Brunswick, studied in Göttingen, passed his doctoral examination in Helmstedt, and from 1807 until his death, was the director of the Göttingen Astronomical Observatory. As a professor of astronomy, he worked in the fields of astronomy, mathematics, geodesy, and physics, where he made world-famous and lasting contributions. In his honour, and to preserve his memory, the Gauss Society was founded in Göttingen in 1962. The present paper aims to give nonspecialists a brief introduction into the life of Gauss and an introduction into the Gauss Society and its history.

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Wittmann, A. D.: Carl Friedrich Gauss and the Gauss Society: a brief overview, Hist. Geo Space. Sci., 11, 199–205, https://doi.org/10.5194/hgss-11-199-2020, 2020.

Carl Friedrich Gauss was one of the most eminent scientists ever, and, like, for example, Archimedes (288–212 BCE) or Sir Isaac Newton (1642–1727), whom he admired most, was competent and singularly made everlasting contributions in more than one field, namely mathematics, astronomy, geodesy, and physics. He was an outstanding genius in mathematics, but his main profession (from which he earned his income) was that of an astronomer. At the age of 30 years, he became a professor of astronomy and the director of the Göttingen Observatory. Another world-famous astronomer, Nicolaus Copernicus (1473–1543), once wrote about this field, as follows: “… while it is a property of all sciences to distract from leading a depraved life, astronomy can do this to an especially high degree, apart from the incredibly high degree of satisfaction which it provides” (Hermanowski, 1996). A similar statement was made by Gauss in 1804: “According to my feelings, practical astronomy – right next to the joy of heart and the inspection of truth in pure mathematics – is the sweetest pleasure which we can have on Earth” (letter to Farkas Bolyai, 25 November 1804). This shows that, as a post-doctoral fellow, Gauss was already interested in astronomy. At that time he was in love with a local woman, looking for a job, and already world-famous because in 1801 he had rediscovered the missing planet of Ceres Ferdinandea. Gauss was born in Brunswick on 30 April 1777. At the age of about 3 years, Gauss's talents in mathematics became evident, and a bit later, in elementary school, he himself discovered a fast algorithm for finding the sum of an arithmetic series. He was 9 years old at the time. Subsequently, Gauss was sponsored by Carl Wilhelm Ferdinand, the Duke of Brunswick, and after completing high school, he received a stipend which enabled him to study “abroad”, at the university in Göttingen, which was famous for its collection of mathematical literature. This was quite unusual because, at that time, Brunswick had a state university of its own in nearby Helmstedt. When he was a student in Göttingen in 1796 (and on a short visit to his parents in Brunswick), Gauss made his first important discovery in mathematics. He found rigorous evidence for the constructibility of the heptadecagon or the 17-gon. This proof – or disproof – had been sought since the time of Euclid, i.e. for more than 2000 years. Even a mathematical genius like Johannes Kepler had considered the heptadecagon as being impossible to construct. This discovery became the first entry in Gauss's famous “mathematical diary”, in which he briefly noted most of his discoveries until 1813. It was typical of Gauss not to publish everything without careful consideration. But his first-ever publication – a note on his discovery concerning the heptadecagon – was so lacking in detail about how his result was derived, gave no earlier references, and it did not actually present his proof that it would have been immediately rejected by a modern editor. Actually, Gauss's papers, due to his laxness in his citation of other publications (he tacitly assumed that everyone would know them anyway), would have been rejected by most of today's peer-review systems. As a student of classical literature and classical languages (in which he was fluent) in Göttingen, Gauss became more and more interested in astronomy and made his first observations of the night sky using a professional telescope (a mural quadrant by John Bird) at the former (the “old”) Göttingen Astronomical Observatory. This was very famous due to the work of Tobias Mayer (1723–1762), whom Gauss always admired greatly. In September 1798 Gauss returned to Brunswick and started his doctoral degree, which he received from the Duke of Brunswick's own university in Helmstedt. In his thesis, Gauss delivered the first rigorous argument for the “fundamental theorem of algebra”. In August 1800, Gauss published a numerical algorithm for calculating the date of Easter. This was his first astronomical publication, and his algorithm is still in use today. In 1801 he published his main mathematical monograph, the Disquisitiones arithmeticae . Together with Newton's Philosophiæ Naturalis Principia Mathematica , this work is considered to be one of the great masterpieces of science. Shortly afterwards, an event occurred which made Gauss turn to astronomy forever and which made him world-famous overnight. It had been known for a while that there was a gap in the planetary distances between Mars and Jupiter. As Lichtenberg had stated in his lecture: “According to the gap in the arithmetical progression, one has to place an imaginary planet between Mars and Jupiter” (Gamauf, 1814).

https://hgss.copernicus.org/articles/11/199/2020/hgss-11-199-2020-f01

Figure 1 Carl Friedrich Gauss, painted by Gottlieb Biermann (1887). Reproduction by the author from a calendar dated June 1939; this is the first known colour print of a portrait of Gauss.

This planet was desperately searched for by many people since it provided a unique opportunity to become famous without an academic education (or even any education at all). On 1 January 1801, the Italian astronomer Giuseppe Piazzi observed a small, star-like object of an eighth magnitude which, on the following nights, moved among the stars in the same way that a planet or a comet would. But he could not continue his observation, and the planet was lost. The most famous astronomers of the time tried to calculate an orbit in order to recover the “lost planet”, but they were wrong by about 10 to 15 ∘ , and it was not until Gauss published his calculations that Ceres – as the planet was finally named – was rediscovered in December 1801 by Franz Xaver von Zach.

In 1805, Gauss married a charming young lady from Brunswick, Johanna Osthoff. She was the great love of his life but, unfortunately, died 4 years later. In 1807 – shortly before Göttingen came under the rule of Jerôme Bonaparte – Gauss was appointed as a professor of astronomy and the director of the Göttingen University Observatory by the Hanoverian government. The observatory was under still construction, slightly to the southeast of Göttingen and just outside the town wall, and was finished in 1816. Following the terrible shock after the loss of his beloved Johanna, Gauss mourned intensively and then married again, this time to Wilhelmine Waldeck, a close friend of his deceased wife, and they had three more children. At approximately this time, Gauss wrote a paper titled Theoria Interpolationis Methodo Nova Tractata , in which, among other things, he developed the theory of the fast Fourier transform (FFT), which was in almost the same form as it is used today. Space constraints do not permit the mention of Gauss's many other contributions to pure and applied mathematics which made him one of the most outstanding mathematicians of all time. In 1809, Gauss published his most important monograph in astronomy, the Theoria Motus Corporum Coelestium , which also contained an account of his method of least squares and the Gaussian distribution curve. If the Nobel Prize had existed in 1809, Gauss might have received it. Of all the academic lectures Gauss held in Göttingen, 70 % dealt with astronomy, 15 % with mathematics, 9 % with geodesy, and 6 % with physics; one would not expect such statistics from a professor of mathematics. Notwithstanding his mathematical talents, Gauss earned his income as an astronomer. Although he did not like lecturing very much, Gauss educated a school of successful astronomers (among them Schumacher, Encke, Nikolai, Möbius, Gould, and Klinkerfues) and a slightly lesser number of successful mathematicians (among them Riemann, Dedekind, Cantor, von Staudt, and Schering). With some of his pupils Gauss maintained lifelong friendships, and his closest friends were Olbers, Schumacher, Gerling, and Encke.

