A Quote by Richard P. Feynman
Mathematics is a language plus reasoning. It's like a language plus logic. Mathematics is a tool for reasoning.
Related Quotes
Mathematics is not just a language. Mathematics is a language plus reasoning.
Across a range of inferences involving not just language but mathematics, logic problems, and spatial reasoning, sleep has been shown to enhance the formation and understanding of abstract relations, so much so that people often wake having solved a problem that was unsolvable the night before.
As an exercise of the reasoning faculties, pure mathematics is an admirable exercise, because it consists of reasoning alone and does not encumber the student with any exercise of judgment.
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.
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.
To create a language all of a piece which would be a women's language, that I find quite insane. There does not exist a mathematics which is only a women's mathematics, or a feminine science.
Inferences of Science and Common Sense differ from those of deductive logic and mathematics in a very important respect, namely, when the premises are true and the reasoning correct, the conclusion is only probable.
Mathematics never reveals man to the degree, never expresses him in the way, that any other field of human endeavour does: the extent of the negation of man's corporeal self that mathematics achieves cannot be compared with anything. Whoever is interested in this subject I refer to my articles. Here I will say only that the world injected its patterns into human language at the very inception of that language; mathematics sleeps in every utterance, and can only be discovered, never invented.
One cannot inquire into the foundations and nature of mathematics without delving into the question of the operations by which the mathematical activity of the mind is conducted. If one failed to take that into account, then one would be left studying only the language in which mathematics is represented rather than the essence of mathematics.
Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems-general and specific statements-can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences.
There is a logic of language and a logic of mathematics.
The deep paradox uncovered by AI research: the only way to deal efficiently with very complex problems is to move away from pure logic.... Most of the time, reaching the right decision requires little reasoning.... Expert systems are, thus, not about reasoning: they are about knowing.... Reasoning takes time, so we try to do it as seldom as possible. Instead we store the results of our reasoning for later reference.
Formal logic is mathematics, and there are philosophers like Wittgenstein that are very mathematical, but what they're really doing is mathematics - it's not talking about things that have affected computer science; it's mathematical logic.
Logic is essentially a tool for getting at truth; it is the tool, for without it no reasoning is possible in any field of human enquiry whatsoever.
Bad reasoning as well as good reasoning is possible; and this fact is the foundation of the practical side of logic.
Poincaré was a vigorous opponent of the theory that all mathematics can be rewritten in terms of the most elementary notions of classical logic; something more than logic, he believed, makes mathematics what it is.
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