Quotes About Mathematics

Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself.

Srinivasa Ramanujan was the strangest man in all of mathematics, probably in the entire history of science. He has been compared to a bursting supernova, illuminating the darkest, most profound corners of mathematics, before being tragically struck down by tuberculosis at the age of 33, like Riemann before him. Working in total isolation from the main currents of his field, he was able to rederive 100 years' worth of Western mathematics on his own. The tragedy of his life is that much of his work was wasted rediscovering known mathematics.

The history of mathematics, lacking the guidance of philosophy, [is] blind, while the philosophy of mathematics, turning its back on the most intriguing phenomena in the history of mathematics, is empty.

The first and foremost duty of the high school in teaching mathematics is to emphasize methodical work in problem solving...The teacher who wishes to serve equally all his students, future users and nonusers of mathematics, should teach problem solving so that it is about one-third mathematics and two-thirds common sense.

Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.

Mathematics... is a bit like discovering oil. ... But mathematics has one great advantage over oil, in that no one has yet ... found a way that you can keep using the same oil forever.

Pure mathematics is on the whole distinctly more useful than applied... For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.

You have this world of mathematics, which is very real and which contains all kinds of wonderful stuff. And then we also have the world of nature, which is real, too. And that, by some miracle, the language that nature speaks is the same language that we invented for mathematics. That's just an amazing piece of luck, which we don't understand.

One of the biggest problems of mathematics is to explain to everyone else what it is all about. The technical trappings of the subject, its symbolism and formality, its baffling terminology, its apparent delight in lengthy calculations: these tend to obscure its real nature. A musician would be horrified if his art were to be summed up as "a lot of tadpoles drawn on a row of lines"; but that"s all that the untrained eye can see in a page of sheet music... In the same way, the symbolism of mathematics is merely its coded form, not its substance.

The so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things.

Mathematics was born and nurtured in a cultural environment. Without the perspective which the cultural background affords, a proper appreciation of the content and state of present-day mathematics is hardly possible.

Mathematics is so much easier than words mathematics makes things clear that words merely muddle and confuse and mess up.

Mathematics is one of the surest ways for a man to feel the power of thought and the magic of the spirit. Mathematics is one of the eternal truths and, as such, raises the spirit to the same level on which we feel the presence of God.

The principles of logic and mathematics are true simply because we never allow them to be anything else. And the reason for this is that we cannot abandon them without contradicting ourselves, without sinning against the rules which govern the use of language, and so making our utterances self-stultifying. In other words, the truths of logic and mathematics are analytic propositions or tautologies.

One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed. This gives students the idea that there is a book somewhere with all the right answers to all of the interesting questions, and that teachers know those answers. And if one could get hold of the book, one would have everything settled. That's so unlike the true nature of mathematics.

The problem is that modern fundamental physics is so far from you and me. The mathematics has become so much more complicated that you need at least 10 years to understand it. Fundamental physics has advanced so far from the understanding of most people that there is really a big disconnect.

Mathematics is a language. We want scientists to be able to read it, speak it, and write it. But we are are not training them to be grammarians.

If a lunatic scribbles a jumble of mathematical symbols it does not follow that the writing means anything merely because to the inexpert eye it is indistinguishable from higher mathematics.

Everyone reads a different book. That's what's interesting. Everyone sees a different film, as well. We bring our past lives to whatever work of art we're experiencing at that moment, and that's what makes it interesting. It's not mathematics. There are different answers for different people.

Mathematics is not a deductive science - that's a cliché... What you do is trial and error, experimentation, guesswork.

We are servants rather than masters in mathematics.

In mathematics, two angles that are said to coincide fit together perfectly. The word "coincidence" does not describe luck or mistakes. It describes that which fits together perfectly.

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.

Nature imitates mathematics.

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.

The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method-more daring than anything that the history of philosophy records-of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason.

That sometimes clear ... and sometimes vague stuff ... which is ... mathematics.

The heart of mathematics is its problems.

... we should not be disappointed that everyday language does not work any longer at the apex of our little theory. It is natural; like poetry, the very reason for the existence of mathematics is that it expresses thoughts and feelings which we cannot express in mundane everyday language.

Logic and mathematics are nothing but specialised linguistic structures.

Mathematics is as much an aspect of culture as it is a collection of algorithms.

In high school I was good at math and everybody wanted me to do something with that - mathematics or engineering - which was a nightmare scenario for me. Meeting other artists and going to punk rock shows at that age, there was a feeling of freedom and community that I wanted to partake in.

The truth shall set you free. When you hear the truth, it sets you free. So mathematics is truth. It adds up. There's no error. Only time there's an error is when man miscalculates his own problems or his own equations.

Increasingly, the mathematics will demand the courage to face its implications.

... geometry became a symbol for human relations, except that it was better, because in geometry things never go bad. If certain things occur, if certain lines meet, an angle is born. You cannot fail. It's not going to fail; it is eternal. I found in rules of mathematics a peace and a trust that I could not place in human beings. This sublimation was total and remained total. Thus, I'm able to avoid or manipulate or process pain.

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.

If you refuse to study anatomy, the arts of drawing and perspective, the mathematics of aesthetics, and the science of color, let me tell you that this is more a sign of laziness than of genius.

The so-called mysteries of quantum mechanics are in its philosophical interpretation, not in its mathematics.

Mathematics is concerned only with the enumeration and comparison of relations.

Thus you see, most noble Sir, how this type of solution to the Königsberg bridge problem bears little relationship to mathematics, and I do not understand why you expect a mathematician to produce it, rather than anyone else, for the solution is based on reason alone, and its discovery does not depend on any mathematical principle.

There are certainly lots of jobs in computer coding, but coding doesn't really require advanced mathematics. And engineering jobs, they vary widely in the amount of demand that we actually need. So, you know, the number of people for whom the job description includes Newton's calculus is not perhaps that high.

Perfection is crucial in building an aircraft, a bridge, or a high-speed train. The code and mathematics residing just below the surface of the Internet is also this way. Things are either perfectly right or they will not work. So much of the world we work and live in is based upon being correct, being perfect.

In my schooling through high school, I excelled mainly in chemistry, physics and mathematics.

We have these amazing gifts of music and mathematics and painting and Olympic running. I mean, we're the animal that is best of all the animals at long-distance running. Why? It is quite amazing. Superfluous gifts you don't really need to survive.

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.

There have been many authorities who have asserted that the basis of science lies in counting or measuring, i.e. in the use of mathematics. Neither counting nor measuring can however be the most fundamental processes in our study of the material universe-before you can do either to any purpose you must first select what you propose to count or measure, which presupposes a classification.

I chose to deal with the science of cryptography. Cryptography began in mathematics. Codes were developed, even from Caesar's time, based on number theory and mathematical principles. I decided to use those principles and designed a work that is encoded.

The best result of mathematics is to be able to do without it.