You're the topologist

[Vorotyntsev]

"To a topologist, a rabbit is the same as a sphere. Neither has a hole."

This made me laugh. A prize (not the Fields) for the smartest comeback.

[bwouns]

That must be one constipated rabbit!

[polarea]

That must be one constipated rabbit!

LOLOLOL!

I wonder whether the mad hatter agrees with your conjecture?

[WendellWit]

"To a topologist, a rabbit is the same as a sphere. Neither has a hole."

I thought the rabbit goes INTO the hole.

And, if I remember 50 years of Bugs & Daffy, it's the duck who gets the holes shot into him.

[ArtVark]

"To a topologist, a rabbit is the same as a sphere. Neither has a hole."

This made me laugh. A prize (not the Fields) for the smartest comeback.

Actually, our entire digestive tracts can be considered one hole. So we, as well as rabbits, cows, warthogs, monitor lizards, and a whole bunch of other organisms are topologically equivalent to doughnuts.

[JD]

"To a topologist, a rabbit is the same as a sphere. Neither has a hole."

I thought the rabbit goes INTO the hole.

And, if I remember 50 years of Bugs & Daffy, it's the duck who gets the holes shot into him.

Bugs: Duck Season.
Daffy: Rabbit Season.
Bugs: Duck Season.
Daffy: Rabbit Season.
Bugs: Rabbit Season.
Daffy: Duck Season.
Bugs: Rabbit Season.
Daffy: I say it's *duck* season... and I say *fire*!

[WendellWit]

Not my creation (wish it were...):

I'm deth-picable.

[Professor John]

FIRE IN THE HOLE!!!

[sparbowl]

My order of when they will be resolved, ignoring the other comments in this thread:

#1 - Riemann Hypothesis. I actually think about this one quite a bit, even though I am sure I don't have enough Math in me to do anything about it. Another pretty good book is "Uncle Petros and Goldbach's Conjecture" by Apostolos Doxiadis. I have to think that the primes have some sort distribution out there, that leads will eventually lead us to it.

#2 - Birch & Swinnerton-Dyer - This will actually be solved on April 13, 2013 by some dude in Tupelo, Mississippi. He won't publish it, his ideas will be read and stolen by some professor at the University of Mississippi...

#3 - Hodge Conjecture - I actually didn't pay all that much attention in the one topology class that I took. All that talk of doughnuts, it made me hungry. (They shouldn't teach those classes before lunch.)

#4 - P vs NP - My guiess is that computer technology will advance to the point that this can be brute forced, and the forcing of it will reveal enough to someone that finally gets it.

#5 - Navier - Stokes Equations

#6 - Yangs-Mills Theory

[Ken Jennings]

Wow, someone actually gave it a shot. Thanks John. Anybody else agree/disagree?

[metsfan001]

Is the rabbit topologically equivalent to the hydra? Semi-serious question here.

[TheConfessor]

As expected, Grigory Perelman declined the Fields Medal today. This means he will never win the Fields, because its rules stipulate that recipients must be under 40 years old, and Perelman turned 40 on June 13th of this year.

Actually, like thoroughbred horses, all mathematicians are considered to have been born on January 1st. So for the purposes of the Fields Award, recipients may be up to 40 years old when they get the award, but not not 41. Sounds like fertile ground for a class action lawsuit on behalf of mature mathematicans.

Original URL: http://www.theregister.co.uk/2006/08/23/maths_medal/

Reclusive Russian turns down Fields Medal
By Lucy Sherriff
Published Wednesday 23rd August 2006 10:01 GMT
A Russian mathematician has turned down one of the discipline's most prestigious awards because he doesn't want to involve himself in self promotion. He was due to have been presented with the Fields Medal by King Juan Carlos of Spain on Tuesday this week.

Grigory Perelman published an outline of a proof for the Poincare conjecture back in 2003 as part of his work on the Geometrisation Conjecture, proposed by American mathematician William Thurston in the 1970s. This seeks to characterise all three dimensional surfaces.

So far, other researchers working to check and flesh out his idea have not found any flaws. Perelman himself has not spoken publicly about his work, saying that before the checking is completed it would be premature to do so.

John Ball, retiring president of the International Mathematical Union, told the BBC that he had gone to visit the reclusive mathematician in St Petersburg to discuss his reasons for declining the award.

He said that he wouldn't disclose Perelman's statements beyond saying that Perelman said he felt isolated from the mathematical community, and therefore had no wish to appear to be one of its leaders.

"He has a different psychological makeup that makes him see life differently," he added.

The Poincare conjecture is one of seven Millennium Prize Problems listed by the Clay Mathematics Institute, with a million dollar bounty offered for a solution. It is considered to be one of the most important questions in topology - the study of the nature of geometric structures.

The Fields Medal is awarded to mathematicians under the age of 40 who are judged to have produced "an outstanding body of work". The three other winners this year were Andrei Okounkov of the University of California, Berkeley, Terence Tao from the University of California, Los Angeles, and Wendelin Werner of the University of Paris-Sud in Orsay, France.

Andrei Okounkov said "I suppose we will have to exhibit exemplary behaviour from now on, because a lot of people will be watching."

The conjecture (http://www.britannica.com/eb/article-69135) "asserts that a simply connected closed three-dimensional manifold is a three-dimensional sphere"*

Essentially, topology is concerned with the study of geometric shapes - whether a shape has holes in it, whether it is all connected, or can be separated into parts. Topologically speaking, there is no difference between a doughnut and a teacup, because one can deform into the other without being broken.

The Poincare conjecture just says that the same is true of a three dimensional sphere, and any other simply connected, closed three dimensional manifold.

As with many things in maths (c.f. Fermat, theorem, the last), the conjecture may be relatively easy to state, but the proof is rarely easy to find.

Bootnote
*"topology". Encyclopædia Britannica. 2006. Encyclopædia Britannica Premium Service. 23 Aug. 2006