Цитаты из книги Division by Zero

Альберт Эйнштейн однажды сказал: «Положе­ния математики в той мере, в какой они описывают реальность, небесспорны; в той мере, в какой они бесспорны, они не описывают реальность».

She, like many, had always thought that mathematics did not derive its meaning from the universe, but rather imposed some meaning onto the universe.

Доказательство, что математика противоречива и что вся ее поразительная красота — всего лишь иллюзия, будет, мне кажется, самым горьким, что может узнать в жизни человек.

In 1936, Gerhard Gentzen provided a proof of the consistency of arithmetic, but to do it he needed to use a controversial technique known as transfinite induction. This technique is not among the usual methods of proof, and it hardly seemed appropriate for guaranteeing the consistency of arithmetic. What Gentzen had done was prove the obvious by assuming the doubtful.

“That’s right. Arithmetic as a formal system is inconsistent.” “That’s because the mathematics they’re using is just a gimmick. It’s a mnemonic trick, like counting on your knuckles to figure out which months have thirty-one days.”