Back مبرهنة النمطية Arabic Teorema de Taniyama-Shimura Catalan Tanijamova–Šimurova domněnka Czech Modularitätssatz German Θεώρημα των Σιμούρα-Τανιγιάμα Greek Teorema de Taniyama-Shimura Spanish Modulaarisuuslause Finnish Théorème de modularité French משפט המודולריות HE Teorema di Taniyama-Shimura Italian
| Field | Number theory |
|---|---|
| Conjectured by | Yutaka Taniyama Goro Shimura |
| Conjectured in | 1957 |
| First proof by | Christophe Breuil Brian Conrad Fred Diamond Richard Taylor |
| First proof in | 2001 |
| Consequences | Fermat's Last Theorem |
The modularity theorem (formerly called the Taniyama–Shimura conjecture, Taniyama–Shimura–Weil conjecture or modularity conjecture for elliptic curves) states that elliptic curves over the field of rational numbers are related to modular forms in a particular way. Andrew Wiles and Richard Taylor proved the modularity theorem for semistable elliptic curves, which was enough to imply Fermat's Last Theorem. Later, a series of papers by Wiles's former students Brian Conrad, Fred Diamond and Richard Taylor, culminating in a joint paper with Christophe Breuil, extended Wiles's techniques to prove the full modularity theorem in 2001.
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