Competent scientists should change their research interests every 10 years during their lives (this is “Fermi's recommendation”), and Gauss did that. From 1821 until 1824 he conducted and actively participated in the project of land surveying (“triangulation”) in northern Germany, which extended westwards into what is today the Netherlands and eastwards to the former capital of Prussia, the town of Berlin. On this occasion, he invented the heliotrope, a device used to direct sunlight, with arcsecond accuracy, in any given direction. This was a forerunner of modern laser devices. And he developed the Gauss–Krüger coordinate system for conformably mapping the surface of the Earth. Since its rediscovery by the US Army in 1947, this system has also become known as the Universal Transverse Mercator (UTM) coordinates and is in global use as GPS coordinates (which are mathematically the same). In Göttingen, Gauss also made important contributions to physics, optics, crystallography, Earth magnetism, insurance mathematics, etc. Gauss and Weber – slightly influenced by Humboldt – initiated what may be called the first international geophysical year by establishing a network of 53 Earth magnetic stations around the world. The results were collected and analysed in Göttingen. And, in April 1833, Gauss and Weber invented the first fully operational electromagnetic telegraph in the world. This was the beginning of today's worldwide communication by telegraph, telefax, and SMS through mobile phones. As a result of his talents and his reputation, Gauss was elected as a member of scientific academies in Germany, Russia, England, Spain, and France, and he received approximately 75 foreign awards, medals, and decorations. But Gauss disliked travelling and never travelled very far. Most of the awards were papers sent to him, and just a few were objects (a pendulum clock from Paris, the Copley medal from London, etc.) which were brought to Göttingen by colleagues or students. Gauss's last scientific achievement was a short, but very sensitive, Foucault-type pendulum, which he invented in 1854. Today, we rank Gauss among the titans of science, like Archimedes and Sir Isaac Newton. His contributions to non-Euclidean geometry and the curvature of space were explicitly acknowledged by Einstein on several occasions. Gauss died peacefully of heart and lung failure on 23 February 1855 at the age of almost 78. A journal in Brunswick wrote, “He ended his life in order to transit into those worlds which he had so diligently observed for a long time” ( Braunschweigisches Magazin , 18 July 1857). Gauss has been honoured posthumously by paintings, busts, statues, medals, coins, postage stamps, banknotes, etc., which are too numerous to be described here.

https://hgss.copernicus.org/articles/11/199/2020/hgss-11-199-2020-f02

Figure 2 Gauss's former observatory, the “Sternwarte Göttingen” (photograph by the author).

Gauss was a well-reputed, honourable, and decent character devoted to science, his family, and to his students, colleagues, and friends. In the late 1950s, there emerged a necessity among some of the local admirers of Gauss to preserve his memory and his achievements. On 17 May 1962 the registered association called the “Gauss-Gesellschaft” (Gauss Society) was founded by a group of 14 persons in Göttingen, among them the mayor of Göttingen, some famous scientists, and – last but not least – Horst Michling (1909–2003), who was the head of the geodesy department of the Göttingen town administration. Michling is considered to be the founder of the Gauss Society. The aims of the society were put in writing in the statutes. Among others, they were to preserve the memory of Gauss, to organise publications and lectures, and, by remaining in close contact with the University of Göttingen and the Göttingen Academy of Sciences, to conduct and publish research on the life and works of Gauss. During the following years, several members of the Gauss Society contributed important research and completely new findings on Gauss and his many unpublished works. Starting in 1964, the Gauss Society has issued an annual publication (a sort of yearbook) called “Mitteilungen der Gauss-Gesellschaft” (ISSN 0435-1452), of which 57 volumes have been published (until 2020; for details, see http://www.gauss-gesellschaft.de , last access: 5 September 2020). This publication is a mayor source of research about the works of Gauss and more recent developments in astronomy, mathematics, physics, and geodesy related to Gauss. Medals dedicated to Gauss were issued in 1856, 1877, 1933, and 2005. The first president of the Gauss Society was the famous geophysicist Julius Bartels (Fig. 3), who, unfortunately, died in March 1964.

In 1977 important celebrations were organised both in Brunswick and in Göttingen in order to commemorate Gauss's 200th birthday. In 1982 the Gauss Society celebrated its 40th anniversary in the ancient town hall of Göttingen. Then, in the year 2005 (which was officially called the “Gauss Year”) many celebrations, a series of public lectures organised by the Göttingen Academy of Sciences, and an exhibition in the ancient town hall of Göttingen were organised, and Gauss medals were issued in both silver and gold. Many new books and articles (both scientific and fiction) about Gauss and his life appeared in that year (Fig. 4)

https://hgss.copernicus.org/articles/11/199/2020/hgss-11-199-2020-f03

Figure 3 The geophysicist Julius Bartels, the first president of the Gauss Society, laying a wreath at the grave of Gauss in 1963 (photograph from the Gauss Society archives).

Since 1962 the Gauss Society has organised 58 annual meetings and approximately 43 excursions, and it has instigated and largely designed monuments at some of the major triangular points of Gauss's land-surveying project (namely, Altona Observatory, Brocken, Kleper, and Hoher Hagen). In 2009 an impressive bust of Gauss was set up and inaugurated during a ceremony at the Walhalla memorial near Regensburg, which is the German hall of fame. In 2012 the Gauss Society celebrated its 50th anniversary in the facilities of the reconstructed Göttingen Astronomical Observatory, which is now called the “Historic Observatory”, and – after 190 years or so – is no longer used as an astronomical observatory. The Gauss Society has members mainly in German-speaking European countries (Germany, Austria, and Switzerland), but also in some other countries, particularly in the United States where most of the descendants from Gauss's second marriage (namely his sons Eugen and Wilhelm) live, whereas most of the descendants from his first marriage (his son Joseph) still live in Germany.

https://hgss.copernicus.org/articles/11/199/2020/hgss-11-199-2020-f04

Figure 4 Some of the biographies of Carl Friedrich Gauss published by members of the Gauss Society. From left: Dunnington (1955), Michling (1976), and Biegel and Reich (2005).

https://hgss.copernicus.org/articles/11/199/2020/hgss-11-199-2020-f05

Figure 5 The “Südliches Meridianzeichen”, or the southern meridian mark, which is owned by the Gauss Society and is officially listed as a historic monument (photograph by the author).

The Gauss Society owns a private archive, a collection of books about Gauss and his fields of work, and a collection of items related to Gauss and his family, some of which were donated by his descendants. It also owns a piece of land on a hill near Friedland, 12 km south of the Göttingen Astronomical Observatory, where Gauss, in 1820, erected the “Südliches Meridianzeichen”, or the southern meridian mark, which, until about 1930, served to properly align the Reichenbach meridian circle to the south. This usually took place during the daytime when sunlight was shining through the slits of the monument as their distances were built in accordance with the angular distance of the vertical wires of the telescope (Fig. 5).

The following is a selection of books about Gauss, in chronological order, which is recommended for further reading.

For an overview of Gauss' works, see Reich (2002) as quoting Gauss himself would be far too numerous a list. Popular books and novels which contain a lot of historical errors are not listed. In the case of multiple or more recent editions, only the first edition is cited.

Sartorius von Waltershausen, W.: Gauß zum Gedächtnis, Verlag S. Hirzel, Leipzig, 108 pp., 1856.

Winnecke, F. A. T.: Gauss, Ein Umriss seines Lebens und Wirkens, Fr. Vieweg und Sohn, Braunschweig, 34 pp., 1877.

Hänselmann, L.: Carl Friedrich Gauß, Zwölf Kapitel aus seinem Leben, Duncker & Humblot, Leipzig, 106 pp., 1878.

Bieberbach, L.: Carl Friedrich Gauß, ein deutsches Gelehrtenleben, Keil Verlag, Berlin, 179 pp., 1938.

Dunnington, G. W.: Carl Friedrich Gauss: Titan of science, Exposition Press, New York, 479 pp., 1955.

Roloff, E. A.: Carl Friedrich Gauss, Verlag A. Fromm, Osnabrück, 80 pp., 1941.

Worbs, E.: Carl Friedrich Gauss – Ein Lebensbild, Verlag Koehler & Amelung, Leipzig, 235 pp., 1955.

Wußing, H.: Carl Friedrich Gauß, B.G. Teubner Verlag, Leipzig, 92 pp., 1974.

Michling, H.: Carl Friedrich Gauß, Episoden aus dem Leben etc., Verlag Göttinger Tageblatt, Göttingen, 141 pp., 1976.

