Mathematics poll

[ciphergoth]

Inspired by a similar poll in palmer1984's journal.

About the "proof" question below: examples of the kind of proof I mean would be a proof that there are infinitely many primes, or that the square root of two is irrational, or of Pythagoras's Theorem. A proof in computer science counts too. By "know a proof off by heart" I mean that you'd be able to convince someone of it at a party, if they had the background to follow the proof.

If you know lots of proofs, feel free to choose one you particularly like in the last question...

[Poll #1351621]

Comments

[ciphergoth.livejournal.com]

So, numbers that can't be expressed don't "exist" but you're prepared to treat them as if they do "exist" if, for example, you're talking about measure theory. I think you think you're doing something terribly important and clever, but from here it looks more like theology than mathematics.

[fizzyboot.livejournal.com]

So, numbers that can't be expressed don't "exist",

Putative symbol-lists (whether you want to think of them as numbers or otherwise) that cannot in principle be expressed, are not expressed anywhere. In that sense they clearly do not exist.

A movie on my hard disk takes up about 1 GB, i.e. it's an 8,000,000,000 digit long binary number. Do all such numbers "exist"? I submit that the only ones that exist, are those that actually have physical representations somewhere; to say otherwise is to say that a movie exists before filming has started on it, which IMO is ridiculous.

I think you think you're doing something terribly important and clever

No, I think it's bloody obvious.

[ciphergoth.livejournal.com]

Naah, it's pretty much a mathematician's green ink letter...