Content deleted Content added
Citation bot (talk | contribs) Add: s2cid. | Use this bot. Report bugs. | Suggested by Horsesizedduck | #UCB_webform |
→History: history sources added |
||
Line 43:
==History==
[[Yutaka Taniyama]]{{sfn|Taniyama|1956}}<!--{{harvs|txt|authorlink=Yutaka Taniyama|last=Taniyama|first=Yutaka|year=1956}}--> stated a preliminary (slightly incorrect) version of the conjecture at the 1955 international symposium on algebraic number theory in [[Tokyo]] and [[Nikkō, Tochigi|Nikkō]]. [[Goro Shimura]] and Taniyama worked on improving its rigor until 1957. André Weil{{sfn|Weil|1967}}<!--{{harvs|txt|authorlink=André Weil|last=Weil|first=André|year= 1967}}--> rediscovered the conjecture, and showed in 1967 that it would follow from the (conjectured) functional equations for some twisted <math>L</math>-series of the elliptic curve; this was the first serious evidence that the conjecture might be true. Weil also showed that the conductor of the elliptic curve should be the level of the corresponding modular form. The Taniyama–Shimura–Weil conjecture became a part of the [[Langlands program]].<ref name="Harris Virtues of Priority">{{cite journal | last=Harris | first=Michael | title=Virtues of Priority | publisher=arXiv | doi=10.48550/ARXIV.2003.08242 | url=https://arxiv.org/abs/2003.08242 | access-date=2022-11-08 | page=}}</ref><ref>{{cite journal
| last = Lang
| first = Serge
| date = November 1995
| title = Some History of the Shimura-Taniyama Conjecture
| journal = Notices of the American Mathematical Society
| volume = 42
| issue = 11
| pages = 1301-1307
| url = https://www.ams.org/notices/199511/forum.pdf
| format = pdf
| access-date = 2022-11-08
}}</ref>
The conjecture attracted considerable interest when Gerhard Frey{{sfn|Frey|1986}}<!--{{harvs|txt|authorlink=Gerhard Frey|last=Frey|first=Gerhard|year=1986}}--> suggested in 1986 that it implies [[Fermat's Last Theorem]]. He did this by attempting to show that any counterexample to Fermat's Last Theorem would imply the existence of at least one non-modular elliptic curve. This argument was completed in 1987 when Jean-Pierre Serre{{sfn|Serre|1987}}<!--{{harvs|txt|authorlink=Jean-Pierre Serre|last=Serre|first=Jean-Pierre|year=1987}}--> identified a missing link (now known as the [[epsilon conjecture]] or Ribet's theorem) in Frey's original work, followed two years later by Ken Ribet{{sfn|Ribet|1990}}<!--{{harvs|txt|authorlink=Ken Ribet|last=Ribet|first=Ken|year=1990}}-->'s completion of a proof of the epsilon conjecture.
| |||