[whitewhim]

When you are an expert in an academic field, you typically have spent many, many years reading about the problems in the field and the main ways to attack them. The same authors, will typically pop up again and again. Through conferences and collaborations one gets to know the main contributors in the field. On top of this, it is very rare for someone to break into a field with a major discovery. Normally people tend to hone their skills on more minor problems over time and obtain a deep understanding of the material. To top all of this off, academics quite regularly receive emails from crackpots claiming to have found a solution to p=np, etc.

I am not saying that Dr. Granville was right to immediately dismiss the concept of an unknown solving such a problem. I am just trying to provide some background for why he may of reacted as he did.

[graycat]

The problem was challenging. The solution was exceptional. So, maybe something about the person who solved the problem might be exceptional, that is, might fail to fit some common patterns?

Or, in this case, we can't call the success luck. So, for considering what is likely to be the situation or characteristics of the person with such an exceptional success, where are we to look? Are we to look at the dozens of people we do know or the thousands of other people, all of whom tried but failed to have such exceptional success?

So, we didn't see him at an AMS conference; he's not a full professor at a top university; he doesn't have a wife, 2.5 children, a 3 bedroom, two bath house, and two late model cars; ...? So?

If we hear a claim of some astounding accomplishment, then maybe (A) the accomplishment is nonsense and the person is exceptional because they are a crackpot or (B) the accomplishment is terrific and the person is exceptional because they were very successful. So, with either (A) or (B) we stand to see things exceptional that don't fit common patterns.

Net, if really want to look for the very best accomplishments, then we shouldn't reject people who look exceptional, that is, don't fit some patterns we learned from people who haven't had some terrific accomplishments.

And, in this thinking, we have to notice, in business there can be essentially some very good luck but not in pure mathematics complete with theorems and proofs that can be checked with high reliability. That is, in business, people who are not very exceptional and do fit common patterns can still be very successful because of essentially luck; so, in business can find people who fit nearly any common pattern and also are exceptionally successful just because of luck; can't do that in pure math there luck doesn't work!

[fspeech]

Hmm there is a difference between a unknown and a crank. Zhang was a trained Ph.D. mathematician with an academic lecturing position. Now I didn't even finish my Ph.D. in physics but I know enough about how to do research to not submit a proof that is not rigorous enough to warrant peer review. One should not refuse to peer review a unknown researcher with the right credentials/trainings who make serious arguments in line with academic practices.

Same as you this is not a comment on Dr. Granville. I wrote in response to your comment on how the field is typically cloistered among a few insiders. I don't think that justifies refusing to review an unknown (as in not famous) researcher who demonstrates training and seriousness (which fortunately they didn't in Zhang's case but Zhang also was extra careful in making his ideas crystal clear). This happens too rarely for the insiders to claim undue burden. Cranks are very obvious to identify (a lack of literature review and understanding of previous works is a tell-tale sign).

[seanmcdirmid]

Cranks and unknowns often look alike. Heck, researcher who diverge just a bit from accepted doctrines often look like cranks until either they repent or their approach bears obvious fruits.

[angdis]

Hmmm, that is plausible, but I can't think of any modern example where some deviation has resulted in a qualified researcher being categorized as a crank-- ignored maybe, or perhaps dismissed but definitely not called a "crank". Actual cranks are very very easy to spot and people won't bother wasting effort addressing them.

[seanmcdirmid]

I'm not sure. Crank is often used as an ad hominem in science, so it is difficult to tell mudslinging from real crankiness, it depends on the sincerity of the one applying the label, and also on the severity of the crankiness. And many people have trouble with groking more benign eccentricity.