Editing 2689: Fermat's First Theorem

{{comic
| number    = 2689
| date      = October 24, 2022
| title     = Fermat's First Theorem
| image     = fermats_first_theorem_2x.png
| imagesize = 280x248px
| noexpand  = true
| titletext = Mathematicians quickly determined that it spells ANT BNECN, an unusual theoretical dish which was not successfully cooked until Andrew Wiles made it for breakfast in the 1990s.
}}

==Explanation==

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.)

The young Fermat here didn't try to prove the mathematical equation, but simply tried to read it as words, treating the "+" sign as a "t" so that "A<sup>N</sup>+" can be read as "ANT". His interpretation was quickly disproved because there's no "A" between "B" and "C", and no "O" between "C" and "N".  It's unclear if this is considered Fermat's First Theorem because it was the first he made, or because it was the first to be conclusively disproved.

In the title text, the "words" are "ANT BNECN", treating the equals sign "=" as an "E"; while "=" doesn't look especially close to "E", it is similar in that it contains horizontal bars in a horizontally symmetrical arrangement (and of course, it can be read as "equals", which begins with "E"). If the letter E is written in sans-serif block text in white on a black background, the "negative space" between the Upper Bar, the Middle Bar and the Lower Bar of the E form a =. The comic shows a blackboard with white letters. The text then references Wiles, asserting that he proved this modified form of Fermat's First Theorem as well by cooking this "ant bnecn" (whatever "bnecn" is) as breakfast.

[[2492: Commonly Mispronounced Equations]] also contains equations pronounced as if they were words in the ordinary sense.

==Transcript==

:[A Hairy-like boy, representing Pierre de Fermat as a child, stands at a blackboard holding a piece of chalk. To his right is Miss Lenhart. The following text is somewhat crudely written on the blackboard:]
:A<sup>N</sup> + B<sup>N</sup> = C<sup>N</sup>
:SPELLS
:ANT BACON

:[Caption below the panel]: 
:Fermat's ''First'' Theorem was quickly disproved

{{comic discussion}}

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[[Category:Comics featuring Miss Lenhart]]
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