Highest level of math - Page 4

Ken G · #91 (**permalink**) 18-August-2006, 04:41 PM

That's amazing-- a proof that is assumed correct until shown to be otherwise, just because it is so long! Not a good development for mathematics, I should think. Hopefully someone will use it to inspire a much more elegant treatment. Still, mathematicians are just crazy enough to really work it all the way through and if there are no flaws found in two years, it's probably solid.

jlhredshift · #92 (**permalink**) 18-August-2006, 04:46 PM

Remember what happened to Andrew Wile!

tdvance · #93 (**permalink**) 18-August-2006, 04:50 PM

Quote:

Originally Posted by Bob

When is a proof a proof?
A Russian mathematician named Perelman recently solved a problem in topology called Poincare's conjecture which was over a hundred years old. The proof is very sophisticated and is published in a 473 page book, so reviewing it for correctness is not trivial. An organization called the Clay Institute will award Dr Perelman its lucrative millenium prize after the proof has been public for two years without successful challenge.

If they can find him, and if he accepts it. See this.

Todd

Bob · #94 (**permalink**) 18-August-2006, 05:54 PM

Quote:

Originally Posted by Ken G

That's amazing-- a proof that is assumed correct until shown to be otherwise, just because it is so long!

Actually this proof isn't too long. It has been peer reviewed and is considered correct.
There are proofs which are too long, though. The proof that the most efficient way of stacking spheres is in a pyramidal pattern runs to hundreds of pages and includes a complicated computer program. The proof of the 4 color map problem includes the results of a computer program which are too long to be reviewed in a human lifetime.

Ken G · #95 (**permalink**) 18-August-2006, 07:29 PM

It kinda makes me glad I'm not a mathematician...

snarkophilus · #96 (**permalink**) 18-August-2006, 09:35 PM

Quote:

Originally Posted by Bob

When is a proof a proof?
A Russian mathematician named Perelman recently solved a problem in topology called Poincare's conjecture which was over a hundred years old. The proof is very sophisticated and is published in a 473 page book, so reviewing it for correctness is not trivial. An organization called the Clay Institute will award Dr Perelman its lucrative millenium prize after the proof has been public for two years without successful challenge.

Rumour has it that Perelman is going to win the Fields medal this year....

Bob · #97 (**permalink**) 22-August-2006, 06:34 PM

Quote:

Originally Posted by tdvance

... if he accepts it.

Looks like he's turning it down.

http://www.cnn.com/2006/TECH/science....ap/index.html

publiusr · #98 (**permalink**) 25-August-2006, 07:18 PM

Tetaration and the extended cardinals allow for numbers to get really big really fast.

I love Rudy Ruckers book Infinity and the Mind.

It begs to be made into a documentary.

crosscountry · #99 (**permalink**) 25-August-2006, 07:52 PM

Quote:

Originally Posted by snarkophilus

You are right. I just assumed that high level and hard were equivalent, which is not necessarily the case. My point was simply to say that the branch with the most definitions is not necessarily the most advanced, which was claimed previously.

I've been thinking about it, and I'm not certain I entirely agree with that statement any more... I do in one sense, but don't in another. For reference:

Quote:

The most advanced stuff is the stuff we don't know much about, the largely untested areas, in which existing results could still be wrong.

But I'm curious as to why you disagree.

Sorry to have been away so long.

I disagree because it seems to me you are inputting your opinion while trying to state a fact. You and I hold different truths about what advanced it. I guess the definition of advanced lends itself to your idea of cutting edge. To me advancement is things we've already solved and accomplished.

Don't know if that answers your question.

crosscountry · #**100** (**permalink**) 25-August-2006, 07:54 PM

Quote:

Originally Posted by Ken G

It kinda makes me glad I'm not a mathematician...

me too. In my grad physics classes often the professor will say something like "this is where we leave it to the mathematicians. ask them for the proof" none of us ever do.

that usually happens when something interesting is happening and we don't want to get bogged down with 200 years of math to exclude other solutions.

snarkophilus · #**101** (**permalink**) 25-August-2006, 10:15 PM

Quote:

Originally Posted by crosscountry

I disagree because it seems to me you are inputting your opinion while trying to state a fact. You and I hold different truths about what advanced it. I guess the definition of advanced lends itself to your idea of cutting edge. To me advancement is things we've already solved and accomplished.

Oh, I see! No, clearly this thread is about opinions only... there's no way to actually measure what might be harder (except perhaps in a statistical sense, which still doesn't tell us a lot). However, (I think that) what I said is probably true for the majority of people.

I should have posted a sign: FACT-FREE ZONE.

crosscountry · #**102** (**permalink**) 26-August-2006, 05:44 AM

I guess you're right 8D

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