## Mathematically Speaking

This is a book full of quotes on the topic of mathematics. As is always the case for books full of quotations, most of the quotes in this book aren’t very good, but occasionally you come across a quote or two that enable you to justify reading on. I’ll likely include some of the good/interesting quotes in the book in future ‘quotes’ posts. Below I’ve added some sample quotes from the book. I’ve read roughly three-fifths of the book so far and I’m currently hovering around a two-star rating on goodreads.

…

“Since authors seldom, if ever, say what they mean, the following glossary is offered to neophytes in mathematical research to help them understand the language that surrounds the formulas …

ANALOGUE. This is an a. of: I have to have *some* excuse for publishing it.

APPLICATIONS. This is of interest in a.: I have to have *some* excuse for publishing it.

COMPLETE. The proof is now c.: I can’t finish it. […]

DIFFICULT. This problem is d.: I don’t know the answer. (*Cf.* Trivial)

GENERALITY. Without loss of g.: I have done an easy special case. […]

INTERESTING. X’s paper is I.: I don’t understand it.

KNOWN. This is a k. result but I reproduce the proof for convenience of the reader: My paper isn’t long enough. […]

NEW. This was proved by X but the following n. proof may present points of interest: I can’t understand X.

NOTATION. To simplify the n.: It is too much trouble to change now.

OBSERVED. It will be o. that: I hope you have not noticed that.

OBVIOUS. It is o.: I can’t prove it.

READER. The details may be left to the r.: I can’t do it. […]

STRAIGHTFORWARD. By a s. computation: I lost my notes.

TRIVIAL. This problem is t.: I know the answer (*Cf.* Difficult).

WELL-KNOWN. The result is w.: I can’t find the reference.” (Pétard, H. [Pondiczery, E.S.]).

Here are a few quotes similar to the ones above, provided by a different, unknown source:

“BRIEFLY: I’m running out of time, so I’ll just write and talk faster. […]

HE’S ONE OF THE GREAT LIVING MATHEMATICIANS: He’s written 5 papers and I’ve read 2 of them. […]

I’VE HEARD SO MUCH ABOUT YOU: Stalling a minute may give me time to recall who you are. […]

QUANTIFY: I can’t find anything wrong with your proof except that it won’t work if x is a moon of Jupiter (popular in applied math courses). […]

SKETCH OF A PROOF: I couldn’t verify all the details, so I’ll break it down into the parts I couldn’t prove.

YOUR TALK WAS VERY INTERESTING: I can’t think of anything to say about your talk.” (‘Unknown’)

“Mathematics is neither a description of nature nor an explanation of its operation; it is not concerned with physical motion or with the metaphysical generation of quantities. It is merely the symbolic logic of possible relations, and as such is concerned with neither approximate nor absolute truth, but only with hypothetical truth. That is, mathematics determines which conclusions will follow logically from given premises. The conjunction of mathematics and philosophy, or of mathematics and science is frequently of great service in suggesting new problems and points of view.” (Carl Boyer)

“It’s the nature of mathematics to pose more problems than it can solve.” (Ivars Peterson)

“the social scientist who lacks a mathematical mind and regards a mathematical formula as a magic recipe, rather than as the formulation of a supposition, does not hold forth much promise. A mathematical formula is never more than a precise statement. It must not be made into a Procrustean bed […] The chief merit of mathematization is that it compels us to become conscious of what we are assuming.” (Bertrand de Jouvenel)

“As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” (Albert Einstein)

“[Mathematics] includes much that will neither hurt one who does not know it nor help one who does.” (J. B. Mencke)

“Pure mathematics consists entirely of asseverations to the extent that, if such and such a proposition is true of *anything*, then such and such another proposition is true of *anything*. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true … *If* our hypothesis is about *anything*, and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.” (Bertrand Russell)

“Mathematical rigor is like clothing; in its style it ought to suit the occasion, and it diminishes comfort and restricts freedom of movement if it is either too loose or too tight.” (G. F. Simmons).

“at a great distance from its empirical source, or after much “abstract” inbreeding, a mathematical subject is in danger of degeneration. At the inception the style is usually classical; when it shows signs of becoming baroque, then the danger signal is up … In any event, whenever this stage is reached, the only remedy seems to me to be the rejuvenating return to the source: the reinjection of more or less directly empirical ideas.” (John von Neumann)

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