Sunday, December 21, 2014
A Mathematical Tension
The unexplained mystery...
"I, for one, find Gödel's incompleteness theorems rather comforting. It means that mathematicians will never be complete. There will always be something else which is undecidable with the current axioms. Should the human species survive another few million years and continue churning out mathematics at the rate we've done for the past few thousand years, we still won't have considered it all. There will always be work for all of the future mathematicians. As always, some of that work will go on to be incredibly useful for the rest of civilization, and much of it will remain the pointless but endlessly amusing plaything of academics.
"There's an unexplained mystery behind all of this, which I've been delicately avoiding throughout the book. If maths is the consequence of games and puzzles, the result of pure intellectual thought, why does it end up being so practically useful? I keep promoting maths as a bit of fun, yet no one can ignore that mathematical techniques are the workhorse of modern technology. In reality, mathematics is a serious industrial endeavor. There's a tension between what I claim to be the origin of maths and where it ends up being used."
-- Matt Parker from "Things To Make and Do In the Fourth Dimension"
[…If you have a favorite math-related passage that might make a nice Sunday morning reflection here let me know (SheckyR@gmail.com). If I use one submitted by a reader, I'll cite the contributor.]