Ages: 14-18

Our math circle will explore the storied history of Fermat’s Last Theorem and some of the underlying mathematics, such as Pell’s and other Diophantine Equations, and Fermat Proofs for Specific Exponents. We will discuss specific work by mathematician Sophie Germain, as well as the drama involved in Andrew Wiles’ Fermat proof. According to Wikipedia, “Fermat’s Last Theorem states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n strictly greater than two. This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica where he claimed he had a proof that was too large to fit in the margin. The first successful proof was released in 1994 by Andrew Wiles, and formally published in 1995, after 358 years of effort by mathematicians. The unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th century. It is among the most notable theorems in the history of mathematics Prior to its proof, it was in the Guinness Book of World Records as the “most difficult mathematical problem”, one of the reasons being that it has the largest number of unsuccessful proofs.”

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