However, as I hope to persuade you, there are some interesting connections between science and magic. They share a belief, as one mathematician put it, that what is visible is merely a superficial reality, not...

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...

The Professor never really seemed to care whether we figured out the right answer to a problem. He preferred our wild, desperate guesses to silence, and he was even more delighted when those guesses led...

Give me a place to stand, and I will move the Earth.

Mathematicians deal with large numbers sometimes, but never in their income.

…and his analysis proved him to be the first of theoretical astronomers no less than the greatest of ‘arithmeticians.

Questions that pertain to the foundations of mathematics, although treated by many in recent times, still lack a satisfactory solution. Ambiguity of language is philosophy’s main source of problems. That is why it is of...

Statement: A girl and a boy jump into a river. The boy swims over to the girl and says, “God, it’s cold.”Question: What’s the probability they will kiss?

Dreams are what guide us, art is what defines us, math is what makes it all possible, and love is what lights our way.

… I succeeded at math, at least by the usual evaluation criteria: grades. Yet while I might have earned top marks in geometry and algebra, I was merely following memorized rules, plugging in numbers and...

The ‘Muse’ is not an artistic mystery, but a mathematical equation. The gift are those ideas you think of as you drift to sleep. The giver is that one you think of when you first...

{Before the time of it never occurred to anyone that mathematical research} was one of the things for which a mathematical department existed. Today it is a commonplace in all the leading universities. Peirce stood...

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...

It is all about numbers. It is all about sequence. It’s the mathematical logic of being alive. If everything kept to its normal progression, we would live with the sadness–cry and then walk–but what really...

It can only be our familiarity with soap bubbles from our earliest recollections, causing us to accept their existence as a matter of course, that prevents most of us from being seriously puzzled as to...

A distinguished writer [Siméon Denis Poisson] has thus stated the fundamental definitions of the science:’The probability of an event is the reason we have to believe that it has taken place, or that it will...

Algebra is numbers forgetting why they’re letters.

The full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobachevsky the Copernicus of Geometry [as did Clifford], for geometry is only a...

As a teacher, Tengo pounded into his students’ heads how voraciously mathematics demanded logic. Here things that could not be proven had no meaning, but once you had succeeded in proving something, the world’s riddles...

I had one class in the morning, the mysteriously named “Further Maths”. It was two hours long and so deeply frightening that I think I went into a trance.

Poincaré [was] the last man to take practically all mathematics, pure and applied, as his province. … Few mathematicians have had the breadth of philosophic vision that Poincaré had, and none in his superior in...

Be honest: did you actually read [the above geometric proof]? Of course not. Who would want to? The effect of such a production being made over something so simple is to make people doubt their...

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...

Some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they’re extremely hard to solve. There’s no...

The manner of Demoivre’s death has a certain interest for psychologists. Shortly before it, he declared that it was necessary for him to sleep some ten minutes or a quarter of an hour longer each...

But in the present century, thanks in good part to the influence of Hilbert, we have come to see that the unproved postulates with which we start are purely arbitrary. They must be consistent, they...

Réduites à des théories générales, les mathématiques seraient une belle forme sans contenu.Reduced to general theories, mathematics would be a beautiful form without content.

Believe me, if Archimedes ever had the grand entrance of a girl as pretty as Gloria to look forward to, he would never have spent so much time calculating the value of Pi. He would...

I think a strong claim can be made that the process of scientific discovery may be regarded as a form of art. This is best seen in the theoretical aspects of Physical Science. The mathematical...

Whenever I meet in Laplace with the words ‘Thus it plainly appears’, I am sure that hours and perhaps days, of hard study will alone enable me to discover how it plainly appears.

In life two negatives don’t make a positive. Double negatives turn positive only in math and formal logic. In life things just get worse and worse and worse.

For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?

If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics…

There have been only three epoch-making mathematicians, Archimedes, Newton, and Eisenstein.

Philosophy [nature] is written in that great book which ever is before our eyes — I mean the universe — but we cannot understand it if we do not first learn the language and grasp...

I’m sorry to hear you’re jobless.” I need to network with people who encounter letters on a daily basis in math equations, not romantic poetry.

the golden eternity is { }

With math, I remember all of the words—and none of the numbers. I’m also like that with love.

What a shame,” signed the Dodecahedron. “They’re so very useful. Why, did you know that if a beaver two feet long with a tail a foot and a half long can build a dam twelve...

5.4 The question of accumulation. If life is a wager, what form does it take? At the racetrack, an accumulator is a bet which rolls on profits from the success of one of the horse...

Logic, it is often said, is the study of valid arguments. It is a systematic attempt to distinguish valid arguments from invalid arguments.

I’ve got a few ideas,” (Amy) admitted. “But I don’t know where we’re going in the long term. I mean – have you ever thought about what this ultimate treasure could be?””Something cool.” (Dan)”Oh, that’s...

Looking at numbers as groups of rocks may seem unusual, but actually it’s as old as math itself. The word “calculate” reflects that legacy — it comes from the Latin word calculus, meaning a pebble...

Further, the same Arguments which explode the Notion of Luck, may, on the other side, be useful in some Cases to establish a due comparison between Chance and Design: We may imagine Chance and Design...

Music is a mixed mathematical science that concerns the origens, attributes, and distinctions of sound, out of which a cultivated and lovely melody and harmony are made, so that God is honored and praised but...

There was yet another disadvantage attaching to the whole of Newton’s physical inquiries, … the want of an appropriate notation for expressing the conditions of a dynamical problem, and the general principles by which its...

I don’t understand people who eat Chinese food with chopsticks when the restaurant also offers silverware. As a tool, chopsticks are inferior to western utensils like the spoon and fork. So why use them? That’s...

This queer crotchet [of Hamilton’s] that algebra is the science of pure time has attracted many philosophers, and quite recently it has been exhumed and solemnly dissected by owlish metaphysicians seeking the philosopher’s stone in...

I confess that Fermat’s Theorem as an isolated proposition has very little interest for me, for a multitude of such theorems can easily be set up, which one could neither prove nor disprove. But I...

He walked straight out of college into the waiting arms of the Navy. They gave him an intelligence test. The first question on the math part had to do with boats on a river: Port...