Reich, K.: Carl Friedrich Gauß 1777/1977, Verlag Moos & Partner, München, 128 pp., 1977.

Küssner, M.: Carl-Friedrich Gauß und seine Welt der Bücher, Musterschmidt Verlag, Göttingen, 184 pp., 1979.

Bühler, W. K.: Gauss. A Biographical Study, Springer-Verlag, Berlin, Heidelberg, New York, 208 pp., 1981.

Biermann, K.-R.: Carl Friedrich Gauß, der Fürst der Mathematiker etc., Urania Verlag, Berlin, 251 pp., 1990.

Reich, K.: Gauss' Werke in Kurzfassung, Dr. Erwin Rauner Verlag, Augsburg, 196 pp., 2002.

Tent, M. B. W.: Carl Friedrich Gauss, The Prince of Mathematics, A.K. Peters, Ltd., Wellesley, MA, 245 pp., 2005.

Biegel, G., and Reich, K.: Carl Friedrich Gauss. Genie aus Braunschweig etc., Joh. Heinr. Meyer Verlag, Braunschweig, 216 pp., 2005.

Mania, H.: Gauß, Eine Biographie, Rowohlt Verlag, Reinbek, 367 pp., 2008.

West, K.: Profiles in Mathematics: Carl Friedrich Gauss, Morgan Reynolds, Greensboro, NC, 112 pp., 2009.

The author declares that there is no conflict of interest.

This paper was edited by Kristian Schlegel and reviewed by Hans Volkert and one anonymous referee.

Biegel, G., and Reich, K.: Carl Friedrich Gauss. Genie aus Braunschweig etc., Joh. Heinr. Meyer Verlag, Braunschweig, 2005. 

Dunnington, G. W.: Carl Friedrich Gauss: Titan of science, Exposition Press, New York, 1955. 

Gamauf, G.: Erinnerungen aus Lichtenbergs Vorlesungen über Astronomie, Geistingersche Buchhandlung, Wien/Triest, p. 206, 1814. 

Hermanowski, G.: Nikolaus Kopernikus Zwischen Mittelalter und Neuzeit, Styria Reprint, Styria, Graz, 284 pp., 193–194 (Copernicus' original handwriting is reproduced on page 193), 1996. 

Michling, H.: Carl Friedrich Gauß, Episoden aus dem Leben etc., Verlag Göttinger Tageblatt, Göttingen, 1976. 

Reich, K.: Gauss' Werke in Kurzfassung, Dr. Erwin Rauner Verlag, Augsburg, 2002. 

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Title: on gauss's first proof of the fundamental theorem of algebra.

Abstract: Carl Friedrich Gauss is often given credit for providing the first correct proof of the fundamental theorem of algebra in his 1799 doctoral dissertation. However, Gauss's proof contained a significant gap. In this paper, we give an elementary way of filling the gap in Gauss's proof.

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 MacTutor

Johann carl friedrich gauss.

to gather new strength in the arms of your friendship - strength for a life which is only valuable because it belongs to my three small children.
... the vain effort to conceal with an untenable tissue of pseudo proofs the gap which one cannot fill out.
to praise it would mean to praise myself .
had the same convictions for 54 years
If an area in R 3 \mathbb{R}^{3} R 3 can be developed ( i.e. mapped isometrically ) into another area of R 3 \mathbb{R}^{3} R 3 , the values of the Gaussian curvatures are identical in corresponding points.
... usually he sat in a comfortable attitude, looking down, slightly stooped, with hands folded above his lap. He spoke quite freely, very clearly, simply and plainly: but when he wanted to emphasise a new viewpoint ... then he lifted his head, turned to one of those sitting next to him, and gazed at him with his beautiful, penetrating blue eyes during the emphatic speech. ... If he proceeded from an explanation of principles to the development of mathematical formulas, then he got up, and in a stately very upright posture he wrote on a blackboard beside him in his peculiarly beautiful handwriting: he always succeeded through economy and deliberate arrangement in making do with a rather small space. For numerical examples, on whose careful completion he placed special value, he brought along the requisite data on little slips of paper.

References ( show )

