However, another conjecture states that every elliptic curve can be represented as a modular form. After Ken Ribet proved Frey’s hypothesis in 1986, the second remained open: it had to be shown that every elliptic curve has an associated modular form. In the mid-1990s, Wiles succeeded in closing this gap as well, thereby proving Fermat’s big theorem.
However, one question remains unanswered: more than three centuries ago, Fermat could not have known about the mathematical relationships that Wiles used in his publication. Elliptical curves and modular forms were not known at that time. Was the scholar joking with the marginal note? Or had he just thought he had found proof and miscalculated? There is a third possibility: there may be a much simpler method of proof that no one has found yet.
Does Homer Simpson refute Fermat’s Big Theorem?
Nobody seriously doubts that Wiles’ approach is correct. Many experts have checked his technical essay, especially since some of his techniques are used again and again to reveal other mathematical relationships. This reduces the likelihood that an error could have crept in somewhere.
But how is it that in the popular TV series, Homer Simpson casually scribbles on a chalkboard an equation that appears to disprove Fermat’s great theorem? Finally represents 398712 + 436512 = 447212 an integer solution of the equation xn + yn = zn for n = 12 – and they shouldn’t really exist.
Fortunately, the mystery can be solved quickly. Calculating the twelfth power of a four-digit number results in an enormous value consisting of 43 digits. Ordinary pocket calculators cannot handle this, their display usually only has ten digits, which is why they round the numerical values up or down. However, if you use a more accurate calculator or computer program, you will find that the results do not agree exactly. For example, is 398712 + 436512 = 4472.000000007057617187512 a better approximation of the actual solution, which is much more complicated.
Fermat was right
In reality, therefore, there is no such thing as a positive integer e.gwhich is the equation 398712 + 436512 = e.g12 solves. So the real problem was not with Fermat or Wiles, but with the limited resolution of conventional pocket calculators.