Mathematical Logic Quotes

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

If indeed, as Hilbert asserted, mathematics is a meaningless game played with meaningless marks on paper, the only mathematical experience to which we can refer is the making of marks on paper.

We may always depend on it that algebra, which cannot be translated into good English and sound common sense, is bad algebra.

Mathematics is a language plus reasoning. It's like a language plus logic. Mathematics is a tool for reasoning.

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

Only Numbers. Pure math. You have to accustom yourself to thinking that way.

Mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics.

if you do not appreciate the mathematics, you cannot see, among the great variety of facts, that logic permits you to go from one to the other

Logic, n. The art of thinking and reasoning in strict accordance with the limitations and incapacities of the human misunderstanding. The basic of logic is the syllogism, consisting of a major and a minor premise and a conclusion - thus: Major Premise: Sixty men can do a piece of work sixty times as quickly as one man. Minor Premise: One man can dig a post-hole in sixty seconds; Therefore- Conclusion: Sixty men can dig a post-hole in one second. This may be called syllogism arithmetical, in which, by combining logic and mathematics, we obtain a double certainty and are twice blessed.

Mathematics is entirely free in its development, and its concepts are only linked by the necessity of being consistent, and are co-ordinated with concepts introduced previously by means of precise definitions.

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.

I'm a mathematician and always have been, as far as I can remember. I don't remember when I first got involved with mathematics, but I think of myself always as a mathematician first.

Mathematics does not grow through a monotonous increase of the number of indubitably established theorems but through the incessant improvement of guesses by speculation and criticism, by the logic of proofs and refutations.

For mathematics, even to the logical forms in which it moves, is entirely dependent on the concept of natural number.

I am interested in mathematics only as a creative art.

… 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.

I like - I love calculus. I love linear algebra, probability and statistics, that kind of stuff. I just really like that.

There are things which seem incredible to most men who have not studied Mathematics.

The old and oft-repeated proposition "Totum est majus sua parte" [the whole is larger than the part] may be applied without proof only in the case of entities that are based upon whole and part; then and only then is it an undeniable consequence of the concepts "totum" and "pars". Unfortunately, however, this "axiom" is used innumerably often without any basis and in neglect of the necessary distinction between "reality" and "quantity", on the one hand, and "number" and "set", on the other, precisely in the sense in which it is generally false.

Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

It is hard to know what you are talking about in mathematics, yet no one questions the validity of what you say. There is no other realm of discourse half so queer.

You can go through your whole life telling yourself that life is logical, life is prosaic, life is sane. Above all sane. And I think it is. I've had a lot of time to think about that. And what I keep coming back to is [her] dying declaration: 'So you understand that when we increase the number of variables, the axioms themselves never change.'

Geometry is the art of correct reasoning from incorrectly drawn figures.

The only thing that might have annoyed some mathematicians was the presumption of assuming that maybe the axiom of choice could fail, and that we should look into contrary assumptions.

But the science of operations, as derived from mathematics more especially, is a science of itself, and has its own abstract truth and value; just as logic has its own peculiar truth and value, independently of the subjects to which we may apply its reasonings and processes.