Gauss's diary
{{No footnotes|date=October 2017}}
{{Short description|Diary of Carl F. Gauss's mathematical discoveries}}
Gauss's diary was a record of the mathematical discoveries of German mathematician Carl Friedrich Gauss from 1796 to 1814. It was rediscovered in 1897 and published by {{harvtxt|Klein|1903}}, and reprinted in volume X1 of his collected works and in {{harv|Gauss|2005}}. There is an English translation with commentary given by {{harvtxt|Gray|1984}}, reprinted in the second edition of {{harv|Dunnington|2004}}.
Sample entries
File:Gauss Tagebuch erster Eintrag.png (1796)]]
Most of the entries consist of a brief and sometimes cryptic statement of a result in Latin.
Entry 1, dated 1796, March 30, states "{{lang|la|Principia quibus innititur sectio circuli, ac divisibilitas eiusdem geometrica in septemdecim partes etc.}}", which records Gauss's discovery of the construction of a heptadecagon by ruler and compass.
Entry 18, dated 1796, July 10, states "ΕΥΡΗΚΑ! {{nowrap|1= num = Δ + Δ + Δ}}" 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. {{harvtxt|Biermann|1997}} 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 {{harvtxt|Chowla|1940}}. More precisely, Gauss observed that if a+bi is a (Gaussian) prime and a–1+bi is divisible by 2+2i, 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+b2.
References
- {{cite book |url=https://gdz.sub.uni-goettingen.de/id/DE-611-HS-3382323 |title=Mathematisches Tagebuch (Ansetzungssachtitel von Bearbeiter/in), Braunschweig, 30.3.1796 - 9.7.1814 |last=Gauss |first=Carl Friedrich |author-link=Carl Friedrich Gauss |publisher=Göttinger Digitalisierungszentrum |date= |access-date=October 8, 2021}}
- {{citation|last=Biermann|first= Kurt-R.|title=Vicimus NAGEG. Bestätigung einer Hypothese|language= German| zbl= 0888.01025
|journal=Mitt., Gauß-Ges. Gött.|volume= 34|pages= 31–34 |year=1997}}
- {{Citation | authorlink1= S. Chowla | last1=Chowla | first1=S. | title=The last entry in Gauss's diary | jstor=88178 | mr=0029394 | year=1940 | journal=Proceedings of the National Academy of Sciences of the United States of America | issn=0027-8424 | volume=35 | issue=5 | pages=244–246 | doi=10.1073/pnas.35.5.244| pmid=16578315 | pmc=1063011 | doi-access=free }}
- {{citation|title=Carl Friedrich Gauss: Titan of Science
|series=MAA spectrum
|first= G. Waldo |last=Dunnington
|editor-first=Jeremy |editor-last=Gray|editor2-first= Fritz-Egbert|editor2-last= Dohse
|edition=2
|publisher =Mathematical Association of America|year= 2004|orig-year=1955|isbn= 9780883855478}}
- {{Citation | last1=Gauss | first1=Carl Friedrich | editor1-last=Biermann | editor1-first=Kurt-R. | title=Mathematisches Tagebuch, 1796–1814 | publisher=Verlag Harri Deutsch | location=Frankfurt am Main | edition=Fifth | series=Ostwalds Klassiker der exakten Wissenschaften | isbn=978-3-8171-3402-1 | mr=2167978 | year=2005 | volume=256}}
- {{Citation | last1=Gray | first1=J. J. | title=A commentary on Gauss's mathematical diary, 1796–1814, with an English translation | mr=783128 | year=1984 | journal=Expositiones Mathematicae | issn=0723-0869 | volume=2 | issue=2 | pages=97–130}}
- {{Citation | authorlink1=Felix Klein | last1=Klein | first1=Felix | title=Gauß' wissenschaftliches Tagebuch 1796–1814 | doi=10.1007/BF01449013 | year=1903 | journal=Mathematische Annalen | issn=0025-5831 | volume=57 | pages=1–34| s2cid=119641638 | url=https://zenodo.org/record/2043763 }}
Category:History of mathematics