| T.R | Title | User | Personal
Name | Date | Lines |
|---|
| 432.1 | | STAR::CALLAS | | Mon Jan 20 1986 18:20 | 3 |
| Hunting for Mersenne primes is the canonical thing to do.
Jon
|
| 432.2 | | TURTLE::GILBERT | | Mon Jan 20 1986 19:35 | 3 |
| If it's a problem that'd really make you famous, then it's likely that
others have already thrown considerable CPU power and/or brains at the
problem. However, there are still many unsolved, interesting problems.
|
| 432.3 | | BEING::POSTPISCHIL | | Tue Jan 21 1986 09:06 | 7 |
| Re .1:
I was thinking of something more final, such as a proof or a counterexample
to a theorem.
-- edp
|
| 432.4 | | JOEL::BERMAN | | Tue Jan 21 1986 10:02 | 6 |
| Just start trying to execute every possible permutation of bits. Before the
clock strikes infinity you will have written programs to prove or disprove
everything.
/joel
Let me have a copy of the Fermat and the Riemann proofs. Thanks.
|
| 432.5 | | PISA::BRETT | | Tue Jan 21 1986 11:12 | 5 |
| re .4:
Sorry, G�del's Theorem says you won't have.
/Bevin
|
| 432.6 | | LATOUR::APPELLOF | | Tue Jan 21 1986 12:41 | 3 |
| re .0
What? I thought you already were famous (in this file at least :-))
|
| 432.7 | | AURORA::HALLYB | | Tue Jan 21 1986 14:01 | 6 |
| I tried this a while back and concluded the electrical power cost me about
$25-$30 per month.
Ahhh, the price of fame...
John
|
| 432.8 | | AJAX::CALLAS | | Wed Jan 22 1986 16:53 | 11 |
| re .4:
I like the idea of executing every possible permutation of bits. As a matter
of fact, it's guarenteed to make you famous. This will work because, after
an infinite amount of time, you will either (1) have proved a theorem worth
making you famous or (2) you won't. If (2), then the fact that you spent
an infinite amount of CPU time without proving anything good is an extremely
useful piece of information for computability theorists, and bound to make
you famous.
Jon
|
| 432.9 | | R2ME2::GILBERT | | Thu Jan 23 1986 16:44 | 6 |
| Thus, by stating your intentions, you should now be "famous" as
"the person who will be famous, regardless".
Here's a curio:
This sentence will be a self-fulfilling prophecy.
|
| 432.10 | | JOEL::BERMAN | | Fri Jan 24 1986 12:32 | 12 |
| re .5
I stand sort of corrected. I won't have proven/disproven things that can't
be proven/disproven within that system; but I would have one heck of a printout
to play with.
Actually I think .0 should spend his time on intuitive, short, proofs.
How many people know what the second major proof to be discovered by
a computer was? What was the computer? Who was the programmer?. A five color
map to the winner? I don't know the answer.
/joel
|
| 432.11 | Fame and Fortune | TAV02::ROSENMAN | David Rosenman | Sun Mar 09 1986 04:16 | 10 |
| Why settle for fame alone when you could have both fame and fortune?
I heard a lecture by a Hungarian number theorist a member of his
country's Academy of Sciences whose name spelled phonetically was
Erdosh. I won't attemt the Hungarian spelling. Anyhow he has
outstanding a series of Conjectures for which he pays around $500
to anyone able to prove the truth or falsity of the conjecture.
I you can obtain a list of them and in that list is one that leads
to a computer solution you are in business.
-David
|
| 432.12 | Goldbach Conjecture? | COMICS::DEMORGAN | Richard De Morgan, UK CSC/CS | Fri Nov 27 1987 10:25 | 2 |
| How about the Goldbach conjecture (os has somebody disproved it/proved
it is unprovable when I wasn't looking?)
|
| 432.13 | :-) | SQM::HALLYB | Profitus Interruptus | Fri Nov 27 1987 21:05 | 4 |
| > How about the Goldbach conjecture (os has somebody disproved it/proved
> it is unprovable when I wasn't looking?)
It comes out as a corollary to one of D'Eramo's earlier notes...
|
| 432.14 | re Paul Erdos | HERON::BUCHANAN | | Mon Nov 30 1987 02:55 | 18 |
| re .11
Erdos' little joke about one of the problems for which he offers
a reward is that it contravenes Minimum Wage Legislation.
I don't know where to get Erdos' shopping list. One might try
the man himself, but he is a nomadic people (sic), so may be hard
to track down.
The problems that I heard, for which $$$ were being offered by Erdos, were
in the area of probabilistic graph theory, a field which he pretty
well invented. This involves looking at the asymptotic behaviour
of families of graphs as the number of vertices becomes infinite.
I can't think immediately how to use a computer as a practical tool
here.
Regards,
Andrew Buchanan
|
| 432.15 | Say anything about me -- just spell my name right! | ZFC::DERAMO | Daniel V. D'Eramo | Mon Nov 30 1987 12:21 | 24 |
| >> > How about the Goldbach conjecture (or has somebody disproved
>> > it/proved it is unprovable when I wasn't looking?)
>> It comes out as a corollary to one of D'Eramo's earlier notes...
I heard that!
Think about what it would mean to prove that something like
Goldbach's Conjecture [GC] or Fermat's Last Theorem [FLT] or
one of their negations is "unprovable" from a given set of axioms.
If Goldbach's conjecture is false, then there is an even number
larger than four that is not the sum of two odd primes. Using
that counterexample it is easy to construct a proof of not-GC.
Similarly, an actual counterexample to FLT can be used to construct
a proof of not-FLT. If one can show by some means that the
negation of GC is unprovable from the usual first order axioms
of arithmetic, then GC must in fact be true in the "standard model".
If GC is unprovable, then it is not true in all models but it can
still be true in the standard model. [Nonstandard models of
arithmetic contain "infinite integers" that are greater than
each of the standard integers 0, 1, 2, 3, ... An infinite
counterexample would not imply the existence of a finite one.]
Dan
|