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.
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!
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).
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.
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.
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.
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.