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Gauss's diary was a record of the mathematical discoveries of German mathematician
Most of the entries consist of a brief and sometimes cryptic statement of a result in Latin.
Entry 1, dated 1796, March 30, states "", which records Gauss's discovery of the construction of a heptadecagon by ruler and compass.
Entry 18, dated 1796, July 10, states " ΕΥΡΗΚΑ! " and records his discovery of a proof that any number is the sum of 3 triangular numbers, a special case of the Fermat polygonal number theorem.
Entry 43, dated 1796, October 21, states "Vicimus GEGAN" (We have conquered GEGAN). The meaning of this was a mystery for many years. found a manuscript by Gauss suggesting that GEGAN is a reversal of the acronym NAGEG standing for Nexum medii Arithmetico-Geometricum Expectationibus Generalibus and refers to the connection between the arithmetic geometric mean and elliptic functions.
Entry 146, dated 1814 July 9, is the last entry, and records an observation relating biquadratic residues and the lemniscate functions, later proved by Gauss and by . More precisely, Gauss observed that if ''a''+''bi'' is a (Gaussian) prime and ''a''–1+''bi'' is divisible by 2+2''i'', then the number of solutions to the congruence 1=''xx''+''yy''+''xxyy'' (mod ''a''+''bi''), including ''x''=∞, ''y''=±''i'' and ''x''=±''i'', ''y''=∞, is (''a''–1)2+''b''2.
Carl Friedrich Gauss
Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...
from 1796 to 1814. It was rediscovered in 1897 and published by , and reprinted in volume X1 of his collected works and in . There is an English translation with commentary given by , reprinted in the second edition of .
Sample entries
Most of the entries consist of a brief and sometimes cryptic statement of a result in Latin.
Entry 1, dated 1796, March 30, states "", which records Gauss's discovery of the construction of a heptadecagon by ruler and compass.
Entry 18, dated 1796, July 10, states " ΕΥΡΗΚΑ! " and records his discovery of a proof that any number is the sum of 3 triangular numbers, a special case of the Fermat polygonal number theorem.
Entry 43, dated 1796, October 21, states "Vicimus GEGAN" (We have conquered GEGAN). The meaning of this was a mystery for many years. found a manuscript by Gauss suggesting that GEGAN is a reversal of the acronym NAGEG standing for Nexum medii Arithmetico-Geometricum Expectationibus Generalibus and refers to the connection between the arithmetic geometric mean and elliptic functions.
Entry 146, dated 1814 July 9, is the last entry, and records an observation relating biquadratic residues and the lemniscate functions, later proved by Gauss and by . More precisely, Gauss observed that if ''a''+''bi'' is a (Gaussian) prime and ''a''–1+''bi'' is divisible by 2+2''i'', then the number of solutions to the congruence 1=''xx''+''yy''+''xxyy'' (mod ''a''+''bi''), including ''x''=∞, ''y''=±''i'' and ''x''=±''i'', ''y''=∞, is (''a''–1)2+''b''2.
References
* * * * * * *{{Citation , authorlink1=Felix Klein , last1=Klein , first1=Felix , title=Gauß' wissenschaftliches Tagebuch 1796–1814 , doi=10.1007/BF01449013 , year=1903 , journal=Mathematische Annalen
''Mathematische Annalen'' (abbreviated as ''Math. Ann.'' or, formerly, ''Math. Annal.'') is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann. Subsequent managing editors were Felix Klein, David Hilbert, ...
, issn=0025-5831 , volume=57 , pages=1–34, s2cid=119641638 , url=https://zenodo.org/record/2043763
History of mathematics
Mathematics literature
Number theory