/sci/ - Science & Math

>>7101013
The method of analytic continuation isn't beautiful? I feel the complex numbers are maybe the purest algebraic structure out there.

I now feel I'm becoming too much of a 1+2+3+...=-1/12 proponent here, a statement which I really do not care for. What bothers me though, is when people think they can rationally argue against it, "It's can't be true, because I haven't seen something like this in Calc 1.", as if claiming this proposition would represent a wrong statement about the world.
It's because somehow people seek to be Platonists. It's math! You can either choose just to learn it, or to do it. The first is equivalent to learning the canon established 150 years ago. The second is to find interesting problems and invent new techniques.
If you do you differential geometry of two-dimensional surfaces, an established field, and somewhere pops up an expression

<span class="math">u=2+\frac{3}{\sum_{k=0}^\infty k}[/spoiler]

then you're pretty much guaranteed that u=2 gives the right results for computing the curvature of a curve or whatnot. If instead you work on an unsolved problems about radiating neutrinos in a star, and you have an idea to model the system, then you don't want to drop the research at the point where your exhaustive literature search on previous math used for particle statistics doesn't tell you what to do anymore. There were no Feynman path integrals or Dirac deltas before those people cooked them up, and they didn't sit down and learned set theory for years before they got back to their problems. They -did- math.

>>7100939
What's the difference between firm and company?
When I decided not to do a PhD at a university, I already dropped officially doing quantum gravity and such. Besides, I don't really know the purpose of money besides getting pussy and assuring health at old age. I hit the gym 3 times a week and it seems I do better than the people around me.