Controversy Over 140-Year-Old Math Problem

sciencehabit writes "British mathematician Darren Crowdy has been bragging all week about how he solved a 140-year-old math problem, as we discussed a few days ago. But three American mathematicians say they had the critical idea first."

American team didn't publish...

[ELProphet]

This anecdote is attributed to Landau (the Russian physicist Lev not the Göttingen mathematician Edmund).

Landau's group was discussing a bright new theory, and one of junior colleagues of Landau bragged that he had independently discovered the theory a couple of years ago, but did not bother to publish his finding.

"I would not repeat this claim if I were you," Landau replied: "There is nothing wrong if one has not found a solution to a particular problem. However, if one has found it but does not publish it, he shows a poor judgment and inability to understand what important is in modern physics".

Actually, from TFA, the American team did publish first, but "didn't realize the relevance of the Schottky groups." Further, the Brit (working independently, and supposedly without knowledge of this obscure paper) says his formula will work every time. The Americans are of course sceptical, but can't seem to find any situation where it won't work. Kudos to both, but it seems history will go to the Brit for this. I'll check Wiki in about a year; I'll bet it talks about the Brit, and mentions the American team in passing.

Re:Its not the thought that counts

[Anonymous Coward]

I always thought it mattered who published first, not thought of it.

Yes, in Mathematics, moreso, even.
The first one to publish a full proof is the one that gets credited with 'solving' the problem. Just coming up with the strategy doesn't mean much, because there's no way of knowing that the strategy will work until you actually carry it out. And doing so is not a trivial thing, either. (or they would've done it immediately)

To take a recent, high-profile example, the Poincaré conjecture was solved by Grigori Perelman. But the strategy he used (of using the Ricci flow) had been suggested years earlier by Richard Hamilton.

At the very least some credit

[Woundweavr]

But mathematicians John Pfaltzgraff of the University of North Carolina, Chapel Hill, and Thomas DeLillo and Alan Elcrat, both of Wichita State University in Kansas, say they had the basic strategy--and a formula--first. Crowdy heard Elcrat talk about that work in 2003, but he says the American trio didn't realize the relevance of the Schottky groups. The Americans' formula, published in 2004, involves the multiplication of an infinite number of terms, which goes haywire if the holes are too close together. Crowdy's formula replaces that product with an obscure beast known as Schottky-Klein prime function. Crowdy says his formula will never fail. "I'm very skeptical" of that claim, says Pfaltzgraff.

Has Crowdy proven that his technique will never fail? The original article claimed that Crowdy overcame the obstacle of holes in the polygon... but at best it seems he overcame having holes too close together. In reality you have four iterations:

Crowdy over came holes that are "too close" together.
The three Americans deserve credit for overcoming the multiple hole obstacle.
The mathematicians in the 1920s overcame a single hole problem
The original mathematicians deserve credit for the formula in general.

The only way, IMO, that Crowdy deserves an equal amount of credit to the Americans is if his formula is actually universal. The additional functionality seems much smaller than that contributed by the three Americans.

Re:History Repeats

[Asmor]

This actually seems to be a recurring pattern... There have been many instances where an idea was discovered by multiple mathematicians in a relatively short time frame, and only one gets the credit... Usually not the first, either.

I'm too lazy to do the research, but off the top of my head I think that Galois and Euler were both beaten to the punch in certain theorems by contemporaries, but ultimately they (Galois & Euler) got the credit.