## “The argument is carried out not in mathematical symbols but in ordinary English, there is no obscure or technical terms. Knowledge of calculus is not presupposed. In fact, one hardly need to know how to count. Yet any mathematician will immediately recognize the argument as mathematical.”

**Test your intuition 44: what is the argument? who and where wrote this view about “what is mathematics”.**

Zero-knowledge answers please.

Comments regarding this view itself and on “what is mathematics” are also welcome.

(Here are other posts on “What is mathematics.”)

PS. The last facetious sentence was omitted in the Journal version of the paper. (Indeed it was a good decision to take it out.) PPS Yannai Gonczarowski pointed out the the journal formulation is also rather condescending (perhaps even more so) towards non-mathematicians.

The proof of the existence of infinitely prime numbers.

Mathematics is best compared to a combination of masochism and opium:

an addiction to the endorphines released after the pain fades from certain self-imposed mental tortures.

And like other addicts, Mathematicians tend to rationalize their indulgences: as “work” on some “important problem”.

Thus the inherent impossibility to “define” Mathematics: YKINMK.

A high school teacher of mine (with a PhD in mathematics) once jokingly gave me this true, but also not very satisfying definition: “Mathematics is what mathematicians do.”

If mathematicians are the only people, who can perceive arguments that require more than two steps, then the world is in a very dire state of affairs. Maybe it is. Most likely it is right in saying that mathematical arguments are arguments with sufficient precision. It sounds about right. Or at least it explains why mathematicians spend quite some time arguing about what is sufficient precision.

My view (with respect to applied mathematicians) is that mathematics is the branch of natural philosophy that concerns itself with only making true statements.

This involves tradeoffs. Most visibly, we gave up our right to say the RH is true (to pick an example) even though it’s been verified as rigorously as almost any law of physics or result in biology. Less visibly, our statements are always conditional (“if A then B”) — we always need axioms. But we also get benefits: our literature largely doesn’t grow stale: results in our literature have half-lives orders of magnitude greater than in the sciences.

I know that this definition sidelines the Grothendieck school emphasis on definitions as opposed to theorems, but I still think it best captures the spirit of pure mathematics.

Lease A Glyph

I would say it’s Coase’s Theorem, except that that is really a result in economics, not mathematics.

Ronald Coase (1960) only gave simple numerical examples based on fascinating historical examples. At Chicago, his departmental colleagues found it too counterintuitive to believe, more of a “what is wrong with this reasoning” puzzle Coase had foisted on them, until finally Milton Friedman had an aha! moment and then convinced everyone else.

I know this one! 🙂 Heard it in a math talk even. It’s about the Gale-Shapley algorithm for the stable marriage problem, if I recall correctly.

This was the talk: https://personal.utdallas.edu/~nxw170830/docs/Presentations/kjw_hawaii_match.MP4. See around the 16 minute mark for where the quote appears.

A strong wind and an insurance company

Gale and Shapley

Stable Marriages?

It was mentioned in the AMS notices or the monthly in the past few years.