which is your favourite mathematical prof/teorem?

[drmwc]

From set theory, my favourite result is probably the Banach-Tarski paradox.

Why?

It gives rise to this joke:
q: What's an anagram on the the Banach-Tarski paradox?
a: Click to show

[Uberdude]

Did someone watch University Challenge last night?

[drmwc]

They asked about the Banach Tarski paradox on the show, or just told the joke? (I didn't watch it.)

[Uberdude]

Banach Tarski was the answer to a question about doubling the sphere, with the clue that it was named after two people; the team of classicists guessed "Smith Wilson".

[aokun]

My favorite theorem ... math, though nestled wholly within physics ... is Noether's theorem. Informally stated, it's that for any symmetry of a physical system, there is a corresponding conservation law. Translational invariance means conservation of momentum, rotational means conservation of angular momentum, invariance in translation through time means conservation of energy, which is a bit mind-blowing. It can be extended to QFT in some way my lack of understanding of which is even beyond me, but which gives a series of "guage symmetries" implying conservation of electric charge and other such quantities.

When I properly read about it, I became very angry at my old college tutors for not doing mechanics with generalized coordinates and the principle of least action in year 1 and QFT in year 3. It's like they told me I'd learned mountain climbing, then drove me up Pike's Peak, without suggesting I give Everest a try. I mean, I could have pursued it all myself, but I was a callow and foolish young man then.

I also have a little affection for the ABC conjecture, but only because Shinichi Mochizuki has apparently proved it by the method of reductio ad nauseam.

[drmwc]

Banach Tarski was the answer to a question about doubling the sphere, with the clue that it was named after two people; the team of classicists guessed "Smith Wilson".

I hope Paxman said "ball" rather than "sphere". It's untrue for a sphere - you need to include (some of) the interior.

Smith-Wilson is a technique for extrapolating yield curves.

[Uberdude]

I hope Paxman said "ball" rather than "sphere". It's untrue for a sphere - you need to include (some of) the interior.

Yes, my mistake, 19:30 in http://www.bbc.co.uk/iplayer/episode/b0 ... pisode_34/

[Shaddy]

I didn't think that was true? The proof of Banach-Tarski that I know does the decomposition for the spherical shell, then extends it to the ball by projecting the decomposition inwards.

[cyclops]

I like the teorem that a continuous real function that assumes at least two values also assumes all values in between.
I like the teorem that every continuous bijection from a disk onto itself at least maps one point onto itself.
I like the rule that in projective 2D geometry every teorem remains true if the word "point" is replaced by "line" and vice versa.

[Magicwand]

e^{i * pi} + 1 = 0

[drmwc]

I didn't think that was true? The proof of Banach-Tarski that I know does the decomposition for the spherical shell, then extends it to the ball by projecting the decomposition inwards.

You're right - I was typing rubbish.