Top 1200 Mathematics Quotes & Sayings - Page 17

Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense.

If there be some who, though ignorant of all mathematics . . . dare to reprove this work, because of some passage of Scripture, which they have miserably warped to their purpose, I regard them not, and even despise their rash judgement.

I was very lucky to be born into a very academic family. I was well-read, well-trained in mathematics. I had lots of advantages to start with.

Well it was not exactly a dissertation in logic, at least not the kind of logic you would find in Whitehead and Russell's Principia Mathematica for instance. It looked more like mathematics; no formalized language was used.

I merely say that all reading for pleasure is escape, whether it be Greek, mathematics, astronomy, Benedetto Croce, or The Diary of the Forgotten Man. To say otherwise is to be an intellectual snob, and a juvenile at the art of living.

What science can there be more noble, more excellent, more useful for men, more admirably high and demonstrative, than this of mathematics?

If you listen to the great Beatle records, the earliest ones where the lyrics are incredibly simple. Why are they still beautiful? Well, they're beautifully sung, beautifully played, and the mathematics in them is elegant. They retain their elegance.

Medicine makes people ill, mathematics make them sad and theology makes them sinful.

The correct statement of the laws of physics involves some very unfamiliar ideas which require advanced mathematics for their description. Therefore, one needs a considerable amount of preparatory training even to learn what the words mean.

The most vitally characteristic fact about mathematics is, in my opinion, its quite peculiar relationship to the natural sciences, or more generally, to any science which interprets experience on a higher than purely descriptive level.

There is a logic of language and a logic of mathematics.

Many of the proofs in mathematics are very long and intricate. Others, though not long, are very ingeniously constructed.

Poor teaching leads to the inevitable idea that the subject (mathematics) is only adapted to peculiar minds, when it is the one universal science and the one whose four ground-rules are taught us almost in infancy and reappear in the motions to the universe.

Poker isn't the roulette wheel of pure chance, nor is it the chess of mathematical elegance and perfect information. Apart from the underlying mathematics, poker depends on the nuanced reading of human intention, interactions, and deceptions.

As a graduate student I studied mathematics fairly broadly, and I was fortunate enough, besides developing the idea which led to 'Non-Cooperative Games,' also to make a nice discovery relating to manifolds and real algebraic varieties.

[In mathematics] There are two kinds of mistakes. There are fatal mistakes that destroy a theory, but there are also contingent ones, which are useful in testing the stability of a theory.

My decision to leave applied mathematics for economics was in part tied to the widely-held popular belief in the 1960s that macroeconomics had made fundamental inroads into controlling business cycles and stopping dysfunctional unemployment and inflation.

I think I realized very early on that you can spend a lot of time constructing a really perfect scene in final draft and just end up throwing it away because you didn't figure out that mathematics of the story first.

I think math is a hugely creative field, because there are some very well-defined operations that you have to work within. You are, in a sense, straightjacketed by the rules of the mathematics. But within that constrained environment, it's up to you what you do with the symbols.

This is a global fight to get the right people in the right place and we're talking about people with PhDs in engineering, computer science, mathematics.

Wherefore it is impossible to succeed in comparing wealth of different eras or different nations. This, in political economy, like squaring the circle in mathematics, is impracticable, for want of a common mean or measure to go by.

You treat world history as a mathematician does mathematics, in which nothing but laws and formulas exist, no reality, no good and evil, no time, no yesterday, no tomorrow, nothing but an eternal, shallow, mathematical present.

In my youth it was said that what was too silly to be said may be sung. In modern economics it may be put into mathematics.

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

One can understand nature only when one has learned the language and the signs in which it speaks to us; but this language is mathematics and these signs are methematical figures.

Probably no branch of mathematics has experienced a more surprising growth than has... topology... Considered as a most specialized and abstract subject in the early 1920's, it is today [1938] an indispensable equipment for the investigation of modern mathematical theories.

Either mathematics is too big for the human mind or the human mind is more than a machine.

No one shall expel us from the paradise which Cantor has created for us. Expressing the importance of Cantor's set theory in the development of mathematics.

