Alan Turing Quotes

Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning. The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings.

Mathematics seems to endow one with something like a new sense.

I don't really get things very... intuitively. I mean, I don't immediately understand things. The only way I really get it is by writing it down.

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

The knowledge of the theory of logic has no tendency whatever to make men good reasoners.

Even the greatest mathematicians, the ones that we would put into our mythology of great mathematicians, had to do a great deal of leg work in order to get to the solution in the end.

Solving wits and puzzles, in a way, helps to develop wit and ingenuity.

I listen to things that are popular and try to think about it in a mathematical way.

The main functions of intelligence, that of inventing solutions and that of verifying them, do not necessarily involve one another. The first partakes of imagination; the second alone is properly logical.

What interests me is the connection between maths and the real world.

I still remember the realization in college at Flinders University in Australia that mathematics was not just an abstract game of symbols but could be used as a tool to analyze and understand the modern world.

Logic is a wonderful thing but doesn't always beat actual thought.

It's strange how few of the world's great problems are solved by people who remember their algebra.

He that gives a portion of his time and talent to the investigation of mathematical truth, will come to all other questions with a decided advantage over his opponents.

The analytical power should not be confounded with simple ingenuity; for while the analyst is necessarily ingenious, the ingenious man is often remarkably incapable of analysis.

Dull minds are never either intuitive or mathematical.

Even in the most purely logical realms, it is insight that first arrives at what is new.

Learning to write programs stretches your mind, and helps you think better, creates a way of thinking about things that I think is helpful in all domains.

Mathematical reasoning may be regarded.

Geometry is beautifully logical, and it teaches you how to think and prove that things are so, step by step by step. Proofs are excellent lessons in reasoning. Without logic and reasoning, you are dependent on jumping to conclusions or - worse - having empty opinions.

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

A dozen more questions occurred to me. Not to mention twenty-two possible solutions to each one, sixteen resulting hypotheses and counter-theorems, eight abstract speculations, a quadrilateral equation, two axioms, and a limerick. That's raw intelligence for you.

Mathematics ... is indispensable as an intellectual technique. In many subjects, to think at all is to think like a mathematician.

I think like a detective.

When I get logical, and I don't trust my instincts - that's when I get in trouble.