I would say that mathematics is the study of the descendants of the concept of number. The arguments about how to separate the fields are something like the arguments about how to classify species, and very often you'll get mules and ligers. On Sat, Jul 4, 2015 at 9:29 AM, Cris Moore <moore@santafe.edu> wrote:
When I talk to kids about math, I tell them that it's not just the study of numbers, but the study of forms, shapes, and patterns. I think of it as the study of structure.
Cris
On Jul 4, 2015, at 8:47 AM, James Propp <jamespropp@gmail.com> wrote:
Welcome (back?), Scott.
It's hard to disentangle the questions "What is mathematics?", "What do mathematicians do?", and "What is a mathematician?" One of my LEAST favorite answers to the last of these questions is Lord Kelvin's: "A mathematician is one to whom *that* [the formula for the integral of exp(-x^2) as x goes from minus infinity to infinity] is as obvious as that twice two makes four is to you." I dislike that for a whole bunch of reasons, not the least of which is that it implies that I am not a mathematician --- I can't even remember whether it's pi or 2 pi inside the square root.
Relating to a different point from Scott's email, here's a fun story that's probably almost completely true (I may have minor details wrong): Probabilists Robin Pemantle and Jeff Steif were at an airport together when Robin said he could often spot mathematicians by their appearance, and when pressed to demonstrate this knack, opined that a particular fellow in the waiting area looked like a mathematician. They asked him, but he said he wasn't a mathematician. Later, on the flight, Robin saw the same person reading a yellow Springer-Verlag text. "Are you -sure- you're not a mathematician?" asked Robin. "I'm not a mathematician," the stranger replied, "I'm a theoretical computer scientist!"
Jim Propp
On Friday, July 3, 2015, SCOTT KIM <scottekim1@gmail.com> wrote:
Love this question and am not happy yet with any answers I've heard. I want a definition that does not just say what math is, but also distinguishes it from its near neighbors (e.g. Computer science and logic) and distinguishes among ways of practicing math, e.g. Pure vs. applied vs. recreational. Thoughts?
Sent from my iPhone
On Jun 11, 2015, at 3:23 PM, James Propp <jamespropp@gmail.com <javascript:;>> wrote:
A couple of weeks ago, in a gathering of mathematicians throwing out candidate definitions of mathematics, I half-seriously ventured the opinion that mathematics is the subset of philosophy consisting of those philosophical questions that actually have answers, along with the answers to those questions.
But I don't think this is original. Whom am I quoting (or paraphrasing) here?
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