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Quote by Jacob T. Schwartz

“Because of mathematics precise, formal character, mathematical arguments remain sound even when they are long and complex. In contast, common sense arguments can generally be trusted only if they remain short; even moderately long nonmathematical arguments rapidly becomes farfetched an dubious.”

Quote by Jacob T. Schwartz

Author

Jacob T. Schwartz

Jacob T. Schwartz was a renowned mathematician known for his contributions to mathematical analysis, functional analysis, and mathematical physics. His research involved partial differential equations, nonlinear functional equations, and other issues in mathematical physics. Schwartz's work had a profound impact on modern mathematics and physics. more

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“In recent years we have become much more preoccupied with streamlining and organizing our subject than with maintaining its overall vitality. If we are not careful, a great adventure of the mind will become yet another profession.”

Ifs Years Mind Subjects Adventure Careful Profession Vitality Maintaining Great Adventure Streamlining

Book:Discrete Thoughts: Essays on Mathematics, Science and Philosophy

Source: Discrete Thoughts: Essays on Mathematics, Science and Philosophy

“The pendulum of mathematics swings back and forth towards abstraction and away from it with a timing that remains to be estimated.”

Mathematics Remains Swings Timing Abstraction Back And Forth Pendulums

Book:Indiscrete Thoughts

Source: Indiscrete Thoughts

“You feed yourself. Make sure you have all the information, whether it's aesthetic, scientific, mathematical, I don't care what it is. Then you walk away from it and let it ferment. You ignore it and pretend you don't care. Next thing you know, the answer comes.”

Knows Care Next Answers Walks Information Don't Care Mathematical I Don't Care Aesthetic

Author:Ray Bradbury

“I think that mathematics can benefit by acknowledging that the creation of good models is just as important as proving deep theorems.”

Thinking Important Creation Prove Benefits Models Mathematics Theorems

Author:David Mumford

“My own view is that no major advance was ever found as a result of a committee's recommendation... We should be honest in telling these agencies we often don't know where some ideas are going to lead, but we hope they are going to clarify a problem.”

Knows Should Ideas Problem Found My Own Results Views Honest Majors Being Honest Agency Committees Recommendations

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“The human brain finds it extremely hard to cope with a new level of abstraction. This is why it was well into the eighteenth century before mathematicians felt comfortable dealing with zero and with negative numbers, and why even today many people cannot accept the square root of minus-one as a genuine number.”

People Humans Wells Hard Today Felt Levels Numbers Brain Accepting Century Comfortable Negative Roots Genuine Zero Squares Mathematician Abstraction Human Brain Minus Square Roots

Author:Keith Devlin

“Mathematics is a field which has often been compared with chess, but differs from the latter in that it is only one's best moments that count and not one's worst.”

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Book:Ex-prodigy: My Childhood and Youth

Source: Ex-prodigy: My Childhood and Youth

“The axiomatic method has many advantages over honest work.”

Honest Advantage Method Honest Work

Author:Bertrand Russell

“Are mathematical ideas invented or discovered? This question has been repeatedly posed by philosophers through the ages and will probably be with us forever.”

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Book:Indiscrete Thoughts

Source: Indiscrete Thoughts

“A lot of people criticize Formula 1 as an unnecessary risk. But what would life be like if we only did what is necessary?”

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Author:Niki Lauda