  • K O May, Biography in Dictionary of Scientific Biography ( New York 1970 - 1990) . See THIS LINK .
  • Biography in Encyclopaedia Britannica. http://www.britannica.com/biography/Carl-Friedrich-Gauss
  • W K Bühler, Gauss: A Biographical Study ( Berlin, 1981) .
  • G W Dunnington, Carl Friedrich Gauss : Titan of Science ( New York, 1955) .
  • T Hall, Carl Friedrich Gauss : A Biography (1970) .
  • G M Rassias ( ed. ) , The mathematical heritage of C F Gauss ( Singapore, 1991) .
  • H Reichardt, Gauss, in H Wussing and W Arnold, Biographien bedeutender Mathematiker ( Berlin, 1983) .
  • H Reichardt ( ed. ) , C F Gauss Gedenkband anlässlich des 100 . Todestages am 23 . Februar 1855 (1957) .
  • W S von Waltershausen, Gauss, a Memorial ( Colorado Springs, Colo., 1966) .
  • C Agostinelli, Some aspects of the life and work of Carl Friedrich Gauss and that of other illustrious members of the Academy ( Italian ) , Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 112 (1978) , suppl., 69 - 88 .
  • G V Bagratuni, Carl Friedrich Gauss, his works on geodesy and his geodetic research ( Russian ) , Izv. Vyss. Ucebn. Zaved. Geod. i Aèrofot. (6) (1977) , 138 - 143 .
  • W Benham, The Gauss anagram : an alternative solution, Ann. of Sci. 31 (1974) , 449 - 455 .
  • H J M Bos, Carl Friedrich Gauss : a biographical note ( Dutch ) , Nieuw Tijdschr. Wisk. 64 (4) (1976 / 77) , 234 - 240 .
  • E Breitenberger, Gauss und Listing: Topologie und Freundschaft, Gauss-Ges. Göttingen Mitt. 30 (1993) , 3 - 56 .
  • E Breitenberger, Gauss's geodesy and the axiom of parallels, Arch. Hist. Exact Sci. 31 (3) (1984) , 273 - 289 .
  • E Buissant des Amorie, Gauss' formula for π ( Dutch ) , Nieuw Tijdschr. Wisk. 64 (4) (1976 / 77) , 200 - 204 .
  • D A Cox,Gauss and the arithmetic - geometric mean, Notices Amer. Math. Soc. 32 (2) (1985) , 147 - 151 .
  • D A Cox, The arithmetic-geometric mean of Gauss, Enseign. Math. (2) 30 (3 - 4) (1984) , 275 - 330 .
  • H S M Coxeter, Gauss as a geometer, Historia Math. 4 (4) (1977) , 379 - 396 .
  • J Dieudonné, Carl Friedrich Gauss : a bicentenary, Southeast Asian Bull. Math. 2 (2) (1978) , 61 - 70 .
  • P J de Doelder, Gauss and function theory ( especially with regard to the lemniscate functions ) ( Dutch ) , Nieuw Tijdschr. Wisk. 64 (4) (1976 / 77) , 176 - 183 .
  • J Dutka, On Gauss' priority in the discovery of the method of least squares, Arch. Hist. Exact Sci. 49 (4) (1996) , 355 - 370 .
  • M Folkerts, C F Gauss' Beitrag zur Besetzung von Professuren an der Universität Göttingen, Gauss-Ges. Göttingen Mitt. 32 (1995) , 3 - 34 .
  • E G Forbes, The astronomical work of Carl Friedrich Gauss (1777 - 1855) , Historia Math. 5 (2) (1978) , 167 - 181 .
  • E G Forbes, Gauss and the discovery of Ceres, J. Hist. Astronom. 2 (3) (1971) , 195 - 199 .
  • A Fryant and V L N Sarma, Gauss' first proof of the fundamental theorem of algebra, Math. Student 52 (1 - 4) (1984) , 101 - 105 .
  • G D Garland, The contributions of Carl Friedrich Gauss to geomagnetism, Historia Math. 6 (1) (1979) , 5 - 29 .
  • S Gindikin, Carl Friedrich Gauss ( on the 200 th anniversary of his birth ) ( Russian ) , Kvant 8 (1977) , 2 - 14 .
  • H Grauert, Wie Gauss die alte Göttinger Mathematik schuf, Proceedings of the 2 nd Gauss Symposium. Conference A : Mathematics and Theoretical Physics ( Berlin, 1995) , 1 - 15 .
  • H-J Felber, Die beiden Ausnahmebestimmungen in der von C F Gauss aufgestellten Osterformel, Sterne 53 (1) (1977) , 22 - 34 .
  • H-J Treder, Gauss und die Gravitationstheorie, Sterne 53 (1) (1977) , 9 - 14 .
  • F Henneman, Gauss' law of errors and the method of least squares : a historical sketch ( Dutch ) , Nieuw Tijdschr. Wisk. 64 (4) (1976 / 77) , 205 - 209 .
  • S H Hollingdale, C F Gauss (1777 - 1855) : a bicentennial tribute, Bull. Inst. Math. Appl. 13 (3 - 4) (1977) , 68 - 76 .
  • K-R Biermann, Aus der Gauss-Forschung, Gauss-Ges. Göttingen Mitt. 29 (1992) , 39 - 42 .
  • K-R Biermann, Zu den Beziehungen von C F Gauss und A v Humboldt zu A F Möbius, NTM Schr. Geschichte Naturwiss. Tech. Medizin 12 (1) (1975) , 12 - 15 .
  • K-R Biermann, Die Gauss-Briefe in Goethes Besitz, NTM Schr. Geschichte Naturwiss. Tech. Medizin 11 (1) (1974) , 2 - 10 .
  • K-R Biermann, C F Gauss in seinem Verhältnis zur britischen Wissenschaft und Literatur, NTM Schr. Geschichte Naturwiss. Tech. Medizin 14 (1) (1977) , 7 - 15 .
  • K-R Biermann, Zu Dirichlets geplantem Nachruf auf Gauss, NTM Schr. Geschichte Naturwiss. Tech. Medizin 8 (1) (1971) , 9 - 12 .
  • R Kooistra, C F Gauss and the fundamental theorem of algebra ( Dutch ) , Nieuw Tijdschr. Wisk. 64 (4) (1976 / 77) , 173 - 175 .
  • R Lehti, Gauss's 'Disquisitiones arithmeticae' ( Finnish ) , Arkhimedes 29 (2) (1977) , 49 - 66 .
  • A F Monna, Gauss and the physical sciences ( Dutch ) , Nieuw Tijdschr. Wisk. 64 (4) (1976 / 77) , 212 - 217 .
  • P Müürsepp, Gauss and Tartu University, Historia Math. 5 (4) (1978) , 455 - 459 .
  • P Müürsepp, Gauss' letter to Fuss of 4 April 1803 , Historia Math. 4 (1977) , 37 - 41 .
  • W Narkiewicz, The work of C F Gauss in algebra and number theory, Festakt und Tagung aus Anlass des 200 . Geburtstages von Carl Friedrich Gauss ( Berlin, 1978) , 75 - 82 .
  • J G O'Hara, Gauss and the Royal Society : the reception of his ideas on magnetism in Britain (1832 - 1842) , Notes and Records Roy. Soc. London 38 (1) (1983) , 17 - 78 .
  • R L Plackett, The influence of Laplace and Gauss in Britain, Bull. Inst. Internat. Statist. 53 (1) (1989) , 163 - 176 .
  • K Reich, Gauss und seine Zeit, Sterne und Weltraum 16 (5) (1977) , 148 - 157 .
  • N Ritsema, Gauss and the cyclotomic equation ( Dutch ) , Nieuw Tijdschr. Wisk. 64 (4) (1976 / 77) , 188 - 196 .
  • D E Rowe, Gauss, Dirichlet and the Law of Biquadratic Reciprocity, The Mathematical Intelligencer 10 (1988) , 13 - 26 .
  • H Schimank, Carl Friedrich Gauss ( German ) , Gauss-Gesellschaft Göttingen, Mitteilungen 8 (1971) , 6 - 31 .
  • V G Selihanovic, Carl Friedrich Gauss ( on the occasion of the 200 th anniversary of his birth ) ( Russian ) , Izv. Vyss. Ucebn. Zaved. Geod. i Aèrofot. (6) (1977) , 131 - 137 .
  • O Sheynin, C F Gauss and geodetic observations, Arch. Hist. Exact Sci. 46 (3) (1994) , 253 - 283 .
  • O B Sheynin, C F Gauss and the theory of errors, Arch. Hist. Exact Sci. 20 (1) (1979) , 21 - 72 .
  • D A Sprott, Gauss's contributions to statistics, Historia Math. 5 (2) (1978) , 183 - 203 .
  • H B Stauffer, Carl Friedrich Gauss, Bull. Malaysian Math. Soc. 6 (1) (1975) , 1 - 3 .
  • G W Stewart, Gauss, statistics, and Gaussian elimination, J. Comput. Graph. Statist. 4 (1) (1995) , 1 - 11 .
  • S M Stigler, The History of Statistics. The Measurement of Uncertainty before 1900 ( Cambridge, Mass.-London, 1986) , 140 -.
  • S M Stigler, Gauss and the invention of least squares, Ann. Statist. 9 (3) (1981) , 465 - 474 .
  • S M Stigler, An attack on Gauss, published by Legendre in 1820 , Historia Math. 4 (1977) , 31 - 35 .
  • B Szénassy, Remarks on Gauss's work on non-Euclidean geometry ( Hungarian ) , Mat. Lapok 28 (1 - 3) (1980) , 133 - 140 .
  • W A van der Spek, The Easter formulae of C F Gauss ( Dutch ) , Nieuw Tijdschr. Wisk. 64 (4) (1976 / 77) , 218 - 233 .
  • W A van der Spek, Gauss' logarithms ( Dutch ) , Nieuw Tijdschr. Wisk. 64 (4) (1976 / 77) , 197 - 199 .
  • F van der Blij, Gauss and analytic number theory ( Dutch ) , Nieuw Tijdschr. Wisk. 64 (4) (1976 / 77) , 184 - 187 .
  • W Waterhouse, Gauss's first argument for least squares, Arch. Hist. Exact Sci. 41 (1) (1990) , 41 - 52 .
  • W Waterhouse, Gauss on infinity, Historia Math. 6 (4) (1979) , 430 - 436 .
  • H Wussing, Carl Friedrich Gauss - Leben und Wirken, Festakt und Tagung aus Anlass des 200 . Geburtstages von Carl Friedrich Gauss ( Berlin, 1978) , 151 - 160 .
  • K Zormbala, Gauss and the definition of the plane concept in Euclidean elementary geometry, Historia Math. 23 (4) (1996) , 418 - 436 .

Additional Resources ( show )

Other pages about Carl Friedrich Gauss:

  • Gauss's Disquisitiones Arithmeticae
  • Richard Dedekind on Carl Friedrich Gauss
  • Wilhelm Ahrens book of quotes
  • Gauss's estimate for the density of primes
  • Comparison with Legendre's estimate
  • Prime Number Theorem
  • A letter from Gauss to Taurinus discussing the possibility of non-Euclidean geometry
  • An extract from Theoria residuorum biquadraticorum (1828 - 32)
  • Preface to Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections
  • Miller's postage stamps
  • Heinz Klaus Strick biography

Other websites about Carl Friedrich Gauss:

  • Dictionary of Scientific Biography
  • Encyclopaedia Britannica
  • A Google doodle
  • Kevin Brown ( Constructing the 17 -gon )
  • Kevin Brown ( Geodesy )
  • S D Chambless ( An obituary of Gauss's son ) and an account of his life in the USA
  • Sci Hi blog
  • Mathematical Genealogy Project
  • MathSciNet Author profile
  • zbMATH entry

Honours ( show )

Honours awarded to Carl Friedrich Gauss

  • Fellow of the Royal Society 1804
  • Fellow of the Royal Society of Edinburgh 1820
  • Royal Society Copley Medal 1838
  • Lunar features Crater Gauss
  • Popular biographies list Number 23
  • Google doodle 2018

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The Göttingen Campus is aiming to provide doctoral candidates with the best possible training and professional development opportunities, of which the major part – supporting them to develop own ideas and strengthen their individual profile – is the role of supervisors.

