By which I mean, are there any mathematical results which you find genuinely disappointing to have to accept?

My one is definitely the result about only (semi-)Eulerian graphs being traversable. As a kid I spent hours walking my way through paths made out of doodles, and when I heard in year 12 that a way out could NEVER be found, I remember actually getting quite upset and disorientated.

I think it's the futility that gets me; how you can start with good intentions, ticking off vertices, and then that crunch moment where you realise you've burned through a point one too many times. It's one of the reasons that I hate combinatorics now

Not really a theorem, but I am upset by the fact you cannot even solve dy/dx = f(x) in general.

I don't really see why the Eulerian graph one should be disappointing, it's not as much a statement that you can't find a path in some graphs as much as it classifies the graphs in which you can. After all, it's pretty easy to see that some graphs aren't Eulerian just by looking at something like . By analogy, Godel's second incompleteness theorem or the undecidability of the Continuum Hypothesis should really make you hate logic and set theory. :P

But I've already got a tactic for dealing with GIT; just put my fingers in my ears and go "lalalalala I can't hear you"

If I find a result upsetting I just try to disprove it, or failing that ignore it's existance, or failing that assert that it is not true but I'm not smart enough to prove it.

Does this explain anything?

So you find it disturbing that there's an infinite number of primes?

More upsetting than disturbing. I'd prefer it if there were graham's number of primes.

Why?...

Assume there are Graham's number of primes. Then yadda yadda yadda, Graham's number plus one, maths wins again

Maths 2101, Alex 0

I'm not saying that there are Graham's number of primes. I just wish it was true and millions of years from now when they finally and shockingly disprove that there are infinite primes, they will look back at a news article in a local paper from 60 years from now about an old man who waved his stick angrily at the guy who disproved the traveling sales man. With a little side note saying he beleives that the primes are finite. Then they'll say this crackpot knew the truth long beofre we did. I plan to be that old man. You might have guessed.

I just wish cosmin could be there, unfortunatly he died from a riemann zeta related accident. Also CJ lives in britain since the isle of man flooded. Luckily now britain is just slightly smaller than the isle of man due to the same flooding. Technically he lives in scottland. He plans to resurrect the isle of man using state of the are floatation devices.

Anyway...

I was genuinely curious as to why you would prefer the number of primes to be finite.

Does this mean Britain will consist of a few mountaintops in Scotland in the future?

Also if you don't the set of primes being infinite then just avoid using the natural numbers above in future.

I don't like the primes being infinite because deep down im an anarchist and the more fundamental somthing is the more fun it will cause when it turns out it's not true. Also it's the first thing I was taught in uni which i didn't immediatly agree with.

In the future the south of england will be flooded. Then the beutiful notrth will go and all that will be left is parts of scottland (nuke willing).

Except it never will turn out to be wrong because it's proven to be true and the proof is beyond any sort of doubt since it's one of the easiest proofs in maths. Besides, supposing the proof is false, how do you actually determine that you've reached the largest prime? You'd need to prove it (by induction, naturally) and then you'd have the same problem of credibility with that proof.

You could have at least chosen something a bit more controversial. If you had claimed that mathematics is inconsistant no one could have argued with you and it would have been an even more fundamental fact.

I know but im stubborn and hold a grudge.

I don't like the primes being infinite because deep down im an anarchist and the more fundamental somthing is the more fun it will cause when it turns out it's not true.

But why the primes? Surely there are far more fundamental results with which you could disagree and get on even more peoples nerves?

Yeah, that's what I was saying as well. The consistency of ZFC is about as fundamental as you can get and since it's unprovable no one can meaningfully argue with you if you say it's inconsistant. It's a much better choice. :p

We're all forgetting, there's a result which is infinitely more annoying than all of these. Or infinitely less annoying. Or neutral.

Oh yeah, sorry I didn't see that.

Basically what Alex is doing is equivalent to taking an English degree and arguing constantly about the usage of the word 'and'.

Well you've just never been hit by that beleif of something bigger...

The infinitude of the primes is just a theory.

I must confess, when I was writing my excursions essay, I found myself humbled, and somewhat depressed. However, since this is old news, I will put forward Arrows Impossibility Theorem as a very saddening theorem. That said, I'm still waiting for Jesus to come back and rule the world, thus relaxing the non-dictatorship condition in a way that should finally be a success.

Sure you'd get equality, but at what cost to the free market?!! Money lending would be crippled overnight! On the plus side, curtain repairs would probably rise!

I have to say there's not much that makes me sad about mathematics; the non-conformality of quaternionic maps is a real pain in the pisser (again, old news!), but nothing that is true can ever be saddening.

History, though vile and turgid with unrivaled hatred, is testament to the power of ideas; that one thought could capture, and be captured by, our self fulfilling circular logic stands absolute for the will of irridescent proclaimations: passion, fear and pain to rise like starved fire: unassuageable in its seem- to be effaced by the cool indifference of time and calculation- or vice versa. History tells us that humanity is caustic but is tempered.

Mathematics is such temper. As reflection of the mind or as reflection of worldview it is the law of assumptions: if X yields Y it is only because we have we have insisted upon X. Mathematics is not true, only consistent: conditional.

It is to humble, but also to inspire that we have built as men such brave consistent edifice: unexpected and beautiful. That we cannot build to heaven should not make light of building higher- we will see closer to horizon yet.

Or something.

I read in the Algebra II revision guide something that said if you could create a multiplication table where each element appeared once in each row and once in each column then it would be a group. This wasn't so much a theorem that made me sad as a statement which made me happy for a bit, till I discovered it was wrong.

tl;dr There's a mistake in the Algebra II revision guide.

Yeah, the structures which are equivalent to what you just said are actually called quasigroups and are a much weaker concept (nothing forces the binary operation to be associative, for example).

Edit: Seems to me that the revision guide only says it's necessary though, which is true.

Edit 2: Just noticed that this is actually the original instudious mathematicians thread, nice. :D

Also notice the universities insite web address at the start of a therorem. Probably a pasting error. God knows how, it looks like it's been \emph{...

That's not as good as 4.2 in the Prob A/B one though. :P