Analytic It is clear that the definition of "logic" or "mathematics" must be sought by trying to give a new definition of the old notion of "analytic" propositions.

Many who have never had an opportunity of knowing any more about mathematics confound it with arithmetic, and consider it an arid science. In reality, however, it is a science which requires a great amount of imagination.

There is much of economic theory which is pursued for no better reason than its intellectual attraction; it is a good game. We have no reason to be ashamed of that, since the same would hold for many branches of mathematics.

I will live a hope-filled life every day. I will handle my problems as opportunities in a different, more effective manner, based on the power of advanced mathematics; "You + God = Enough

All science requires mathematics. The knowledge of mathematical things is almost innate in us. This is the easiest of sciences, a fact which is obvious in that no one's brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.

Angling may be said to be so like the Mathematics that it can never be fully learnt; at least not so fully but that there will still be more new experiments left for the trial of other men that succeed us.

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 is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.

My early education was in the public school system of Omaha, where, retrospectively, I realize that my high school training served me in good stead for the basic subjects of mathematics, English, foreign languages and history.

I went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics.

You are not supposed to get it. It's a paradox. All of mathematics is built on paradoxes. That's the biggest paradox of all-all this orderliness, and at the heart, impossibility. Contradiction. Heaven built on the foundations of hell.

I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe - because, like Spinoza's God, it won't love us in return.

Mathematics is the summit of human thinking. It has all the creativity and imagination that you can find in all kinds of art, but unlike art-charlatans and all kinds of quacks will not succeed there.

Unless the chemist learns the language of mathematics, he will become a provincial and the higher branches of chemical work, that require reason as well as skill, will gradually pass out of his hands.

The general mental qualification necessary for scientific advancement is that which is usually denominated "common sense," though added to this, imagination, induction, and trained logic, either of common language or of mathematics, are important adjuncts.

In a lot of scientists, the ratio of wonder to skepticism declines in time. That may be connected with the fact that in some fields-mathematics, physics, some others-the great discoveries are almost entirely made by youngsters.

I didn't know what kinds of questions to ask in mathematics. In physics, I could see there were things that were known and things that weren't.

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

I find all of my performances come down to mathematics in a sense - how do you approach the problem of this character? Sometimes I crack that problem, sometimes I don't.

The mathematics of quantum mechanics very accurately describes how our universe works. And it tells us our reality is continually branching into different possibilities, just like a coral.

One merit of mathematics few will deny: it says more in fewer words than any other science. The formula, e^i? = -1 expressed a world of thought, of truth, of poetry, and of the religious spirit "God eternally geometrizes."

For a physicist mathematics is not just a tool by means of which phenomena can be calculated, it is the main source of concepts and principles by means of which new theories can be created.

To a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-footed animal is an animal.

My Ph.D. is in operations research. I was interested in making things work better and using mathematics to help do that. So operations research is what I studied as an undergraduate and graduate student.

Only in mathematics and physics was I, through self-study, far beyond the school curriculum, and also with regard to philosophy as it was taught in the school curriculum.

If you are going to learn mathematics, you have to learn it not simply as an abstraction but as it is applied. I always say to teachers, for goodness sake, take the kids out first to look at the stars in order to understand infinity.

Many who have had an opportunity of knowing any more about mathematics confuse it with arithmetic, and consider it an arid science. In reality, however, it is a science which requires a great amount of imagination.

Language is remarkable, except under the extreme constraints of mathematics and logic, it never can talk only about what it's supposed to talk about but is always spreading around.

Without the concepts, methods and results found and developed by previous generations right down to Greek antiquity one cannot understand either the aims or achievements of mathematics in the last 50 years. [Said in 1950]

Chess is not Mathematics, where ten is always more than one; in chess the King with a pawn can beat opponent's King with all pieces if they are placed badly.

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

The dairy man had a Ph.D. in mathematics, and he must have had some training in philosophy. He liked what he was doing and he didn't want to be somewhere else - one of the few contented people I met in my whole journey.

We could use up two Eternities in learning all that is to be learned about our own world and the thousands of nations that have arisen and flourished and vanished from it. Mathematics alone would occupy me eight million years.