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Mathematical Quotes

Supposing you knew - not by sight or by instinct, but by sheer intellectual knowledge, as I know the truth of a mathematical proposition - that what we call empty space was full, crammed. Not with lumps of what we call matter like hills and houses, but with things as real - as real to the mind Picture Quote #1

I mused upon the ironic fate which had compelled a mathematical genius to make his sole confidant of a philistine lawyer, and induced that lawyer to repeat it confusedly to an ignoramus at twilight on a Scotch hill Picture Quote #1

Mathematics is a logical method.... Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics Picture Quote #1

The peculiarity of the evidence of mathematical truths is that all the argument is on one side Picture Quote #1

As for everything else, so for a mathematical theory: beauty can be perceived but not explained Picture Quote #1

It is with children that we have the best chance of studying the development of logical knowledge, mathematical knowledge, physical knowledge, and so forth Picture Quote #1

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Some people are born with a brain that has this weird, magical mathematical thing that makes them an amazing jazz musician Picture Quote #1

The time was not yet ripe for the growth of mathematical science among us, and any development that might have taken place in that direction was rudely stopped by the civil war Picture Quote #1

To emphasize only the beautiful seems to me to be like a mathematical system that only concerns itself with positive numbers Picture Quote #1

We have failed to protect science against speculative extensions of nature, continuing to assign physical and mathematical properties to hypothetical entities beyond what is observable in nature Picture Quote #1

When I speak of the beauty of a game of chess, then naturally this is subjective. Beauty can be found in a very technical, mathematical game for example. That is the beauty of clarity Picture Quote #1

A pure mathematical series would be one in which each term is derived from the preceding term by a rule Picture Quote #1

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Well, gauge theory is very fundamental to our understanding of physical forces these days. But they are also dependent on a mathematical idea, which has been around for longer than gauge theory has Picture Quote #1

Logical positivists have never taken psychology into account in their epistemology, but they affirm that logical beings and mathematical beings are nothing but linguistic structures Picture Quote #1

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 Picture Quote #1

I did what I could to inflate the rumor I was on my way to stardom. What I was on my way to, by any mathematical standards known to man, was oblivion, by way of obscurity Picture Quote #1

Thus, the more succinctly a train of thought was expounded, and the more comprehensive the unity of its basic idea, the closer it would approximate to the prerequisites of the mathematical way of thinking Picture Quote #1

My suggestion is that at each state the proper order of operation of the mind requires an overall grasp of what is generally known, not only in formal logical, mathematical terms, but also intuitively, in images, feelings, poetic usage of language, etc Picture Quote #1

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No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful Picture Quote #1

I realize that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers Picture Quote #1

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 different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science Picture Quote #1

The traditional mathematician recognizes and appreciates mathematical elegance when he sees it. I propose to go one step further, and to consider elegance an essential ingredient of mathematics: if it is clumsy, it is not mathematics Picture Quote #1

The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved Picture Quote #1

The analysis of variance is not a mathematical theorem, but rather a convenient method of arranging the arithmetic Picture Quote #1

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And for mathematical science, he that doubts their certainty hath need of a dose of hellebore Picture Quote #1

There exists, if I am not mistaken, an entire world which is the totality of mathematical truths, to which we have access only with our mind, just as a world of physical reality exists, the one like the other independent of ourselves, both of divine creation Picture Quote #1

A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street Picture Quote #1

How thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler methods which, at the same time, assist in understanding earlier theories and in casting aside some more complicated developments Picture Quote #1

Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts Picture Quote #1

The further a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separated branches of the science Picture Quote #1

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Supposing you knew - not by sight or by instinct, but by sheer intellectual knowledge, as I know the truth of a mathematical proposition - that what we call empty space was full, crammed. Not with lumps of what we call matter like hills and houses, but with things as real - as real to the mind (Mathematical Quotes) I mused upon the ironic fate which had compelled a mathematical genius to make his sole confidant of a philistine lawyer, and induced that lawyer to repeat it confusedly to an ignoramus at twilight on a Scotch hill (Mathematical Quotes) Mathematics is a logical method.... Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics (Mathematical Quotes) The peculiarity of the evidence of mathematical truths is that all the argument is on one side (Mathematical Quotes) As for everything else, so for a mathematical theory: beauty can be perceived but not explained (Mathematical Quotes) It is with children that we have the best chance of studying the development of logical knowledge, mathematical knowledge, physical knowledge, and so forth (Mathematical Quotes) Some people are born with a brain that has this weird, magical mathematical thing that makes them an amazing jazz musician (Mathematical Quotes) The time was not yet ripe for the growth of mathematical science among us, and any development that might have taken place in that direction was rudely stopped by the civil war (Mathematical Quotes) To emphasize only the beautiful seems to me to be like a mathematical system that only concerns itself with positive numbers (Mathematical Quotes) We have failed to protect science against speculative extensions of nature, continuing to assign physical and mathematical properties to hypothetical entities beyond what is observable in nature (Mathematical Quotes) When I speak of the beauty of a game of chess, then naturally this is subjective. Beauty can be found in a very technical, mathematical game for example. That is the beauty of clarity (Mathematical Quotes) A pure mathematical series would be one in which each term is derived from the preceding term by a rule (Mathematical Quotes) Well, gauge theory is very fundamental to our understanding of physical forces these days. But they are also dependent on a mathematical idea, which has been around for longer than gauge theory has (Mathematical Quotes) Logical positivists have never taken psychology into account in their epistemology, but they affirm that logical beings and mathematical beings are nothing but linguistic structures (Mathematical Quotes) 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 (Mathematical Quotes) I did what I could to inflate the rumor I was on my way to stardom. What I was on my way to, by any mathematical standards known to man, was oblivion, by way of obscurity (Mathematical Quotes) Thus, the more succinctly a train of thought was expounded, and the more comprehensive the unity of its basic idea, the closer it would approximate to the prerequisites of the mathematical way of thinking (Mathematical Quotes) My suggestion is that at each state the proper order of operation of the mind requires an overall grasp of what is generally known, not only in formal logical, mathematical terms, but also intuitively, in images, feelings, poetic usage of language, etc (Mathematical Quotes) No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful (Mathematical Quotes) I realize that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers (Mathematical Quotes) 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 different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science (Mathematical Quotes) The traditional mathematician recognizes and appreciates mathematical elegance when he sees it. I propose to go one step further, and to consider elegance an essential ingredient of mathematics: if it is clumsy, it is not mathematics (Mathematical Quotes) The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved (Mathematical Quotes) The analysis of variance is not a mathematical theorem, but rather a convenient method of arranging the arithmetic (Mathematical Quotes) And for mathematical science, he that doubts their certainty hath need of a dose of hellebore (Mathematical Quotes) There exists, if I am not mistaken, an entire world which is the totality of mathematical truths, to which we have access only with our mind, just as a world of physical reality exists, the one like the other independent of ourselves, both of divine creation (Mathematical Quotes) A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street (Mathematical Quotes) How thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler methods which, at the same time, assist in understanding earlier theories and in casting aside some more complicated developments (Mathematical Quotes) Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts (Mathematical Quotes) The further a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separated branches of the science (Mathematical Quotes)

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