[FOM] Proof assistants and conjectures
Vaughan Pratt
pratt at cs.stanford.edu
Thu Jan 8 01:50:11 EST 2009
Roger Bishop Jones wrote:
> There is a list of "The Hundred greatest theorems" at:
> http://personal.stevens.edu/~nkahl/Top100Theorems.html
Taking this list at face value (how come that remarkable and
fundamentally useful theorem, that every vector space is free, is bumped
in favor of the birthday problem, Cramer's rule, the Buffon needle
problem, etc?), and assigning half a dozen of the undated candidates at
least to centuries, leaving about 10 unassigned, the following table
bins the remaining 90 theorems by century.
BC
18th 1
5th 2
4th 1
3rd 10
AD
1st 1
2nd 1
14th 2
16th 3
17th 9
18th 17
19th 32
20th 11
Despite a growing population of research mathematicians, the 20th
century has barely stayed ahead of the 17th, and even more narrowly just
edged out the third century B.C.
The question then arises, how will our descendants a century hence view
the 20th century? Will they continue to assess the 19th century as the
peak of mathematical discovery, much like that century's great gold
rushes, or will the standards have changed by then to acknowledge a
great many contributions of the 20th century whose greatness we have
simply been unable to see at such close range?
It may be just a brand recognition issue. The apparent productivity of
19th century mathematics might have more to do with how the 20th century
has marketed the 19th than with which century has advanced the subject
further.
Vaughan Pratt
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