Quotes about mathematics

That logic, as a science, is susceptible of very wide applications is admitted; but it is equally certain that its ultimate forms and processes are mathematical.

It is not of the essence of mathematics to be conversant with the ideas of number and quantity.

There is not only a close analogy between the operations of the mind in general reasoning and its operations in the particular science of Algebra, but there is to a considerable extent an exact agreement in the laws by which the two classes of operations are conducted.

Mathematics thought that there were numbers associated with tones—frequencies, wavelengths. Music, at its most fundamental level, was math.

There is terror in numbers. [...] Perhaps we suffer from a trauma induced by grade-school arithmetic.

We need heuristic reasoning when we construct a strict proof as we need scaffolding when we erect a building.

The cookbook gives a detailed description of ingredients and procedures but no proofs for its prescriptions or reasons for its recipes; the proof of the pudding is in the eating. … Mathematics cannot be tested in exactly the same manner as a pudding; if all sorts of reasoning are debarred, a course of calculus may easily become an incoherent inventory of indigestible information.

To peer through the quick stubble of mathematics and see the wonders lurking behind was to momentarily live in the infinite, beyond the press of the ordinary world where everyone else dwelled in ignorance.

That was what drew him to mathematics. Not because it was rarefied, but because it probed to the subtle, deeper reality. People said that mathematicians were unworldly, and yammered on about how Einstein couldn’t make correct change. Nonsense. Einstein just didn’t give a damn. It was the subtle, the beautiful that concerned him.

“One of the laws of nature,” Gordon said, “is that half the people have got to be below average.”

”For a Gaussian distribution, yeah,” Cooper said. “Sad, though.”

As far as the laws of probability, my lady, these cannot be broken, any more than any other mathematical principle. But laws of physics and mathematics are like a coordinate system that runs in only one dimension. Perhaps there is another dimension perpendicular to it, invisible to those laws of physics, describing the same things with different rules, and those rules are written in our hearts, in a deep place where we cannot go and read them except in our dreams.

...the entire physical world is depicted as being governed according to mathematical laws. We shall be seeing in later chapters that there is powerful (but incomplete) evidence in support of this contention. On this view, everything in the physical universe is indeed governed in completely precise detail by mathematical principles — perhaps by equations, such as those we shall be learning about in chapters to follow, or perhaps by some future mathematical notions fundamentally different from those which we would today label by the term ‘equations’. If this is right, then even our own physical actions would be entirely subject to such ultimate mathematical control, where ‘control’ might still allow for some random behaviour governed by strict probabilistic principles.