The GAUSS Office in close collaboration with the GGNB Office and the Dean’s Offices of the faculties is offering a wide range of support and services for the doctoral candidates in mathematics and natural sciences throughout their stay. Doctoral candidates do not only have the possibility to choose from a broad qualification and training program but can also benefit from scientific networking, advice and counselling. Additionally, the structured doctoral process in GAUSS is aiming to facilitate administrative procedures to support the supervisors and doctoral candidates so that they can concentrate on their research projects and scientific development.

An overview of the different phases of the doctoral process in GAUSS including the corresponding required tasks and obligations by both, the doctoral candidate as well as the supervisor and thesis advisory committee, can be found in our Roadmap to a GAUSS Doctorate .

GAUSS_Roadmap-PhD

Please click on the different topics in order to see more details.

Requirements In general, prospective doctoral candidates need to have a university degree (Master, Diploma or equivalent state examination) in a relevant or related field in mathematics, natural and life sciences completed with above-average results. For detailed admission requirements please see §4 of the doctoral regulations of GAUSS ( German , English translation ) as well as the individual regulations of the different doctorate programs . Decisions on the fulfilment of additional requirements for admission are made by the respective doctoral program.

International Doctoral students

Recruiting international doctoral candidates is supported by different services across the Göttingen Campus. The International Office of the University is in charge of the enrolment of all international doctoral students. For questions regarding visas and immigration, please contact the the University’s Welcome Centre , which can also assist with questions about living in Göttingen. The recognition of degrees from foreign universities is assessed by the respective doctoral program. In case of further questions, please contact the GAUSS Office or the program office.

Application steps

  • Research topic, funding, GAUSS program The first step for interested doctoral candidates is to find an exciting research topic and a supervisor for their dissertation. It is crucial that both parties are discussing early on in the application process funding options. The prospective supervisor should also advise on the GAUSS doctoral program most suitable for the student.
  • Compose thesis advisory committee (TAC) Thesis advisory committees are comprised of three members: the main supervisor and one additional examination accredited person (see list of GAUSS faculty members ) as well as one further academic holding a doctoral degree. They advise the doctoral student and monitor his/her progress throughout the doctoral process. TACs serve two main purposes, (1) to provide critical feedback to the research progress and data interpretation, and (2) to mediate potentially upcoming difficult situations between the doctoral student and supervisor. For these reasons, a careful choice of TAC members should acknowledge (1) a sufficiently broad scientific background to be able to comment on the research progress from different and proficient perspectives and (2) the independence of each other to ensure impartiality. Usually, the first two members of the TAC serve as referees of the doctoral thesis. Due to the fact that at least one of the reviewers must be a Professor at the University of Göttingen (full professorship; not “apl. Professor” or honorary; see §11, doctoral degree regulations ( German , English translation )), we would strongly suggest that theTAC is composed accordingly from the outset. If in doubt, please do not hesitate to contact us and we will advise you accordingly.
  • Admission & supervision agreement The next step for each doctoral candidate is to request admission to the program of his/her choice. It is mandatory for the student to register for enrolment in GAUSS and to sign the supervision agreement, which you can find in a single form in English or German . If the PhD candidate has been enrolled at the University of Göttingen before, she/he has to login via eCampus to access the pre-filled form. This document also serves for the digital matriculation process and includes the mandatory doctoral student’s declaration. Applications have to be submitted within max. three month after start of the PhD - in the best case, already before.

The Role of the Graduate School GAUSS is committed to provide its doctoral students with the best possible support and training to successfully complete their research work and dissertation. They are guided through the entire doctoral process including the examination ensuring high quality standards. GAUSS not only supports the doctoral programs and encourages scientific networks but also provides additional qualification, counseling and career advice for doctoral candidates. This enables the doctoral students to acquire important key skills to qualify for careers within and outside of academia. The GAUSS qualification program is including a variety of methods and skills courses as well as language courses and statistical consulting. Thereby, it is completing numerous scientific events organized by the faculties, institutes and centers of the Göttingen Campus such as seminar series, invited lectures, journal clubs, and symposia. GAUSS is offering financial support for retreats, symposia, career related events, emergencies and family-related and diversity schemes. For further information or additional services provided by different players on the Göttingen Campus, go to the section Doctoral candidates .

The Role of the Supervisor As a PhD supervisor one of your integral roles is to mentor your students, apply your scientific expertise to promote their independence, and support them in making their achievements visible in the scientific community. It is crucial that you are available for regular scientific discussions and actively engage your abilities and experience in scientifically challenging phases. In close cooperation with the other members of the thesis advisory committee, you critically and supportively follow the doctoral process and give constructive feedback to regular progress reports and meetings. Together, you are the first point of contact for technical matters, career planning and cases of conflict (see also Rules of good practice for doctoral supervision in English or German ). This applies not only for scientific-related issues but also in other matters (e.g. health or family), in particular when they might affect the performance or success of the PhD. You should also support the student’s integration in the academic environment on the Göttingen Campus and beyond. If you have international students, please support them as much as possible in their social and cultural integration. Challenging and promoting doctoral candidates is vital for their development, which should be well-balanced to prevent discouragement. Please take into consideration and respect family responsibilities, different work patterns and requests for further training. To avoid misunderstandings from the outset it is recommendable to agree on a time management plan for the doctorate including milestones and objectives where possible. As you are mentoring your students for a few years, you are a vital part of their development into scientific independence and increased responsibilities.

  • members of the doctoral candidate’s thesis committee
  • spokesperson of the doctoral program the student is enrolled in
  • GAUSS Managing Board
  • GAUSS Office
  • Central Conflict Management
  • GAUSS person of trust

If you are seeking advice, everything will be treated strictly confidential. In case of a possible scientific misconduct, you can also contact the Office of Ombudsman and Good Scientific Practice for confidential consultation. In case you are encountering mobbing or sex-related violence, please contact the Equal Opportunities Office .

Once the doctoral candidate has submitted the PhD thesis, the two referees (one additional external referee in case of a proposed summa cum laude ; chosen by the program committee/dean's office - ( §13 (6) ) have up to four weeks to evaluate the dissertation and submit a report including a recommended grade. Usually, the oral examination will take place four to six weeks after submission. The thesis defense lasts 60-90 minutes and is open to University members. The first 30 minutes are reserved for a presentation by the doctoral candidate placing his/her dissertation in a larger scientific context. This is followed by 30-60 minutes of questions, which are initially only permitted by members of the examination committee, followed by potential questions by the audience. Afterwards, the examination committee decides on an overall grade for the doctoral examination in a closed meeting.

The publication of the PhD thesis is mandatory and must not take place later than one year after the thesis defense date. In exceptional cases and upon written request only, this deadline may be extended once by one additional year. Prior to publication the doctoral candidate is obliged to discuss any modifications with the doctoral thesis committee and the supervisor has to sign the revision certificate ( English , German ) on behalf of the committee.

Under specific circumstances and only for a good reason, the publication of the thesis can be restricted (embargo) by publishing via the SUB, which requires a joint written request by the supervisor and the doctoral candidate. In this case only the abstract of the thesis is publicly available, whereas the remaining dissertation is treated confidentially. For further information please see doctoral regulations §21 section 8 ( German , English translation ) or contact the GAUSS Office. Approving the good reasons as well as the request for restricted publication / embargo of the thesis is solely incumbent upon the examination board. Once your application is granted, the thesis has to be published with the SUB using the restriction notice.

gauss doctoral thesis

Physics Ph.D. candidate wins 2024 Three Minute Thesis competition

3/22/2024 By | Katya Hrichak , Cornell University Graduate School

“I want you to remember a time when you were in a setting where you felt like you didn’t belong. I want you to remember how you felt in that setting, maybe isolated or out of place, and how much you felt like you wanted to continue going back to that setting—probably not much. These feelings are all too familiar for undergraduate women pursuing their studies in science, and in physics specifically,” began Meagan Sundstrom, a doctoral candidate in physics at the ninth annual Cornell University Three Minute Thesis (3MT) competition.

