On 4/29/2012 12:36 PM, Veit Elser wrote:
Isn't this obsession -- with looking for relationships where there almost certainly aren't any -- a waste of time?
Only Adam Goucher took up my challenge of discovering a relationship that was actually meaningful.
How are the transient approximate relationships between the orbits of random inconsequential chunks of space rock more meaningful than a permanent approximate relation between fundamental constants? But seriously, as far as wasting time goes, here's is a summary of my contributions to mathematics: - I worked on the OEIS. - I did a little work on Eric Weisstein's Treasure Trove of Mathematics. - I found a relationship between the Collatz conjecture and regular expressions. Jeff Shallit wrote a paper for me, "The 3x+1 Problem and Finite Automata", which gave me Erdos number 2. The proof in the paper is elementary to anyone versed in the subject, I think it ended up as a textbook problem. - I asked a question about prime divisors that sent John Conway and some associates to the blackboard for a few minutes. The result was the discovery of "Twin Peaks" (which see on MathWorld). - I found density waves in the Ulam sequence. Don Knuth actually contacted me about this. - John Conway was looking for a name for a polyhedron with holes in all its faces, and I came up with "holyhedron." This got me a mention in Pickover's "The Math Book", but it took true geniuses to actually construct one of these things. - I found the fifth taxicab number, which had in fact been published 3 years earlier. - I may have salvaged pi^4 + pi^5 ~= e^6 from the USENET dustbin. Doubtless it would have been rediscovered. - I made up an arguably clever graph for deciding if a number is divisible by 7, which is on Tanya's site. All in all, I think I've overachieved, but in all honesty, my greatest achievements barely rise above the level of a waste of time. Twenty minutes after I'm gone, I'll be about as noteworthy as any Sumerian bean farmer. So I don't worry much about wasting my time, given my talents, that's pretty much a foregone conclusion.