A Quote by Peter Galison
Here is a quilted book about mathematical practice, each patch wonderfully prepared. Part invitation to number theory, part autobiography, part sociology of mathematical training, Mathematics without Apologies brings us into contemporary mathematics as a living, active inquiry by real people. Anyone wanting a varied, cultured, and penetrating view of today's mathematics could find no better place to engage.
Quote Topics
About
Active
Anyone
Autobiography
Better
Better Place
Book
Brings
Contemporary
Could
Cultured
Each
Engage
Find
Inquiry
Invitation
Living
Mathematical
Mathematics
Number
Part
Patch
Penetrating
People
Place
Practice
Prepared
Real
Real People
Sociology
Theory
Today
Training
Us
Varied
View
Wanting
Without
Wonderfully
Quote Author
Related Quotes
This is a wonderful book, unique and engaging. Diaconis and Graham manage to convey the awe and marvels of mathematics, and of magic tricks, especially those that depend fundamentally on mathematical ideas. They range over many delicious topics, giving us an enchanting personal view of the history and practice of magic, of mathematics, and of the fascinating connection between the two cultures. Magical Mathematics will have an utterly devoted readership.
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.
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.
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.
One may say that mathematics talks about the things which are of no concern to men. Mathematics has the inhuman quality of starlight - brilliant, sharp but cold ... thus we are clearest where knowledge matters least: in mathematics, especially number theory.
Mathematical thinking is not the same as doing mathematics - at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box - a valuable ability in today's world.
Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances suggest the contrary, but there are easy explanations. Music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity
Mathematics is the most exact science, and its conclusions are capable of absolute proof. But this is so only because mathematics does not attempt to draw absolute conclusions. All mathematical truths are relative, conditional. In E. T. Bell Men of Mathematics, New York: Simona and Schuster, 1937.
All our surest statements about the nature of the world are mathematical statements, yet we do not know what mathematics "is"... and so we find that we have adapted a religion strikingly similar to many traditional faiths. Change "mathematics" to "God" and little else might seem to change. The problem of human contact with some spiritual realm, of timelessness, of our inability to capture all with language and symbol-all have their counterparts in the quest for the nature of Platonic mathematics.
To criticize mathematics for its abstraction is to miss the point entirely. Abstraction is what makes mathematics work. If you concentrate too closely on too limited an application of a mathematical idea, you rob the mathematician of his most important tools: analogy, generality, and simplicity. Mathematics is the ultimate in technology transfer.
But there is another reason for the high repute of mathematics: it is mathematics that offers the exact natural sciences a certain measure of security which, without mathematics, they could not attain.
We know that mathematicians care no more for logic than logicians for mathematics. The two eyes of science are mathematics and logic; the mathematical set puts out the logical eye, the logical set puts out the mathematical eye; each believing that it sees better with one eye than with two. Note that De Morgan, himself, only had sight with only one eye.
For me, rhythm is a type of divine mathematics in a way. No matter where you're from, we can all understand the mathematics of rhythm. I try to apply this mathematical thinking to my playing.
It is almost as hard to define mathematics as it is to define economics, and one is tempted to fall back on the famous old definition attributed to Jacob Viner, "Economics is what economists do," and say that mathematics is what mathematicians do. A large part of mathematics deals with the formal relations of quantities or numbers.
[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing - one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me.
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.
Related Authors
Allen W. Wood Quotes
American
Professor
Clayton Christensen Quotes
American
Professor
Glenn Reynolds Quotes
American
Professor
Gordon S. Wood Quotes
American
Professor
Jeffrey Pfeffer Quotes
American
Professor
Jerry A. Coyne Quotes
American
Professor
Michael Hudson Quotes
American
Professor
Richard A. Falk Quotes
American
Professor
Robert S. Kaplan Quotes
American
Professor
Ruth Simmons Quotes
American
Professor
Seyyed Hossein Nasr Quotes
Iranian
Professor