Alongside seven other finalists, Sundstrom presented her dissertation research in just three minutes on March 20 to a panel of judges and an audience from across campus while additional friends, family, advisors, and lab mates watched online. In the first in-person Cornell 3MT since 2019, presentations were judged by how clearly and compellingly students summarized their research to a general audience, using only one static slide.

Sundstrom’s presentation, “Recognizing and Removing Barriers for Women in Physics,” earned her first place and $1,500. Second place and $1,000 was awarded to information science doctoral student Sterling Williams-Ceci for her presentation, “AI Helps us Write – but at What Cost?”

After nearly 60 in-person and 70 virtual audience members cast their ballots, votes were tallied and the People’s Choice Award and $250 were presented to biomedical and biological sciences doctoral candidate Sharada Gopal for her presentation, “Worming Our Way to a Longer Life.”

This year’s judges included Jane Bunker, director of Cornell University Press; Joe Ellis, director of online degree program development at eCornell; David Lodge, the Francis J. DiSalvo Director of the Cornell Atkinson Center for Sustainability; and Bob Riter, patient advocate for the Cornell Community Cancer Partnership. Organization of the competition and coaching of presenters was provided by the Graduate School Office of Career and Professional Development.

“As grad students, there are a lot of opportunities to give your elevator pitch at conferences and more professional settings to more senior people in your field, and I thought this would be a really cool opportunity for me to try to tailor that pitch to a more general audience—how would I describe my research to my family and friends?—so that was fun,” said Sundstrom.

Being able to “zoom out” and view her topic from a different perspective was also helpful for Sundstrom, who is currently writing her dissertation and appreciates having both formulated a storyline and thought about the broader impacts of her work.

Williams-Ceci similarly enjoyed the chance to speak to a different type of audience than she is used to addressing.

“I hadn’t really had an opportunity in grad school to try communicating to a broad audience, it’s always just to my lab, so I wanted to practice having a chance to really tell a story and not just go through the slides,” she said. “It really helped me know for a fact that I can tell a convincing story about a project that I’ve done.”

Gopal shared that the 3MT was a fun way to combine her longtime artistic interests with her science.

“It seemed like such a fun event. I did a lot of theatre in college so I thought, ‘What can I do artistically here?’ and this seemed like a good mix of my scientific interest and my artistic theatre interests,” she said, adding that she also benefitted from looking at the bigger picture of her work and its impacts.

The 3MT competition was first held in 2008 at the University of Queensland and has since been adopted by over 900 universities in over 85 countries. 3MT challenges research degree students to present a compelling story on their dissertation or thesis and its significance in just three minutes, in language appropriate to a non-specialist audience.

Cornell’s Graduate School first hosted a 3MT competition in 2015 and the event has grown steadily since that time. As the winner of Cornell’s competition, Sundstrom will now go on to compete in northeast regional competitions.

“Our Three Minute Thesis final round is a highlight of the year for those of us in the Graduate School—literally we talk about it all year long,” said Kathryn J. Boor, dean of the Graduate School and vice provost for graduate education. “We look forward to it because it’s just plain fun, and it’s an opportunity for us to watch and learn from our accomplished and creative graduate researchers.”

“I could not possibly be more proud of the work we saw,” she said.

Read the story on the Cornell University Graduate School website.

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Eight students advance to 3MT finals

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Replica theory shows deep neural networks think alike

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Choosing connection: Physics professor teaches Arab youth in Israel

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Poised for Oscar gold, Oppenheimer boasts a Big Red distinction

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IOE alumni named winners of the 2024 BERA Master’s Dissertation and Doctoral Thesis awards

27 March 2024

Dr Emily Macleod (PhD) and Kate Fox (Education and International Development MA) have won the British Educational Research Association (BERA) Doctoral and Master’s Thesis prizes respectively.

Left: Emily Macleod. Right: Kate Fox. Image permission: Emily Macleod and Kate Fox.

The awards are given in recognition of academic excellence and research rigour within the field of educational research. 

Emily Macleod won for her thesis, “The status and safety of teaching: A longitudinal study of why some young people in England become teachers, and why others do not.” She investigated young people’s motivations behind pursuing – or not pursuing – the profession amidst the context of national and international teacher shortages. 

She completed her PhD at IOE’s Department of Education, Practice and Society in 2023, and was a co-host on IOE’s podcast series Research for the Real World . She continues on as an honorary postdoctoral fellow. She also worked on the ASPIRES research project studying young people's science and career aspirations, before which she was a secondary school teacher. 

Kate Fox won for her MA dissertation entitled “Building bridges or barriers? A study of home, community, and school literacy practices in rural Tanzania.”

Her dissertation centres the experiences of parents from rural communities within the Tanzanian education system – and the diverse ways families and communities contribute to young children’s literacy learning.

Kate completed her Master’s degree at IOE in 2023. She is now a Research Officer with the IOE Research Development team, and a Research Assistant working on two multi-institutional projects: Climate-U and Equitable research cultures . Her career in education spans 20 years as a teacher, headteacher and teacher trainer in Tanzania and the UK.

Related links

  • Read more: BERA announces 2024 Master’s Dissertation and Doctoral Thesis winners
  • Emily on ‘Why do people aspire to become teachers?’ RFTRW: S19E03
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  • More about Dr Emily Macleod 
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Publication-based doctorate: is it for me?

Potential research higher degree candidates from academia or industry will need to decide between a doctorate by thesis or by publication. Here are key questions to ask before embarking on the doctoral journey

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Prospective doctoral candidates have much less understanding of the process and requirements for a publication-based doctorate than they do for the more popular thesis-based route. Completing a doctorate, thesis- or publication-based, takes time and effort. Selecting the right mode is important before starting a research higher degree (RHD), so that the prospective doctoral candidate can be confident of completing it.

Here, I discuss the questions that future doctoral candidates should ask if they are considering a publication-based doctorate.

  • Why get a PhD by publication (and other career tips)
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What is my goal in completing a doctorate?

A thesis-based doctorate helps the candidate to explore a subtopic of a research field as deeply as possible, based on few theoretical variables and within a limited practical context (for example, a limited dataset from a single socio-economic setting). A publication-based doctorate could explore a topic with more variables and contexts (for example, different publications on same topic would have different variables and datasets). It gives a publication-based doctorate a little more flexibility to explore a topic more widely. Therefore, the goal of exploring a subtopic area as widely as possible could fit better for a publication-based doctorate.

What is my thesis?

Yes, even for a publication-based doctorate, candidates need to produce a thesis, a theory or a proposition on a single topic, in combination with the overall contributions of published papers. As a result, the candidates need to think about how they can draw together the relevant findings from published papers to produce new knowledge on a single topic.

Are my publications cohesive?

For a publication-based doctorate, the publications you may already have and the outputs you plan to produce within an agreed time frame should focus on and contribute to a single subtopic. So ask yourself: how unified are my existing and planned publications? Designing the research aim, research question, methodology and contribution of your intended publications in relation to these sections among your existing publications is instrumental to ensuring that your publications are cohesive.

Where am I publishing?

Understanding where you publish should be a key consideration, as not all publications will be eligible for inclusion in your submission. All fields of studies have their own benchmark publications. For example, in business, the journal lists of the Association of Business Schools in the UK and the Australian Business Deans’ Council are often used to indicate a publication’s quality. In general, a publication-based doctorate could consist of journal papers, book chapters or published conference proceedings. Industry-based publications could be considered as well in some instances (for example, if you have an article published by a reputable chamber of commerce). Articles in predatory journals and publications such as brief op-ed articles or blogs might not be considered for a doctorate by publication.

