Plenty of mathematicians, Hardy knew, could follow a step-by-step discursus unflaggingly—yet counted for nothing beside Ramanujan. Years later, he would contrive an informal scale of natural mathematical ability on which he assigned himself a 25...

If a mathematician wishes to disparage the work of one of his colleagues, say, A, the most effective method he finds for doing this is to ask where the results can be applied. The hard...

A brick can be used to represent the zero probability of this book being any good.

Where there is no mathematics, there is no freedom.

The apex of mathematical achievement occurs when two or more fields which were thought to be entirely unrelated turn out to be closely intertwined. Mathematicians have never decided whether they should feel excited or upset...

How is it that there are so many minds that are incapable of understanding mathematics? … the skeleton of our understanding, … and actually they are the majority. … We have here a problem that...

It (proof by contradiction) is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

Abstract mathematics combined with physics can discover and see more than any eye ever could.

It appeared that way, Lawrence, but this raised the question of was mathematics really true or was it just a game played with symbols? In other words—are we discovering Truth, or just wanking?

Do you know what the mathematical expression is for longing? … The negative numbers. The formalization of the feeling that you are missing something.

We have a closed circle of consistency here: the laws of physics produce complex systems, and these complex systems lead to consciousness, which then produces mathematics, which can then encode in a succinct and inspiring...

All mathematicians live in two different worlds. They live in a crystalline world of perfect platonic forms. An ice palace. But they also live in the common world where things are transient, ambiguous, subject to...

Mathematics is Open Source.

Everything can be summed up into an equation.

The mathematicians are the priests of the modern world.

At his “World of Physics” Web site, Eric W. Weisstein notes that the fine structure constant continues to fascinate numerologists, who have claimed that connections exist between alpha, the Cheops pyramid, and Stonehenge!

Euclid’s Elements has been for nearly twenty-two centuries the encouragement and guide of that scientific thought which is one thing with the progress of man from a worse to a better state. The encouragement; for...

Luck is not some esoteric, godlike phenomenon. Luck is countable but undefinable. Luck easily can be explained as number of factors acting in a favour of a person. These factors’ behaviour could be statistically proved...

The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them.

Primary causes are unknown to us; but are subject to simple and constant laws, which may be discovered by observation, the study of them being the object of natural philosophy.Heat, like gravity, penetrates every substance...

What believer of faith among us can claim to understand the exact mechanistic structure of a world created by a god/God?

Who rebels with mathematics?

The language of categories is affectionately known as “abstract nonsense,” so named by Norman Steenrod. This term is essentially accurate and not necessarily derogatory: categories refer to “nonsense” in the sense that they are all...

The Ludolphian number is fixed in eternity— not a digit out of place, all characters in their proper order, an endless sentence written to the end of the world by the division of the circle’s...

I was impressed by the delicate weaving of the numbers. No matter how carefully you unraveled a thread, a single moment of inattention could leave you stranded, with no clue what to do next. In...

The more I study physics, the more I am drawn to metaphysics.

It is the definition of the word ‘object’ which destroys all religions.

So-called professional mathematicians have, in their reliance on the relative incapacity of the rest of mankind, acquired for themselves a reputation for profundity very similar to the reputation for sanctity possessed by theologians.

Science attempts to find logic and simplicity in nature. Mathematics attempts to establish order and simplicity in human thought.

The only reason I don’t know more about love is because there just isn’t more to know. In fact, I’ve reduced love to a mathematical formula: Hdgk(X)=H2k(X,Q)∩Hk,k(X). Actually, that’s not right. That’s the statement piece...

Do not try the parallels in that way: I know that way all along. I have measured that bottomless night, and all the light and all the joy of my life went out there.[Having himself...

Life is about solving for x

Turing attended Wittgenstein’s lectures on the philosophy of mathematics in Cambridge in 1939 and disagreed strongly with a line of argument that Wittgenstein was pursuing which wanted to allow contradictions to exist in mathematical systems....

Too large a proportion of recent “mathematical” economics are mere concoctions, as imprecise as the initial assumptions they rest on, which allow the author to lose sight of the complexities and interdependencies of the real...

Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether say, an airplane would or would not fly could depend on this difference? If such were...

So how does one go about proving something like this? It’s not like being a lawyer, where the goal is to persuade other people; nor is it like a scientist testing a theory. This is...

This success permits us to hope that after thirty or forty years of observation on the new Planet [Neptune], we may employ it, in its turn, for the discovery of the one following it in...

He calculated the number of bricks in the wall, first in twos and then in tens and finally in sixteens. The numbers formed up and marched past his brain in terrified obedience. Division and multiplication...

Physicists have come to realize that mathematics, when used with sufficient care, is a proven pathway to truth.

It is not knowledge, but the act of learning, not the possession of but the act of getting there, which grants the greatest enjoyment.

How to describe the excitement I felt when I saw this beautiful work and realized its potential? I guess it’s like when, after a long journey, suddenly a mountain peak comes in full view. You...

In real life, I assure you, there is no such thing as algebra.

…numerical precision is the very soul of science, and its attainment affords the best, perhaps the only criterion of the truth of theories and the correctness of experiments.

The difference between the poet and the mathematician is that the poet tries to get his head into the heavens while the mathematician tries to get the heavens into his head.

Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler’s equation reaches down...

Ohm found that the results could be summed up in such a simple law that he who runs may read it, and a schoolboy now can predict what a Faraday then could only guess at...

Without mathematics, your world becomes foggy! For a clear vision, you need to be educated in the Temple of Mathematics!

Mathematical Knowledge adds a manly Vigour to the Mind, frees it from Prejudice, Credulity, and Superstition.

[Seniors] believe they need a Nobel Prize in mathematics to understand this program, … They are confused and this booklet just worsens it.

I entered Princeton University as a graduate student in 1959, when the Department of Mathematics was housed in the old Fine Hall. This legendary facility was marvellous in stimulating interaction among the graduate students and...