Editing 2689: Fermat's First Theorem
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==Explanation== | ==Explanation== | ||
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This is a reference to {{w|Fermat's Last Theorem}}, humorously implying that {{w|Pierre de Fermat}} created a similar theorem as a child. Fermat's Last Theorem states that no three positive integers ''a'', ''b'', and ''c'' satisfy the equation ''a''<sup>''n''</sup>+''b''<sup>''n''</sup>=''c''<sup>''n''</sup> for any integer value of ''n'' greater than 2. It is notable for having remained unproved for hundreds of years, despite many attempts to prove it; it's called his 'last' theorem because it was the last one left without proof or disproof. The Taniyama–Shimura conjecture (now known as the Modularity theorem) and the epsilon conjecture (now known as Ribet's theorem) together imply that Fermat's Last Theorem is true. The epsilon conjecture, proposed by Jean-Pierre Serre, became provable thanks to Ken Ribet in 1986. {{w|Andrew Wiles}}, with assistance from his former student {{w|Richard Taylor (mathematician)|Richard Taylor}}, succeeded in proving a special case of the Taniyama-Shimura conjecture for semistable elliptical curves in 1995, which finally established the proof of Fermat's Last Theorem. (The full Modularity theorem was subsequently established as correct by Wiles's former students Brian Conrad, Fred Diamond and Richard Taylor, and Christophe Breuil in 2001.) | This is a reference to {{w|Fermat's Last Theorem}}, humorously implying that {{w|Pierre de Fermat}} created a similar theorem as a child. Fermat's Last Theorem states that no three positive integers ''a'', ''b'', and ''c'' satisfy the equation ''a''<sup>''n''</sup>+''b''<sup>''n''</sup>=''c''<sup>''n''</sup> for any integer value of ''n'' greater than 2. It is notable for having remained unproved for hundreds of years, despite many attempts to prove it; it's called his 'last' theorem because it was the last one left without proof or disproof. The Taniyama–Shimura conjecture (now known as the Modularity theorem) and the epsilon conjecture (now known as Ribet's theorem) together imply that Fermat's Last Theorem is true. The epsilon conjecture, proposed by Jean-Pierre Serre, became provable thanks to Ken Ribet in 1986. {{w|Andrew Wiles}}, with assistance from his former student {{w|Richard Taylor (mathematician)|Richard Taylor}}, succeeded in proving a special case of the Taniyama-Shimura conjecture for semistable elliptical curves in 1995, which finally established the proof of Fermat's Last Theorem. (The full Modularity theorem was subsequently established as correct by Wiles's former students Brian Conrad, Fred Diamond and Richard Taylor, and Christophe Breuil in 2001.) | ||