Will the findings and contributions of my publications stand the test of time?

Doctoral candidates may already have publications, perhaps even in good academic journals, but they may be 10 years old. The knowledge produced perhaps made a contribution to your field of study, but the subsequent progress of the field may have surpassed your work or made it obsolete over time. So considering the potential significance of publications during the projected time of a doctoral submission is important. Comparing your work with existing publications in your field is a good way to understand the significance of the work you produce.

What is the extent of my theoretical and practical contribution?  

All doctorates should make significant contribution of theoretical knowledge and practical implication. But we know that the extent of theoretical and practical contribution of a RHD can differ based on the type of doctorate someone would undertake. For example, a doctor of philosophy needs to produce significant theoretical knowledge, whereas a professional doctorate would need more practical implications. Therefore, the candidate needs to consider the extent of theoretical and practical implications of their publications, in order to decide whether a doctor of philosophy or a professional doctorate would be more relevant.

Am I publishing as a sole author or a co-author?

Often, we work in a team and publish with our co-authors. Therefore, if you are planning to include one or several co-authored publications in a publication-based doctorate, securing permission from co-authors to include the relevant sections (that you have contributed to those co-authored publications) into a publication-based doctoral thesis will be helpful in avoiding any future conflict of interest among co-authors.

What is my career stage?

Career stage would have an influence on whether to opt for a doctorate by publication. For example, a candidate may already have five or 10 years of academic teaching or industry experience but has perhaps produced few academic or industry-based publications. In general, working to publish more papers in next two years, and combining them with existing publications to produce a new knowledge, would be useful to submit a thesis by publication. Mid-career candidates from either academia or industry might be considering a publication-based doctorate alongside other commitments but find that their work-life balance is unsustainable. In this case, a doctor of philosophy would be more appropriate for academic candidates, while a professional doctorate would be more relevant for candidates from industry.

How do I find a PhD supervisor?

Irrespective of whether the doctorate is by thesis or publication, RHD supervisors play a significant role in training their candidates to become independent researchers. So looking at the prospective supervisors’ profile, comparing your topic with their research area, emailing them to share your draft proposal, and requesting an appointment to talk about it further will be valuable for prospective candidates. It will help them to develop their topic of research, understand research procedures and requirements, and secure a supervisor.

These questions will help an academic or an industry professional considering a doctorate by publication to weigh their options carefully.

Riad Shams is assistant professor and head of the PhD programme at the Newcastle Business School at Northumbria University, UK. He is a board member of the Northern Advanced Research Training Initiative, a fellow of the Higher Education Academy and the EuroMed Academy of Business, and associate editor of the Journal of Social Entrepreneurship .

If you would like advice and insight from academics and university staff delivered direct to your inbox each week, sign up for the Campus newsletter .

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Altenbach, H. (2020). Gauß, Johann Carl Friedrich. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55771-6_114

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PhD Student Wins Research Award for Work on Aging in 3-Minute Thesis Competition

Can you explain your thesis in just three minutes, in a way that anyone can grasp?

Christi Lero, a doctoral student in social work at the Brown School, did just that, delivering the winning presentation at the  Three-Minute Thesis (3MT) Competition , earning the 2024 Mark S. Wrighton Award on Aging. 

Organized by the Harvey A. Friedman Center for Aging, the 3MT competition challenges PhD students to present their research in a concise and accessible way for a diverse audience. The Mark S. Wrighton Research Award recognizes doctoral students who show outstanding promise as researchers on topics relevant to older adults and aging society.

On March 6, in a captivating display of succinct scholarship, Lero presented her dissertation, titled “Using Self-Compassion to Enhance Wellbeing of Caregivers of People with Neurodegenerative Disease,” impressing a panel of judges from various fields.

“Winning this competition and award is an honor and certainly motivates me to continue doing research in a meaningful and accessible way,” Lero said. “Competitions like 3MT and awards like the Mark S. Wrighton Research Award on Aging are platforms for budding researchers to share their work but also practice talking about complicated things in an accessible way.”

Lero’s success was no happenstance; it was a product of thorough preparation. When asked about her approach, she attributed her triumph to rehearsing, refining, and even reaching out to a stranger.

“Practice, practice, practice!” she remarked of her readiness plan. “I am very fortunate to have the most supportive spouse, friends, and mentors who listened to my speech and helped me revise. There is even a kind student worker in the Brown School library that volunteered three minutes of their time and gave some feedback.” 

Lero’s dissertation research focuses on using self-compassion as a mechanism to help caregivers maintain well-being during and after caregiving.

She explained: “Caregivers of people with diseases like ALS, Huntington’s, and dementia dedicate years of their lives to making sure their loved ones receive care that is respectful and dignified, but that means sacrificing quite a lot of their time, energy, resources, and selves.”

Recognizing the collaborative nature of her scientific work, Lero expressed gratitude to the caregivers who shared their experiences with her.

“Science is a team sport and great work isn’t done alone,” she said. “I am so grateful for all the support I have received, and especially for all the caregivers who have let me walk beside them in their most difficult times. Any recognition I receive reflects the dedication and care I have witnessed from them.” 

Lero’s thesis advisor is Nancy Morrow-Howell, the Betty Bofinger Brown Distinguished Professor of Social Policy. Lero, an NIH T32 Predoctoral Fellow, will be honored at the  Annual Friedman Lecture and Awards  on April 5, where she will discuss her research in more detail.

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  1. About the homies [ Gauss

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  3. 3-Minute Thesis Competition 2023

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  6. GUASS SEIDEL METHOD

COMMENTS

  1. PDF New Proof of the Theorem That Every

    Gauss submitted this outstanding work to the University of Helmstedt, Germany, as his doctoral dissertation and was awarded the degree in 1799, at the age of 22. He published two further proofs, in Latin like this first proof, in 1816, and a fourth proof, in German, in 1850. The first

  2. Carl Friedrich Gauss

    In his doctoral thesis from 1799 Gauss proved the fundamental theorem of algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. Mathematicians including Jean le Rond d'Alembert had produced false proofs before him, and Gauss' dissertation contains a critique of d'Alembert ...

  3. PDF Gauss, the Prince of Mathematicians

    Gauss entered Caroline College at the age of 15 years and three years later moved to Göttingen where he received his doctor's degree in 1799. The title of his doctoral thesis was "A New Proof That Every Rational Integral Function of One Variable Can Be Resolved into Real Factors of the First or the Second Degree." The only thing wrong with this

  4. The Historical Significance of Carl Friedrich Gauss in Mathematics and

    His doctoral thesis (1799) constituted the first rigorous proof of the fundamental theorem of algebra, viz? that every equation of degree n ... Gauss a generation earlier (1799) had been fully conscious of the idea and its importance, from which Abel's and Jacobi's achievements origi-

  5. PDF On Gauss's First Proof of the Fundamental Theorem of Algebra

    Carl Friedrich Gauss is often given credit for providing the first correct proof of the fundamental theorem of algebra in his 1799 doctoral disser-tation. However, Gauss's proof contained a significant gap. In this paper, we give an elementary way of filling the gap in Gauss's proof. 1 Introduction.

  6. Carl Friedrich Gauss and the Gauss Society: a brief overview

    In September 1798 Gauss returned to Brunswick and started his doctoral degree, which he received from the Duke of Brunswick's own university in Helmstedt. In his thesis, Gauss delivered the first rigorous argument for the "fundamental theorem of algebra". In August 1800, Gauss published a numerical algorithm for calculating the date of Easter.

  7. On Gauss's first proof of the fundamental theorem of algebra

    Carl Friedrich Gauss is often given credit for providing the first correct proof of the fundamental theorem of algebra in his 1799 doctoral dissertation. However, Gauss's proof contained a significant gap. In this paper, we give an elementary way of filling the gap in Gauss's proof. 9 pages, 1 figure.

