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From: Greg Kuperberg <greg_at_MATH.UCDAVIS.EDU>

Date: Thu, 7 Dec 2000 08:40:45 -0800

On Thu, Dec 07, 2000 at 02:04:02PM +0000, Stevan Harnad wrote:

*> > I already gave what I consider evidence, although I wouldn't
*

*> > expect it to sweep away deep skepticism.
*

*> I am afraid all you gave was anecdote and opinion.
*

The quantifiable evidence is that only a fraction of arXiv users, about

20% in math, ever add the journal reference to their own papers in the

arXiv. Generally speaking authors would prefer the journal reference to

be there, but the reason gives is usually "Oh, I haven't gotten around

to it." Evidently they have only a weak incentive to add this attribute

for the reader's benefit. If the journal title were such a crucial

stamp of quality it would be different.

This is consistent with my own perceived incentives as a research

mathematician. I do systematically add the journal references to the

arXiv, but that is because of my involvement in the project and my

librarian tendencies. I have never seen it as a pressing concern.

By contrast when I write a new paper I can't wait to send it to the

arXiv (so that everyone will see it) or submit it to a journal

(to get credit from my university).

*> But do you think other disciplines worry much less, a priori, about
*

*> a mistake or slip-up?
*

I won't speak for other disciplines, but I do see some difference between

a talk in pure math or string theory on the one hand and a talk in

computational math or experimental physics on the other. Experimental

papers are founded on data, while computational math talks are founded

on simulations. The audience is not usually in a position to question

the raw data; the most that a listener could do is find a mistake in

the interpretation.

But for most pure mathematics, all you have is the arguments presented

(or at least outlined) in the talk. If you are trying to convince other

experts of your results for the first time, that is really the moment

of truth. Even very good mathematicians have seen their new results

crumble to dust at that moment. If you're careful you can avoid outright

fallacy, but there is no conclusive way to determine whether your "hard"

theorem has a 3-line proof.

I can also say that mathematics, unlike some disciplines, does not

normally divide into factions that dismiss each others theories as wrong.

Very occassionally you see that in applied mathematics, but most people

see it as something that shouldn't happen and not as the status quo.

So if someone alleges a mistake in your work, you don't normally get any

protection from "your side". (On the other hand, there are factions

of mathematicians who allege that each other's work is unimportant.

But "unimportant" is very different from "wrong".)

There is a corresponding difference in anonymous refereeing in math

versus physics. In math many referees still systematically check the work

under review. Physics is much closer to the standard of simply judging

whether or not a paper is important, not whether or not it is correct.

As a result refereeing in mathematics takes longer than in physics.

A referee sitting on a paper for a full year is almost unheard of in

physics; in math it is quite common.

I suspect that for the same reason the "avenue of broken dreams",

ie. the withdrawn papers, is proportionately longer in the math arXiv

than in the physics arXiv.

Date: Thu, 7 Dec 2000 08:40:45 -0800

On Thu, Dec 07, 2000 at 02:04:02PM +0000, Stevan Harnad wrote:

The quantifiable evidence is that only a fraction of arXiv users, about

20% in math, ever add the journal reference to their own papers in the

arXiv. Generally speaking authors would prefer the journal reference to

be there, but the reason gives is usually "Oh, I haven't gotten around

to it." Evidently they have only a weak incentive to add this attribute

for the reader's benefit. If the journal title were such a crucial

stamp of quality it would be different.

This is consistent with my own perceived incentives as a research

mathematician. I do systematically add the journal references to the

arXiv, but that is because of my involvement in the project and my

librarian tendencies. I have never seen it as a pressing concern.

By contrast when I write a new paper I can't wait to send it to the

arXiv (so that everyone will see it) or submit it to a journal

(to get credit from my university).

I won't speak for other disciplines, but I do see some difference between

a talk in pure math or string theory on the one hand and a talk in

computational math or experimental physics on the other. Experimental

papers are founded on data, while computational math talks are founded

on simulations. The audience is not usually in a position to question

the raw data; the most that a listener could do is find a mistake in

the interpretation.

But for most pure mathematics, all you have is the arguments presented

(or at least outlined) in the talk. If you are trying to convince other

experts of your results for the first time, that is really the moment

of truth. Even very good mathematicians have seen their new results

crumble to dust at that moment. If you're careful you can avoid outright

fallacy, but there is no conclusive way to determine whether your "hard"

theorem has a 3-line proof.

I can also say that mathematics, unlike some disciplines, does not

normally divide into factions that dismiss each others theories as wrong.

Very occassionally you see that in applied mathematics, but most people

see it as something that shouldn't happen and not as the status quo.

So if someone alleges a mistake in your work, you don't normally get any

protection from "your side". (On the other hand, there are factions

of mathematicians who allege that each other's work is unimportant.

But "unimportant" is very different from "wrong".)

There is a corresponding difference in anonymous refereeing in math

versus physics. In math many referees still systematically check the work

under review. Physics is much closer to the standard of simply judging

whether or not a paper is important, not whether or not it is correct.

As a result refereeing in mathematics takes longer than in physics.

A referee sitting on a paper for a full year is almost unheard of in

physics; in math it is quite common.

I suspect that for the same reason the "avenue of broken dreams",

ie. the withdrawn papers, is proportionately longer in the math arXiv

than in the physics arXiv.

-- /\ Greg Kuperberg (UC Davis) / \ \ / Visit the Math ArXiv Front at http://front.math.ucdavis.edu/ \/ * All the math that's fit to e-print *Received on Mon Jan 24 2000 - 19:17:43 GMT

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