Top 1002 Quotes & Sayings by Famous Mathematicians - Page 2

Time makes fools of us all. Our only comfort is that greater shall come after us.

Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.

People think they don’t understand math, but it’s all about how you explain it to them. If you ask a drunkard what number is larger, 2/3 or 3/5, he won’t be able to tell you. But if you rephrase the question: what is better, 2 bottles of vodka for 3 people or 3 bottles of vodka for 5 people, he will tell you right away: 2 bottles for 3 people, of course.

Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions.

Information is the resolution of uncertainty.

At a time when so many scholars in the world are calculating, is it not desirable that some, who can, dream ?

Mathematics is the science which uses easy words for hard ideas.

Algebraic geometry seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics. In one respect this last point is accurate.

Absolute certainty is a privilege of uneducated minds and fanatics. - It is, for scientific folk, an unattainable ideal.

God made the integers; all else is the work of man.

It is not of the essence of mathematics to be conversant with the ideas of number and quantity.

Newton took no exercise, indulged in no amusements, and worked incessantly, often spending eighteen or nineteen hours out of the twenty-four in writing.

I have made the most important discovery of my career, the most important discovery of my life: It is only in the mysterious equations of love that any logic or reasons can be found.

Who does not understand should either learn, or be silent.

In the simplest array of digits [Ramanujan] detected wonderful properties: congruences, symmetries and relationships which had escaped the notice of even the outstandingly gifted theoreticians.

Mathematics my foot! Algorithms are mathematics too, and often more interesting and definitely more useful.

One of the pleasures of looking at the world through mathematical eyes is that you can see certain patterns that would otherwise be hidden.

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.

I'm an academic. It's publish or perish.

We are servants rather than masters in mathematics.

A typical mathematician does not actively try to be useful. Individual mathematicians are motivated primarily by a subtle mixture of ambition and intellectual curiosity, and not by a wish to benefit society, nevertheless, mathematics as a whole does benefit society.

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils.

Mathematics is the science of patterns.

As long as algebra and geometry have been separated, their progress have been slow and their uses limited; but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection.

By peace we mean the capacity to transform conflicts with empathy, without violence, and creatively- a never-ending process

A random sequence is one that cannot be algorithmically compressed : the shortest description of a random sequence is simply the sequence itself.

What is man? ... What a strange union of matter and mind! A machine for converting material into spiritual force.

In mathematics, if a pattern occurs, we can go on to ask, Why does it occur? What does it signify? And we can find answers to these questions. In fact, for every pattern that appears, a mathematician feels he ought to know why it appears.

Mathematics is nothing more, nothing less, than the exact part of our thinking.

What the use of P [the significance level] implies, therefore, is that a hypothesis that may be true may be rejected because it has not predicted observable results that have not occurred.

Michael Harris opens the doors and gently guides you into a magic world. Once inside, you can't help but feel mesmerized, eager to see how deep the rabbit hole goes. And no wonder: a major thinker of our time is talking to you about math and so much more, like you've never heard before.

Ampere was the Newton of Electricity.

An embedded growth obligation is how fast a structure has to grow in order to maintain its honest positions.

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

God exists since mathematics is consistent, and the Devil exists since we cannot prove it.

Fertility is measured by offspring, not by honours.

Mathematics is the supreme judge; from its decisions there is no appeal.

I believe that the World Wide Web is, as a matter of fact, the noogenesis of the noosphere of the future. This is it!

One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories.

Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life.

A good problem should be more than a mere exercise; it should be challenging and not too easily solved by the student, and it should require some "dreaming" time.

Emptiness is everywhere and it can be calculated, which gives us a great opportunity. I know how to control the universe. So tell me, why should I run for a million?

It can be of no practical use to know that Pi is irrational, but if we can know, it surely would be intolerable not to know.

The harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty.

I understood that the will could not be improved before the mind had been enlightened.

If you want to be a reference librarian, you must learn to overcome not only your shyness but also the shyness of others!

A person's behavior is rational if it is in his best interests, given his information

Adaptability to change is itself a hallmark of successful education.

This common and unfortunate fact of the lack of adequate presentation of basic ideas and motivations of almost any mathematical theory is probably due to the binary nature of mathematical perception. Either you have no inkling of an idea, or, once you have understood it, the very idea appears so embarrassingly obvious that you feel reluctant to say it aloud.

There are surely worse things than being wrong, and being dull and pedantic are surely among them.

All I remember about the examination is that there was a question on Sturm's theorem about equations, which I could not do then and cannot do now.

Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them.

On foundations we believe in the reality of mathematics, but of course, when philosophers attack us with their paradoxes, we rush to hide behind formalism and say 'mathematics is just a combination of meaningless symbols,'... Finally we are left in peace to go back to our mathematics and do it as we have always done, with the feeling each mathematician has that he is working with something real. The sensation is probably an illusion, but it is very convenient.

The shortest path between two truths in the real domain passes through the complex domain.

Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.

A generating function is a clothesline on which we hang up a sequence of numbers for display.

No number before zero. The numbers may go on forever, but like the cosmos, they have a beginning.

The greatest advantage in gambling lies in not playing at all.

There is great exhilaration in breaking one of these things. ... Ramanujan gives no hints, no proof of his formulas, so everything you do you feel is your own.[About verifying Ramanujan's equations in a newly found manuscript.]

Sometimes a line of mathematical research extending through decades can be thought of as one long conversation in which many mathematicians take part. This is fortunately true at present.