George Boole Quotes

My father was a world-class scientist and my mother was a prolific painter. I could see that my parents had completely different ways of knowing and understanding the world, and relating to it. My father approached things through scientific inquiry and exploration, while my mother experienced things through her emotions and senses.

Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.

Geometry is not true, it is advantageous.

You can get a certain amount of pleasure as a mathematical spectator, reading and watching some of the most beautiful arguments that have been created in the history of humanity. But that's too passive.

Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness.

When I am working on a problem, I never think about beauty but when I have finished, if the solution is not beautiful, I know it is wrong.

It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress.

One of the most amazing things about mathematics is the people who do math aren't usually interested in application, because mathematics itself is truly a beautiful art form. It's structures and patterns, and that's what we love, and that's what we get off on.

When something is beautiful in math, everything is just perfectly lined up, and you see through sheer thought that something really beautiful can take place.

Mathematics are the result of mysterious powers which no one understands, and which the unconscious recognition of beauty must play an important part. Out of an infinity of designs a mathematician chooses one pattern for beauty's sake and pulls it down to earth.

As for everything else, so for a mathematical theory: beauty can be perceived but not explained.

Metaphysical thinking will always no doubt be a strong element in her mentality, and it is to be hoped that she will never lose her great, her sovereign powers in that direction.

It is hard to rationalise or explain why you love what you love. But I have always been interested in science and maths, and in high school I was struck that you could use maths to understand nature and science.

When I was in school, I liked math because all the problems had answers. Everything else seemed very subjective.

The further a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separated branches of the science.

Among the thousand-and-one faces whereby form chooses to reveal itself to us, the one that fascinates me more than any other, and continues to fascinate me, is the structure hidden in mathematical things.

A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street.

In my own research when I'm working with equations, I never feel like I really understand what I'm doing if I'm solely relying on the mathematics for my understanding. I need to have a visual picture in my mind. I'm constantly translating from the math to some intuitive mind's-eye picture.

I think one of the important evolutions is that we no longer feel compulsively the need to argue, or to justify things on a kind of rational level. We are much more willing to admit that certain things are completely instinctive and others are really intellectual.

What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?

The traditional mathematician recognizes and appreciates mathematical elegance when he sees it. I propose to go one step further, and to consider elegance an essential ingredient of mathematics: if it is clumsy, it is not mathematics.

It is impossible to be a mathematician without being a poet in soul.

But mathematics is the sister, as well as the servant, of the arts and is touched by the same madness and genius.

I have a hard time with abstractions. I always go to the personal.

Pure mathematics is, in its way, the poetry of logical ideas.