Mathematics Quotes
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My first degree was in mathematics. That was great, but it didn't help with many of the things that puzzled me. I became a philosopher because I wanted to understand everything, especially those things that didn't make sense. And that has continued to be my philosophical motivation. That's one reason I have such a roving philosophical eye - once I have figured out a philosophical topic to my satisfaction, I find myself moving on to new problems.
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We humans have a wide range of abilities that help us perceive and analyze mathematical content. We perceive abstract notions not just through seeing but also by hearing, by feeling, by our sense of body motion and position. Our geometric and spatial skills are highly trainable, just as in other high-performance activities. In mathematics we can use the modules of our minds in flexible ways - even metaphorically. A whole-mind approach to mathematical thinking is vastly more effective than the common approach that manipulates only symbols.
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I think mathematics is a vast territory. The outskirts of mathematics are the outskirts of mathematical civilization. There are certain subjects that people learn about and gather together. Then there is a sort of inevitable development in those fields. You get to the point where a certain theorem is bound to be proved, independent of any particular individual, because it is just in the path of development.
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Numbers are the most certain things we have.
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Mathematics is the art of accurate reasoning on inaccurately-drawn figures... let that be our motto.
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The object of mathematics is the honor of the human spirit.
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Though determinants and matrices received a great deal of attention in the nineteenth century and thousands of papers were written on these subjects, they do not constitute great innovations in mathematics.... Neither determinants nor matrices have influenced deeply the course of mathematics despite their utility as compact expressions and despite the suggestiveness of matrices as concrete groups for the discernment of general theorems of group theory.
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Both my parents instilled an interest in science and mathematics.
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Although I liked especially physics and mathematics for which I had considerable talent, I decided to study medicine. This profession had for me a strong emotional appeal, which was reinforced by having an uncle who was an excellent surgeon.
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Though a skilled mathematician, Alfred Marshall used mathematics sparingly. He saw that excessive reliance on this instrument might lead us astray in pursuit of intellectual toys, imaginary problems not conforming to the conditions of real life: and further, might distort our sense of proportion by causing us to neglect factors that could not easily be worked up in the mathematical machine.
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When, therefore, I had long considered this uncertainty of traditional mathematics, it began to weary me that no more definite explanation of the movement of the world-machine established in our behalf by the best and most systematic builder of all, existed among the philosophers who had studied so exactly in other respects the minutest details in regard to the sphere.
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Mathematics is, in many ways, the most precious response that the human spirit has made to the call of the infinite.
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Mathematics is often erroneously referred to as the science of common sense. Actually, it may transcend common sense and go beyond either imagination or intuition. It has become a very strange and perhaps frightening subject from the ordinary point of view, but anyone who penetrates into it will find a veritable fairyland, a fairyland which is strange, but makes sense, if not common sense.
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Perhaps the most surprising thing about mathematics is that it is so surprising. The rules which we make up at the beginning seem ordinary and inevitable, but it is impossible to foresee their consequences. These have only been found out by long study, extending over many centuries. Much of our knowledge is due to a comparatively few great mathematicians such as Newton, Euler, Gauss, or Riemann; few careers can have been more satisfying than theirs. They have contributed something to human thought even more lasting than great literature, since it is independent of language.
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The proof of Fermat's Last Theorem underscores how stable mathematics is through the centuries - how mathematics is one of humanity's long continuous conversations with itself.
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I think that mathematics can benefit by acknowledging that the creation of good models is just as important as proving deep theorems.
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Mathematics is a body of knowledge, but it contains no truths.
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The manuscript looks chaotic, even by mathematics standards.
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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.
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Of Belief Human mathematics, so to speak, like the length of life, are subject to the doctrine of chances.
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I came into history from a primary concern with mathematics and science. This has been a tremendous help to me as a person and as a historian, although it must be admitted it has served to make my historical interpretations less conventional than may be acceptable of many of my colleagues in the field.
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Though the structures and patterns of mathematics reflect the structure of, and resonate in, the human mind every bit as much as do the structures and patterns of music, human beings have developed no mathematical equivalent to a pair of ears. Mathematics can only be "seen" with the "eyes of the mind". It is as if we had no sense of hearing, so that only someone able to sight read music would be able to appreciate its patterns and harmonies.
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We must always emphasize research and development of science and mathematics, and I can think of no better way to achieve this than through our future in space.
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Perhaps, a bigger point is that it is perfectly OK if something is unclear. That’s how I feel 90 percent of the time when I do mathematics, so welcome to my world! The feeling of confusion (even frustration, sometimes) is an essential part of being a mathematician. But look at the bright side: how boring would life be if everything in it could be understood with little effort! What makes doing mathematics so exciting is our desire to overcome this confusion; to understand; to lift the veil on the unknown. And the feeling of personal triumph when we do understand something makes it all worthwhile.
