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abelian curves |
made abelian surfaces statement more accurate |
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Several theorems in number theory similar to FLT follow from the modularity theorem. For example: no cube can be written as a sum of two [[coprime]] {{mvar|n}}th powers, {{math|''n'' ≥ 3}}.{{efn|The case {{math|''n'' {{=}} 3}} was already known by [[Euler]].}}
In 2025, modularity was extended to over 10% of [[abelian surfaces]].<ref>{{Cite web |last=Howlett |first=Joseph |date=2025-06-02 |title=The Core of Fermat’s Last Theorem Just Got Superpowered |url=https://www.quantamagazine.org/the-core-of-fermats-last-theorem-just-got-superpowered-20250602/ |access-date=2025-08-06 |website=Quanta Magazine |language=en}}</ref>
==Generalizations==
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