Computational Studies
In the latter half of the 20th century, computational methods were used to extend Kummer's approach to the irregular primes. In 1954, Harry Vandiver used a SWAC computer to prove Fermat's Last Theorem for all primes up to 2521. By 1978, Samuel Wagstaff had extended this to all primes less than 125,000. By 1993, Fermat's Last Theorem had been proven for all primes less than four million.
Read more about this topic: Fermat's Last Theorem
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“The conduct of a man, who studies philosophy in this careless manner, is more truly sceptical than that of any one, who feeling in himself an inclination to it, is yet so over-whelm’d with doubts and scruples, as totally to reject it. A true sceptic will be diffident of his philosophical doubts, as well as of his philosophical conviction; and will never refuse any innocent satisfaction, which offers itself, upon account of either of them.”
—David Hume (1711–1776)