  8. PDF The Fundamental Theorem of Algebra

    mathematician Carl Gauss in his doctoral thesis [2]. The aim of these notes is to provide a proof of the Fundamental Theorem of Algebra using concepts that should be familiar to you from your study of Calculus, and so we begin by providing an explicit formulation. Theorem 1 (Fundamental Theorem of Algebra). Given any positive integer n ≥ 1 ...

  9. On Gauss's First Proof of the Fundamental Theorem of Algebra

    Carl Friedrich Gauss is often given credit for providing the first correct proof of the fundamental theorem of algebra in his 1799 doctoral dissertation. However, Gauss's proof contained a ...

  10. Carl Friedrich Gauss

    Gauss's first significant discovery, in 1792, was that a regular polygon of 17 sides can be constructed by ruler and compass alone. Its significance lies not in the result but in the proof, which rested on a profound analysis of the factorization of polynomial equations and opened the door to later ideas of Galois theory. His doctoral thesis of 1797 gave a proof of the fundamental theorem of ...

  11. PDF 7 Gauss's Derivation of the Normal Distribution and the ...

    Gauss succeeded in keeping up a steady scientific activity of great originality in pure and applied mathematics. In his doctoral dissertation in 1799 he proved the fundamental theorem of algebra and showed that a real polynomial can be written as a product of linear and quadratic factors with real coe!cients. Another early mathemat-

  12. The Fundamental Theorem of Algebra

    Gauss's doctoral dissertation, submitted to the University of Helmstedt in 1799 and written in Latin, was entitled Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse Footnote 6 — that is, "New proof of the theorem that every rational ...

  13. Gauss, Carl Friedrich (1777-1855)

    His mentor in Helmstedt was J.F. Pfaff (1765-1825). The thesis submitted was a complete proof of the fundamental theorem of algebra. His studies on number theory published in Latin language as Disquitiones arithimeticae in 1801 made Carl Friedrich Gauss immediately one of the leading mathematicians in Europe. Gauss also made further ...

  14. Johann Carl Friedrich Gauss

    Gauss's dissertation was a discussion of the fundamental theorem of algebra. With his stipend to support him, Gauss did not need to find a job so devoted himself to research. ... From 1850 onwards Gauss's work was again nearly all of a practical nature although he did approve Riemann's doctoral thesis and heard his probationary lecture. His ...

  15. Gauss, Johann Carl Friedrich

    Riemann's doctoral thesis. Indeed a titan of science [1], Gauss was extraordinarily productive throughout his life, although his personal life was not without turmoil. After developing heart disease, Gauss died in his sleep in late February, 1855. References [1] Dunnington, G.W. (1955). Carl Friedrich Gauss, Titan of

  16. PhD Thesis

    Thesis extension. The duration of doctoral studies within GAUSS should be three years. Therefore, the thesis should be submitted three years after you started to work on the doctoral project and got accepted for one of the GAUSS programs. The oral examination and publication of the thesis does not have to take place within this three year deadline.

  17. On Gauss's First Proof of the Fundamental Theorem of Algebra

    Carl Friedrich Gauss is often given credit for providing the first correct proof of the fundamental theorem of algebra in his 1799 doctoral dissertation. However, Gauss's proof contained a significant gap. In this paper, we give an elementary way of filling the gap in Gauss's proof. 1. INTRODUCTION.

  18. polynomials

    This was not his doctoral thesis: it is dated 1812. His doctoral dissertation "Demonstratio Nova Theorematis Omnem Fvnctionem Algebraicam Rationalem Integram Vnus Variabilis In Factores Reales Primi Vel Secvndi Gradvs Resolvi Posse" from Helmstedt was in 1799, and was about the Fundamental Theorem of Algebra.

  19. Algebra

    The first complete proof of the theorem was given by the German mathematician Carl Friedrich Gauss in his doctoral dissertation of 1799. Subsequently, Gauss provided three additional proofs. A remarkable feature of all these proofs was that they were based on methods and ideas from calculus and geometry, rather than algebra.

  20. Doctoral Candidates Documents

    Thesis Extension (Handout , Application form.docx , Application form.pdf ) Countdown to doctoral degree (Handout/Checklist) Thesis submission and application for admission to the doctoral examination (via eCampus; detailed information) SUB restriction notice / embargo for thesis publication (for RerNat-O 2018 as .docx or .pdf in German)

  21. Doctoral Process

    An overview of the different phases of the doctoral process in GAUSS including the corresponding required tasks and obligations by both, the doctoral candidate as well as the supervisor and thesis advisory committee, can be found in our Roadmap to a GAUSS Doctorate . Please click on the different topics in order to see more details.

  22. Physics Ph.D. candidate wins 2024 Three Minute Thesis competition

    As the winner of Cornell's competition, Sundstrom will now go on to compete in northeast regional competitions. "Our Three Minute Thesis final round is a highlight of the year for those of us in the Graduate School—literally we talk about it all year long," said Kathryn J. Boor, dean of the Graduate School and vice provost for graduate ...

  23. Gauss, Carl Friedrich

    Gauss left Göttingen in 1798 without a diploma, ... His dissertation is a proof of the fundamental theorem of algebra (FTA) [2,3]. The fundamental theorem of algebra states that. FormalPara Theorem 1 Every polynomial equation of degree n has n roots in the complex numbers. Gauss is usually credited with the first proof of the FTA. ...

  24. IOE alumni named winners of the 2024 BERA Master's Dissertation ...

    Dr Emily Macleod (PhD) and Kate Fox (Education and International Development MA) have won the British Educational Research Association (BERA) Doctoral and Master's Thesis prizes respectively. The awards are given in recognition of academic excellence and research rigour within the field of educational research.

  25. Publication-based doctorate: is it for me?

    A thesis-based doctorate helps the candidate to explore a subtopic of a research field as deeply as possible, based on few theoretical variables and within a limited practical context (for example, a limited dataset from a single socio-economic setting). A publication-based doctorate could explore a topic with more variables and contexts (for ...

  26. Penn State community invited to attend Three Minute Thesis, Graduate

    The Graduate School at Penn State will host the 39th annual Graduate Exhibition from March 18-22 on the University Park campus and online, followed by the final round of the inaugural Three Minute Thesis competition at 10 a.m. March 23 at the Penn Stater Hotel and Conference Center and online. Both events are free and open to Penn State students, staff, faculty and community members.

  27. Ph.D. Dissertation Defense in Plastics Engineering: Nahal Aliheidari 4/

    The Francis College of Engineering, Department of Plastics Engineering, invites you to attend a Doctoral Dissertation defense by Nahal Aliheidari on "Long-Term Environmental Durability Assessment of Fiber-Reinforced Composite/Adhesive Joints." Location: Ball Hall 313 and virtual via Zoom. Please email advisor [email protected] for link.

  28. Ph.D. Dissertation Proposal Defense in Energy Engineering

    The Francis College of Engineering, Department of Energy Engineering - Nuclear, invites you to attend a Doctoral Dissertation Proposal defense by Ankit Mishra on: "Energy Systems Modeling" Candidate Name: Ankit Mishra Degree: Doctoral Defense Date: Thursday, April 4, 2024 Time: 3:30-5:30 p.m. Location: Southwick 250 Committee: Advisor Sukesh ...

  29. Gauß, Johann Carl Friedrich

    In 1799 he defended his doctoral thesis at the Academia Julia (University of Helmstedt). Gauß remained mentally active into his old age, even while suffering from gout and general unhappiness. For example, at the age of 62, he taught himself Russian. ... The Gauß (sometimes Gauss), symbol G, sometimes Gs, is in the cgs system of units based ...

  30. PhD Student Wins Research Award for Work on Aging in 3-Minute Thesis

    Organized by the Harvey A. Friedman Center for Aging, the 3MT competition challenges PhD students to present their research in a concise and accessible way for a diverse audience. The Mark S. Wrighton Research Award recognizes doctoral students who show outstanding promise as researchers on topics relevant to older adults and aging society.