Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem

God exists since mathematics is consistent, and the Devil exists since we cannot prove it.

Pascal was even convinced that he could use his theories to justify a belief in God. He stated that ‘the excitement that a gambler feels when making a bet is equal to the amount he might win multiplied by the probability of winning it’. He then argued that the possible prize of eternal happiness has an infinite value and that the probability of entering heaven by leading a virtuous life, no matter how small, is certainly finite. Therefore, according to Pascal’s definition, religion was a game of infinite excitement and one worth playing, because multiplying an infinite prize by a finite probability results in infinity.

Pascal was even convinced that he could use his theories to justify a belief in God. He stated that ‘the excitement that a gambler feels when making a bet is equal to the amount he might win multiplied by the probability of winning it’.

What is the least number of weights that can be used on a set of scales to weigh any whole number of kilograms from 1 to 40?

Maths is one of the purest forms of thought, and to outsiders mathematicians may seem almost other-worldly.

Proof is what lies at the heart of maths, and is what marks it out from other sciences. Other sciences have hypotheses that are tested against experimental evidence until they fail, and are overtaken by new hypotheses. In maths, absolute proof is the goal, and once something is proved, it is proved forever, with no room for change.

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. ‘Immortality’ may be a silly word, but probably a mathematician has the best chance of whatever it may mean. G.H. Hardy 23

The mathematical life of a mathematician is short. Work rarely improves after the age of twenty-five or thirty. If little has been accomplished by then, little will ever be accomplished.

Although this may seem a paradox, all exact science is dominated by the idea of approximation.

Euclid discovered that perfect numbers are always the multiple of two numbers, one of which is a power of 2 and the other being the next power of 2 minus 1.