All models are wrong, but some are useful.
[The works of Archimedes] are without exception, monuments of mathematical exposition; the gradual revelation of the plan of attack, the masterly ordering of the propositions, the stern elimination of everything not immediately relevant to the purpose, the finish of the whole, are so impressive in their perfection as to create a feeling akin to awe in the mind of the reader.
I tell students that even if they don't like math right now, they can use math as a brain-sharpening tool - a tool that not only builds the foundation for a great career, but that also builds self-confidence, no matter what they choose to do with their lives.
Proof is an idol before which the mathematician tortures himself.
He who can properly define and divide is to be considered a god.
There's a snobbery at work in architecture. The subject is too often treated as a fine art, delicately wrapped in mumbo-jumbo. In reality, it's an all-embracing discipline taking in science, art, maths, engineering, climate, nature, politics, economics.
We can and should place special emphasis on developing in our youth constructive incentives - a love of science, engineering, and math, so that they will want to take advanced scientific courses and thereby help meet the needs of our times. Just as a musician has a love of music which drives him to become outstanding in that field, so we must inculcate in some of our qualified young people such an interest in science that they will turn to it of themselves.
In any case, do you really think kids even want something that is relevant to their daily lives? You think something practical like compound interest is going to get them excited? People enjoy fantasy, and that is just what mathematics can provide - a relief from daily life, an anodyne to the practical workaday world.
The two operations of our understanding, intuition and deduction, on which alone we have said we must rely in the acquisition of knowledge.
Number was the substance of all things.
When we cannot use the compass of mathematics or the torch of experience. . . it is certain we cannot take a single step forward.
There are no sects in geometry.
Physics is much too hard for physicists.
My knowledge of science came from being with Carl, not from formal academic training. Carl gave me a thrilling tutorial in science and math that lasted the 20 years we were together.
There are two ways to do great mathematics. The first is to be smarter than everybody else. The second way is to be stupider than everybody else - but persistent.
Man is full of desires: he loves only those who can satisfy them all. "This man is a good mathematician," someone will say. But I have no concern for mathematics; he would take me for a proposition. "That one is a good soldier. " He would take me for a besieged town. I need, that is to say, a decent man who can accommodate himself to all my desires in a general sort of way.
I was a normal human being, but I did like that. I read a lot. I also liked math and science.
Australian schools have cool uniforms. I wish I had to wear a woven straw hat for maths.
[Mathematics] is an independent world created out of pure intelligence.
It will be another million years, at least, before we understand the primes.
