“A central problem in teaching mathematics is to communicate a reasonable sense of taste—meaning often when to, or not to, generalize, abstract, or extend something you have just done.”

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)

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Richard Hamming90

American mathematician and information theorist 1915–1998

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Steve Jobs (1955–2011) American entrepreneur and co-founder of Apple Inc.

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“The real problem in speech is not precise language. The problem is clear language. The desire is to have the idea clearly communicated to the other person. It is only necessary to be precise when there is some doubt as to the meaning of a phrase, and then the precision should be put in the place where the doubt exists. It is really quite impossible to say anything with absolute precision, unless that thing is so abstracted from the real world as to not represent any real thing.Pure mathematics is just such an abstraction from the real world, and pure mathematics does have a special precise language for dealing with its own special and technical subjects. But this precise language is not precise in any sense if you deal with real objects of the world, and it is only pedantic and quite confusing to use it unless there are some special subtleties which have to be carefully distinguished.”

Richard Feynman (1918–1988) American theoretical physicist

" New Textbooks for the "New" Mathematics http://calteches.library.caltech.edu/2362/1/feynman.pdf", Engineering and Science volume 28, number 6 (March 1965) p. 9-15 at p. 14 <br class="br">Paraphrased as "Precise language is not the problem. Clear language is the problem."

“There is no agreed upon definition of mathematics, but there is widespread agreement that the essence of mathematics is extension, generalization, and abstraction… [which] often bring increased confidence in the results of a specific application, as well as new viewpoints.”

Richard Hamming (1915–1998) American mathematician and information theorist

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)

“The more abstract the truth you wish to teach, the more you need to seduce the senses to it.”

Friedrich Nietzsche (1844–1900) German philosopher, poet, composer, cultural critic, and classical philologist

“Push yourself beyond when you think you are done with what you have to say. […] It is beyond the point when you think you are done that often something strong comes out.”

Natalie Goldberg book Writing Down the Bones

Essay, "Go further". p.112
Writing Down the Bones (1986)

“We are mainly interested in the processes… not… in presenting mathematics in its most abstract form. …we will often begin with concrete forms and then exhibit the process of abstraction.”

Richard Hamming (1915–1998) American mathematician and information theorist

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)

“I thought we should require physical determinations, and not abstract integrations. A pernicious taste begins to infiltrate, from which real science will suffer far more than it will progress, and it would be often better for the true physics if there were no mathematics in the world.”

Daniel Bernoulli

Ich vermeinte, man verlange physische Determinationen und nicht abstracte integrationes. Es fängt sich ein verderblicher goût an einzuschleichen, durch welchen die wahren Wissenschaften viel mehr leiden, als sie avancirt werden, und wäre es oft besser für die realem physicam, wenn keine Mathematik auf der Welt wäre.
Letter to Leonhard Euler, 26 January 1750, published in [Correspondance mathématique et physique de quelques célèbres géomètres du XVIIIème siècle, P. H. Fuss, Saint Petersburg, 1843, 650]

“I think it's a problem that people are considered immoral if they're not religious. That's just not true. This might earn me some enemies, but in some ways they may be even more moral. If you do something for a religious reason, you do it because you'll be rewarded in an afterlife or in this world. That's not quite as good as something you do for purely generous reasons.”

Lisa Randall (1962) American theoretical physicist and an expert on particle physics and cosmology

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“In general, corruption tends to exist whenever governments have favors to extend, or something to sell.”

Alan Greenspan (1926) 13th Chairman of the Federal Reserve in the United States

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“A model that unifies all types of selection (chemical, sociological, genetical, and every other kind of selection) may open the way to develop a general ‘Mathematical Theory of Selection’ analogous to communication theory… Selection has been studied mainly in genetics, but of course there is much more to selection than just genetical selection… yet, despite the pervading importance of selection in science and life, there has been no abstraction and generalisation from genetical selection to obtain a general selection theory and general selection mathematics”

George R. Price (1922–1975) American population geneticist

Price, G.R. (1995). "The nature of selection." Journal of Theoretical Biology 175:389-396 (written circa 1971)

“A central problem in teaching mathematics is to communicate a reasonable sense of taste—meaning often when to, or not to, generalize, abstract, or extend something you have just done.”

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Richard Hamming90

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