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From: Silvano Di Zenzo on 1 Jul 2008 07:07
We know that there are hundreds of people around who think they have solved
PvsNP. The history of math is full of similar situations: Open problems
attract the attention of many.

It seems that on this occasion, I mean PvsNP, there is enormous concern,
especially in blogs, regarding the number of naive papers.

Some have calculated the number of years that they would spend if they had
to read all the naive papers on PvsNP. Others dream of decalogues that would
allow automatic screening of bad papers by statistical recognition
techniques: Presence of certain adverbs in text, color of hair of author,
etc.

It seems to me that all this concern is out of place: A mathematician is
able to tell the papers that deserve to be read carefully (if there are any
of them) among hundreds of papers, in time of the order of minutes.

Regards,
Silvano Di Zenzo


From: Le Chaud Lapin on 5 Jul 2008 14:22
On Jul 1, 6:07 am, "Silvano Di Zenzo" <curbas...(a)tiscali.it> wrote:
> We know that there are hundreds of people around who think they have solved
> PvsNP. The history of math is full of similar situations: Open problems
> attract the attention of many.
>
> It seems that on this occasion, I mean PvsNP, there is enormous concern,
> especially in blogs, regarding the number of naive papers.
>
> Some have calculated the number of years that they would spend if they had
> to read all the naive papers on PvsNP. Others dream of decalogues that would
> allow automatic screening of bad papers by statistical recognition
> techniques: Presence of certain adverbs in text, color of hair of author,
> etc.
>
> It seems to me that all this concern is out of place: A mathematician is
> able to tell the papers that deserve to be read carefully (if there are any
> of them) among hundreds of papers, in time of the order of minutes.

This is a keen obversvation.

The Academy has created an insular institution that, while effective
in blocking out kooks and crackpots, does not tolerate the innjection
of original thought from disruptive sources. One of the many excuses
for subscribing to this pathology pertains to what you note:

"We do not have time to read papers written by those without
credibility."

Right.

It takes only a few seconds for a serious mathematician to determine
if a paper contains ideas worth further investigation.

A relevant contemporary example, Grigori Perelman's proof of
Poincaré's conjecture and subsequent declination of Fields Medal,
illustrates what I believe to be the truth: The Academy has created an
environment where incremental discovery and mutual back-scratching are
far more rewarded than revolutionary thinking. Anyone who threatens
this environment is severely punished. Though obviously, Perelman is
not without credibility, either within The Academy or without, the
same pathology is at play:

http://en.wikipedia.org/wiki/Grigori_Perelman

***As of the spring of 2003, Perelman no longer works at the Steklov
Institute.[4] His friends are said to have stated that he currently
finds mathematics a painful topic to discuss; some even say that he
has abandoned mathematics entirely.[13] According to a 2006 interview,
Perelman is currently jobless, living with his mother in Saint
Petersburg.[4]

Although Perelman says in a The New Yorker article that he is
disappointed with the ethical standards of the field of mathematics,
the article implies that Perelman refers particularly to Yau's efforts
to downplay his role in the proof and play up the work of Cao and Zhu.
Perelman has said that "I can’t say I’m outraged. Other people do
worse. Of course, there are many mathematicians who are more or less
honest. But almost all of them are conformists. They are more or less
honest, but they tolerate those who are not honest."[3] He has also
said that "It is not people who break ethical standards who are
regarded as aliens. It is people like me who are isolated."[3]

This, combined with the possibility of being awarded a Fields medal,
led him to quit professional mathematics. He has said that "As long as
I was not conspicuous, I had a choice. Either to make some ugly
thing" (a fuss about the mathematics community's lack of integrity)
"or, if I didn’t do this kind of thing, to be treated as a pet. Now,
when I become a very conspicuous person, I cannot stay a pet and say
nothing. That is why I had to quit.”[3]***

Conformists. Toleration of dishonesty. Alienation of the innocent.
Being treated like a pet.

There is a dynamic here that exists within The Academy that makes it
insurmountably difficult for one to have one's cake and eat it too,
which might be what Perelman wanted. The "treated like a pet"
reference becomes even more illuminating when one combines it with a
statement made of Perelman's proof by Terence Tao in the same
Wikipedia article:

"[Perelman's proof of the Poincare Conjecture] is a fantastic
achievement, the most deserving of all of us here in my opinion. Most
of the time in mathematics you look at something that's already been
done, take a problem and focus on that. But here, the sheer number of
breakthroughs...well it's amazing.. "

Amazing indeed, which is probably why Perelman decided to work alone.
He instinctively knew what would have happened if he had
"collaborated":

Pet-owners typically dislike sheer numbers of breakthroughs from their
pet, especially if the pet is able to generate such ideas in a closet
with very little assistance from the owner or other pet owners. If
such breakthroughs are made abruptly and simultaneously with no
forewarning, the contempt from peers is guaranteed. If they are made
outside The Academy, the contempt becomes widespread and
institutionalized. If they are made outside of The Academy, and the
"fig leaf" offered by members of The Academy (the Fields Medal) is
rejected by the renegade thinker, the contempt is immeasurable and the
wounds unforgivable.

Perelman said it best with regard to The Academy's recognition for his
work:

"He went on to say that the prize "was completely irrelevant for me.
Everybody understood that if the proof is correct then no other
recognition is needed."[3]".

I doubt that members of The Academy are particularly interested in
hearing these types of comments. They would much rather he just accept
the Damn Award, for the benefit of All. But Perelman made the right
choice, IMHO. If he indeed, had allowed himself to be adopted as
someone's pet, his work probably would have been rapaciously
misappropriated and diffused over a period of time so long, an area
so wide, that proper attribution of credit would have been a certain
uncertainty. All kinds of excuses would have been made by the pet
owners and peers of those pet owners about why the diffusion was
necessary:

"Well Grigori..."

1. "Publish or perish."
2. "You really need to maintain good relationships to be successful in
your work."
3. "You should acknowledge work of others."
4. "You should learn what has not been done so you do not make same
mistakes."
5. "You should let people see where you are so they can help you to
where you are going - you cannot get there yourself."
6. "The government needs proof that your work is not being funded in
vain."
7. "We have always done it This Way. It has proven to be the most
effective way to advance the art."

No mention will ever be made of the fact that, the more siginficant,
the more original, the more correct the ideas are, the more likely
that they will be misappropriated, and the more likely that the
misappropriation will be tolerated by those who observe the
misappropriation.

For the benefit of All.

-Le Chaud Lapin-
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