FOM: Fields Medal process

[Harvey Friedman]

This is a reply to Hersh 12:46PM 9/14/98:

There is a real danger that this particular discussion can get too far away
from f.o.m., and I will continue to try to explicitly relate it to f.o.m.

>Norbert Wiener resigned from the National Academy of Science.
>He regretted having accepted membership in the first place.
>
>Of course election to the NAS is by secret ballot, but Wiener's
>main issue was not secrecy, but the very existence of competitive
>honors and awards.  He believed that competition and disappointment
>in not receiving such awards was harmful to the work of young
>scientists, and receiving them late in one's career could
>make one complacent about no longer being creative or productive.

I think there is some truth to Wiener's issue, but it is also somewhat
balanced by the positive effects of such honors and awards *if those honors
and awards are implemented in an appropriate way.* Details follow.

>I think most mathematicians like the Fields Prize.

In the past, I almost never heard anything negative about the Fields Prize
from mathematicians (outside logic). Nowadays, I continually hear
complaints. One difference that may be relevant is that in the past, a
large number of the medalists were very well known long before they got the
medal, whereas that is not as true anymore - sources say. Let me move on to
a more interesting point.

>It tells us
>what the leaders of our profession consider important and promising.

This is the **crucial point** about the Fields Medal for me. It definitely
has this enormous influence. The committee is made up human beings, who
inevitably carry their own biases and ignorance like everyone else.
Furthermore, their high status in the profession inevitably leads to
reinforcement of these biases and ignorance. Since, as you say, the process
"tells us what the leaders of our profession consider important and
promising," these biases and ignorance then get reinforced throughout the
profession - especially since mathematicians still by and large (as you
say) like the Fields Prize.

I am now going to propose a different kind of process. Before doing so, let
me focus on the problem that a subject like f.o.m. or mathematical logic
has in the current process. I'm sure that other subjects have similar
difficulties.

First of all, I think it is somewhat clear that the typical person on the
Fields Committee probably is unfamiliar with even propositional calculus.
However, they probably think they are competent to judge high level work in
logic and f.o.m. in comparison to high level work in core mathematics -
partly because they are commissioned to do so, and have agreed to do so.
Yet the subtleties involved in doing so are of quite a different nature
than the subtleties involved in judging the relative merits of high level
work in core mathematics.

Even if there were to be some Committee member who had some knowledge of
logic that included propositional calculus, that does not make up for the
rest of the Committee who doesn't. And knowing something about the
propositional calculus is really not near enough to be able to judge work
in logic and f.o.m. at the highest level.

And even explicitly picking a senior logician to be on this Committee would
not really help.

So here is my solution to this problem. The process should be opened up
entirely as follows.

1. Nominations are solicited worldwide. Even self nominations are encouraged.
2. All nominations, including self nominations, are maintained on a website.
3. Nominators are especially encouraged to talk about the importance of
their field generally, as an educational component of the process.
4. Attacks and defenses of these nominations and their supporting
statements are solicited worldwide.
5. Questions are solicited worldwide for the nominators and those making
attacks and defenses.
6. The whole process is maintained electronically on a website, with the
help of a moderator in order to control matters if they get out of control.
7. The material is archived, so that it is available for the next round of
awards.
8. Finally, a committee has to examine this material, discuss the issues,
and determine the Medalists.
9. All deliberations of the committee are videorecorded and are made
available to the public - perhaps in real time on the web. Feedback is
solicited worldwide both in real time and between committee meetings.
10. The Committee writes a report with its decision and this report is also
made available to the public.

Note that a lot is to be gained by this process from the point of view of
logic and f.o.m. (and, I am sure, some other fields). For the archive
created will contain lots of documents pertaining to the importance of
logic and f.o.m. And this will be available worldwide, with worldwide
feedback.

I don't think core mathematicians are incapable of understanding, say, the
propositional calculus and its reason for being. It just doesn't fit in too
well with what they normally like to think about, and logic and f.o.m. (and
the importance thereof) has to be carefully explained **interactively** in
order to be noticed. The process I outlined above will facilitate this. If
not the first round or two, then in later rounds. For then, there will be
an *acumulation of material* that is accessible. I.e., the logic/f.o.m.
people will, by trial and error and reflection, figure out how to explain
this stuff to the very sophisticated people involved in deciding the Fields
Medals.

There is another advantage to this process. The "almost" Fields Medalists
also have their work thoroughly examined and disseminated worldwide.

>But does it harm those who hope to get it and don't?

It is likely (not certain) that anyone close to deserving it will have
their work closely examined by lots of people worldwide, under this
process. Even just one fairly prominent supporter can create a lot of
thought provoking and forceful material on their behalf.

>Does it
>foster  a self-perpetuating elite?

Much less so in this open procedure. Complaints can be more focused, with
ready access to such an amount of relevant material. It would be much
easier to challenge a self-perpetuating elite.

>Does it do harm to fields
>like logic which are not included in what the leaders consider "hot"?

The harm to logic/f.o.m. would all but disappear if people in logic/f.o.m.
actively and forcefully participate in the process, working hard to
creatively and interactively explain the material and its importance.

>In cold war years, and even since then, there have been charges
>of bias for or against certain nationalities.
>Would open ballotting worsen such nationalistic pressures?
>Would it pressure judges to vote for friends whom
> they would not have chosen in secret?

Can be more easily exposed under this process.

>Are there examples of great mathematicians who failed to get
>Fields prizes because of personal or political or national
>differences, or because their work was underrated by the judges?

Without even considering anything about it except the current process, the
answer must be yes.

>Prizes, awards and so on are so prevalent in our society and
>in our scientific and academic life, there is no chance thatmathematicians
>will  give them up.  Maybe open voting would be more harmful
>than secret ballots.

I agree with the first sentence. Let's make the most of it, educationally
and interactively, so that it becomes a positive experience for all of us.