I can add a few: "The duty of abstract mathematics, as I see it, is precisely to expand our capacity for hypothesizing possible ontologies." --- Norm Levitt A physicist goes off to a conference. After a week his suit’s gotten soiled and crumpled, so he goes out to look for a dry cleaner. Walking down the main street of town, he comes upon a store with a lot of signs out front. One of them says “Dry Cleaning.” So he goes in with his dirty suit and asks when he can come back to pick it up. The mathematician who owns the shop replies, “I’m terribly sorry, but we don’t do dry cleaning.” “What?” exclaims the puzzled physicist. “The sign outside says ‘Dry Cleaning’!” “We do not do anything here,” replies the mathematician. “We only sell signs!” --- Alain Connes, in Changeux "A mathematician is like a mad tailor: he is making "all possible clothes" and hopes to make also something suitable for dressing" --- Stanislaw Lem, Summa Techologiae "Mathematics is part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap." --- Vladimir Arnold. "Math is a cybervirus that lives in human minds, evolves therein and reproduces itself via language." --- Stephen Paul King Brent Meeker On 7/5/2015 2:29 PM, Thane Plambeck wrote:
i just noticed there are several proposed definitions (some of them familiar to me, others not), on the wikipedia page for bertrand russell, and dropped in below
Bertrand Russell wrote this famous tongue-in-cheek definition, describing the way all terms in mathematics are ultimately defined by reference to undefined terms:
The subject in which we never know what we are talking about, nor whether what we are saying is true.[12] <https://en.m.wikipedia.org/wiki/Definitions_of_mathematics#cite_note-12> Bertrand Russell <https://en.m.wikipedia.org/wiki/Bertrand_Russell> 1901
Many other attempts to characterize mathematics have led to humor or poetic prose:
"Mathematics is about making up rules and seeing what happens."[13] <https://en.m.wikipedia.org/wiki/Definitions_of_mathematics#cite_note-13> Vi Hart <https://en.m.wikipedia.org/wiki/Vi_Hart>
A mathematician is a blind man in a dark room looking for a black cat which isn't there.[14] <https://en.m.wikipedia.org/wiki/Definitions_of_mathematics#cite_note-14> Charles Darwin <https://en.m.wikipedia.org/wiki/Charles_Darwin>
A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. G. H. Hardy <https://en.m.wikipedia.org/wiki/G._H._Hardy>, 1940
Mathematics is the art of giving the same name to different things.[8] <https://en.m.wikipedia.org/wiki/Definitions_of_mathematics#cite_note-eves-8> Henri Poincaré <https://en.m.wikipedia.org/wiki/Henri_Poincar%C3%A9>
Mathematics is the science of skilful operations with concepts and rules invented just for this purpose. [this purpose being the skilful operation ....][15] <https://en.m.wikipedia.org/wiki/Definitions_of_mathematics#cite_note-15> Eugene Wigner <https://en.m.wikipedia.org/wiki/Eugene_Wigner>
Mathematics is not a book confined within a cover and bound between brazen clasps, whose contents it needs only patience to ransack; it is not a mine, whose treasures may take long to reduce into possession, but which fill only a limited number of veins and lodes; it is not a soil, whose fertility can be exhausted by the yield of successive harvests; it is not a continent or an ocean, whose area can be mapped out and its contour defined: it is limitless as that space which it finds too narrow for its aspirations; its possibilities are as infinite as the worlds which are forever crowding in and multiplying upon the astronomer's gaze; it is as incapable of being restricted within assigned boundaries or being reduced to definitions of permanent validity, as the consciousness of life, which seems to slumber in each monad, in every atom of matter, in each leaf and bud cell, and is forever ready to burst forth into new forms of vegetable and animal existence.[16] <https://en.m.wikipedia.org/wiki/Definitions_of_mathematics#cite_note-StewartFrom-16> James Joseph Sylvester <https://en.m.wikipedia.org/wiki/James_Joseph_Sylvester>
What is mathematics? What is it for? What are mathematicians doing nowadays? Wasn't it all finished long ago? How many new numbers can you invent anyway? Is today's mathematics just a matter of huge calculations, with the mathematician as a kind of zookeeper, making sure the precious computers are fed and watered? If it's not, what is it other than the incomprehensible outpourings of superpowered brainboxes with their heads in the clouds and their feet dangling from the lofty balconies of their ivory towers? Mathematics is all of these, and none. Mostly, it's just different. It's not what you expect it to be, you turn your back for a moment and it's changed. It's certainly not just a fixed body of knowledge, its growth is not confined to inventing new numbers, and its hidden tendrils pervade every aspect of modern life.[16] <https://en.m.wikipedia.org/wiki/Definitions_of_mathematics#cite_note-StewartFrom-16> Ian Stewart <https://en.m.wikipedia.org/wiki/Ian_Stewart_(mathematician)>
On Sunday, July 5, 2015, Andy Latto <andy.latto@pobox.com> wrote:
While you and I may both agree that the set of things that we couldn't imagine were otherwise roughly corresponds to mathematics, there are a lot of theological arguments that porport to prove that there is a God, and that he has certain properties, and that this couldn't possibly be otherwise. So I don't see a good way to patch this definition to exclude theology.
Andy
On Sat, Jul 4, 2015 at 3:30 PM, James Propp <jamespropp@gmail.com <javascript:;>> wrote:
Here's a start of a different sort of approach to the question of what math is, taking off from a remark in Jordan Ellenberg's book "How Not To Be Wrong" about how a times b equals b times a, for all a and b, "because it couldn't be otherwise".
Let's make this more modest and say that we can't IMAGINE how it could be otherwise.
That is: I can just barely imagine (with a mental squint, and with an inner acknowledgments of my limitations as a reasoner) *that* ordinary multiplication of ordinary natural numbers might not be commutative. But I cannot imagine in any kind of detail *how* it might fail to be commutative. There are probably lots of things that humans aren't able to doubt (such as "I exist") that don't count as mathematics, so this definition will need to be modified before it comes close to drawing the line between math and non-math in approximately the right place.
A variant of this approach would be to define pure mathematics as the study of fantasies that possess a certain kind of coherence.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Andy.Latto@pobox.com <javascript:;>
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun