Mathematical Quotes

Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.

It is with children that we have the best chance of studying the development of logical knowledge, mathematical knowledge, physical knowledge, and so forth.

Logical positivists have never taken psychology into account in their epistemology, but they affirm that logical beings and mathematical beings are nothing but linguistic structures.

The universal medicine for the Soul is the Supreme Reason and Absolute Justice; for the mind, mathematical and practical Truth; for the body, the Quintessence, a combination of light and gold.

The great appeal of the doctrine that the mind is a blank slate is the simple mathematical fact that zero equals zero.

As far as I know, only a small minority of mathematicians, even of those with Platonist views, accept the idea that there may be mathematical facts which are true but unknowable.

A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.

I was very much on the mathematical side, where you probably do your best work before you're forty-five. Having passed that significant date, I thought I would do something else.

Mathematical discoveries, small or great are never born of spontaneous generation.

The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law.

I think part of the appeal of mathematical logic is that the formulas look mysterious - You write backward Es!

The mathematical framework of quantum theory has passed countless successful tests and is now universally accepted as a consistent and accurate description of all atomic phenomena.

The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.

The thing that got me started on the science that I've been building now for about 20 years or so was the question of okay, if mathematical equations can't make progress in understanding complex phenomena in the natural world, how might we make progress?

You kind of alluded to it in your introduction. I mean, for the last 300 or so years, the exact sciences have been dominated by what is really a good idea, which is the idea that one can describe the natural world using mathematical equations.

Some people are born with a brain that has this weird, magical mathematical thing that makes them an amazing jazz musician.

Nobody before the Pythagorean had thought that mathematical relations held the secret of the universe. Twenty-five centuries later, Europe is still blessed and cursed with their heritage. To non-European civilizations, the idea that numbers are the key to both wisdom and power, seems never to have occurred.

You go through a lot of ways of rationalizing something like this. You go through all of the mathematical calculations. We did buy this team in hopes of having a rationalized business. We're not just going to throw money away, but this was an investment in the future of this team.

There is nothing that can be said by mathematical symbols and relations which cannot also be said by words. The converse, however, is false. Much that can be and is said by words cannot successfully be put into equations, because it is nonsense.

It's originally a mathematical term, ... Something that veers off the line is eccentric, not concentric. If you look at the poetry of that, there really isn't anything wrong with going off the line and exploring different things.

Every mathematical discipline goes through three periods of development: the naive, the formal, and the critical.

If a lunatic scribbles a jumble of mathematical symbols it does not follow that the writing means anything merely because to the inexpert eye it is indistinguishable from higher mathematics.

Music is a secret and unconscious mathematical problem of the soul.

Democracy is not a mathematical deduction proved once and for all time. Democracy is a just faith fervently held, commitment to be tested again and again in the fiery furnace of history.

The discovery in 1846 of the planet Neptune was a dramatic and spectacular achievement of mathematical astronomy. The very existence of this new member of the solar system, and its exact location, were demonstrated with pencil and paper; there was left to observers only the routine task of pointing their telescopes at the spot the mathematicians had marked.