Math in The Simpsons – Science Spectrum

However, there is another intuition that states that each elliptical curve can be represented as a standard shape. After Ken Ribbett proved Frey’s hypothesis in 1986, the second remained open: it had to be shown that each hypomorphic curve had an associated standard shape. In the mid-1990s, Wells successfully bridged this gap as well, thus proving Fermat’s Great Theorem.

However, one question remains unanswered: more than three centuries ago, Fermat did not know about the mathematical relationships that Wells used in his book. Elliptical curves and standard shapes were not known at the time. Was the scientist joking with the marginal note? Or did he just think he found the evidence and miscalculated? There is a third possibility: there might be a much simpler method of proof that no one has found yet.

Does Homer Simpson refute Fermat’s big theory?

No one seriously doubts the correctness of Wells’ approach. His technical article has been reviewed by many experts, especially since some of his techniques are repeatedly used to reveal other mathematical relationships. This reduces the possibility of the error creeping in somewhere.

But how is it that in the popular TV series, Homer Simpson casually scribbles on the board an equation that seems to disprove Fermat’s great theory? Finally represents 3987¹² +4365¹² = 4472¹² Solve the equation integer xⁿ + pⁿ = zⁿ to n = 12 – and it shouldn’t already exist.

Fortunately, the puzzle can be solved quickly. Calculating the twelfth power of a four-digit number yields a massive 43-digit value. Ordinary pocket calculators can’t handle this, their display usually contains only ten digits, which is why numerical values ​​are rounded up or down. However, if you use a more accurate calculator or computer program, you will find that the results are not quite consistent. For example, it is 3987¹² +4365¹² = 4472.000000070576171875¹² A better approximation of the actual solution, which is more complex.

Fermat was right

So, in fact, there is no such thing as a positive integer for exampleWhich is the equation 3987¹² +4365¹² = for example¹² Solve. So the real problem wasn’t with Fermat or Wiles, but with the limited accuracy of traditional pocket calculators.