Proof of Fermat's Last Theorem By Infinite Descent
Fermat's last theorem, one of the most challenging theories in the history of mathematics, has been conjectured by French lawyer Pierre de Verma in 1637. Since then, it wasconsidered the most difficult and unsolvable mathematical problem. However, more than three centuries later, a first proof was proposed by the British mathematician Andrew Wiles in 1994, relying on 20th-century techniques. Wiles's proof is based on elliptic (oval) curves that were not available at the time when the theory was first proposed. Most mathematicians argued that it was impossible to prove Fermat's theorem according to basic principles of arithmetic, though Harvey Friedman's grand conjecture states that mathematical theorems, including Fermat's Last Theorem, can be solved in very weak systems such as the Elementary Function Arithmetic (EFA). Friedman's grand conjecture states that "every theorem published in the journal, Annals of Mathematics, whose statement involves only finitary mathematical objects (i.e., what logicians call an arithmetical statement) can be proved in EFA, which is the weak fragment of Peano Arithmetic based on the usual quantifier free axioms for 0,1,+,x, exp, together with thescheme of induction for all formulas in the language all of whose quantifiers are bounded." *