David Berlinski Quotes

One cannot really argue with a mathematical theorem.

Here at Wisconsin we didn't get an undergraduate course in mathematical logic until the '60s.

There is no royal road to geometry.

A mathematical theorem can be true whether or not it is realized in the world.

… mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

Mathematics, in its widest significance, is the development of all types of formal, necessary, deductive reasoning.

I am obliged to interpolate some remarks on a very difficult subject: proof and its importance in mathematics. All physicists, and a good many quite respectable mathematicians, are contemptuous about proof. I have heard Professor Eddington, for example, maintain that proof, as pure mathematicians understand it, is really quite uninteresting and unimportant, and that no one who is really certain that he has found something good should waste his time looking for proof.

For hundreds of pages the closely-reasoned arguments unroll, axioms and theorems interlock. And what remains with us in the end? A general sense that the world can be expressed in closely-reasoned arguments, in interlocking axioms and theorems.

Geometry is not true, it is advantageous.

Well it was not exactly a dissertation in logic, at least not the kind of logic you would find in Whitehead and Russell's Principia Mathematica for instance. It looked more like mathematics; no formalized language was used.

Neither Aristotelian nor Russellian rules give the exact logic of any expression of ordinary language; for ordinary language has no exact logic.

I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect.

It would be very discouraging if somewhere down the line you could ask a computer if the Riemann hypothesis is correct and it said, 'Yes, it is true, but you won't be able to understand the proof.'

Mathematicians aren't satisfied because they know there are no solutions up to four million or four billion, they really want to know that there are no solutions up to infinity.

There are proofs that date back to the Greeks that are still valid today.

An ounce of algebra is worth of a ton of verbal argument.

Formal logic is mathematics, and there are philosophers like Wittgenstein that are very mathematical, but what they're really doing is mathematics - it's not talking about things that have affected computer science; it's mathematical logic.

In math, you're either right or you're wrong.

I remember having this vague idea that what mathematicians did was that some authority, someone, gave them problems to solve, and they just sort of solved them.

The reason the gifted students of the world like Khan Academy is because we don't say, 'Memorize this formula,' but say, 'Let's try to derive it from core principles,' or, 'I forgot my trig identity, so I'm going to just try to prove this to you.'

Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras (jabbre and maqabeleh) are geometric facts which are proved by propositions five and six of Book two of Elements.

I accept no principles of physics which are not also accepted in mathematics.

The one [the logician] studies the science of drawing conclusions, the other [the mathematician] the science which draws necessary conclusions.

I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for men thus endowed seem to have an extra sense.

Mathematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning.