Mathematical Consistency Quotes

As you say, the way string theory requires all these extra dimensions and this comes from certain consistency requirements about how string should behave and so on.

I have no fault to find with those who teach geometry. That science is the only one which has not produced sects; it is founded on analysis and on synthesis and on the calculus; it does not occupy itself with the probable truth; moreover it has the same method in every country.

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

The most important single thing about string theory is that it's a highly mathematical theory, and the mathematics holds together in a very tight and consistent way. It contains in its basic structure both quantum mechanics and the theory of gravity. That's big news.

Mathematics catalogues everything that is not self-contradictory; within that vast inventory, physics is an island of structures rich enough to contain their own beholders.

The shell game that we play ... is technically called 'renormalization'. But no matter how clever the word, it is still what I would call a dippy process! Having to resort to such hocus-pocus has prevented us from proving that the theory of quantum electrodynamics is mathematically self-consistent. It's surprising that the theory still hasn't been proved self-consistent one way or the other by now; I suspect that renormalization is not mathematically legitimate.

Mathematics is universal. It's discovered by human beings, but the rules of mathematics are the same throughout the universe and the laws of the universe.

The same equations have the same solutions

I maintain that two and two would continue to make four, in spite of the whine of the amateur for three, or the cry of the critic for five.