The corrected complete proof of Fermat’s Last Theorem was done by Andrew Wiles in 1995. But by then he was too old for a Fields Medal (the equivalent of a Nobel Prize for mathematics). Nonetheless, the Fields Institute honored his achievement by a special silver plate award in 1998. He was also awarded the Wolf Prize earlier in 1996. Incidentally, his proof required several advances in pure mathematics such as the theory of ideals, elliptical curves, and modular forms.

On the other hand, the structural equation of Fermat’s Last theorem is really equivalent to the much older Pythagorean Theorem which basically says that if there exist three positive integers: A, B, and C such that A < B < C then there are infinitely many sets of triple {A,B,C} such that A + B = C is always true. Each set of Pythagorean triple can be determined for two positive indices m and n where n < m and the triple are given n - m, 2mn, and n + m. For m = 1 and n = 2, the corresponding Pythagorean triple is {3,4,5}. For m = 2 and n = 3, the triple is {5,12,13}. Consequently, disproving Fermat’s Last Theorem is the same as finding sets of triple that would at the least satisfy A + B = C or A + B = C. For a test, a good starting point would be to use one of the infinitely many Pythagorean triples. But 3 + 4 < 5 and 3 + 4 << 5, that is to say the left hand side (LHS) becoming less and less than the right hand side (RHS) as the power increases. For fractional powers (extracting roots) the LHS is always greater than the RHS. However, the difference approaches unity as the power decreases harmonically: ½, 1/3, ¼, 1/5, 1/6, 1/7, 1/8, 1/9,….