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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

432.0. "Easy Road to Fame" by BEING::POSTPISCHIL () Mon Jan 20 1986 20:33

One thing I plan to do when I get a computer for home is to leave a background
process continually working on some problem.  On a multiprogramming system, it
would run at the lowest possible priority, otherwise it would save its state on
demand so that other work could be done.  Eventually, the hours of processor
time will add up to weeks, months, and years, and the program will solve the
problem and make me famous.

Does anybody know of any problems that would be suitable for this sort of
attack?


				-- edp
T.RTitleUserPersonal
Name
DateLines
432.1STAR::CALLASMon Jan 20 1986 21:203
Hunting for Mersenne primes is the canonical thing to do.

	Jon
432.2TURTLE::GILBERTMon Jan 20 1986 22:353
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.
432.3BEING::POSTPISCHILTue Jan 21 1986 12:067
Re .1:

I was thinking of something more final, such as a proof or a counterexample
to a theorem.


				-- edp
432.4JOEL::BERMANTue Jan 21 1986 13:026
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.

432.5PISA::BRETTTue Jan 21 1986 14:125
432.6LATOUR::APPELLOFTue Jan 21 1986 15:413
re .0
What? I thought you already were famous (in this file at least :-))

432.7AURORA::HALLYBTue Jan 21 1986 17:016
I tried this a while back and concluded the electrical power cost me about
$25-$30 per month.

Ahhh, the price of fame...

  John
432.8AJAX::CALLASWed Jan 22 1986 19:5311
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
432.9R2ME2::GILBERTThu Jan 23 1986 19:446
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.
432.10JOEL::BERMANFri Jan 24 1986 15:3212
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
                                           
432.11Fame and FortuneTAV02::ROSENMANDavid RosenmanSun Mar 09 1986 07:1610
    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
    
432.12Goldbach Conjecture?COMICS::DEMORGANRichard De Morgan, UK CSC/CSFri Nov 27 1987 13:252
    How about the Goldbach conjecture (os has somebody disproved it/proved
    it is unprovable when I wasn't looking?)
432.13:-)SQM::HALLYBProfitus InterruptusSat Nov 28 1987 00:054
>    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...
432.14re Paul ErdosHERON::BUCHANANMon Nov 30 1987 05:5518
    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
432.15Say anything about me -- just spell my name right!ZFC::DERAMODaniel V. D'EramoMon Nov 30 1987 15:2124
>>    >    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