Response to Jaffe and Quinn
of Mathematics and Theoretical Physics’, by A. Jaffe and F. Quinn”
Bulletin of the American Mathematical Society 30 (1994) 178–207
The paper distorts the relation of experiment to theoretical physics. To paraphrase Fermi (perhaps badly): an experiment which finds the unexpected is a discovery; an experiment which finds the expected is a measurement.
I have the impression that applying rigor to a theoretical idea is given substantial credit when it disconfirms the theoretical idea or when the proof is especially difficult or when the ideas of the proof are original, interesting and fruitful. This seems quite enough to motivate the application of rigor, for those who are motivated by the prospect of credit. Perhaps pedestrian proofs do get only a little recognition, but should they really get more? Is it useful to formulate explicit general rules for assigning credit in mathematics?
Is there really any evidence that mathematics is suffering from the theoretical influence? Are mathematicians really finding it difficult to read theoretical papers critically, detecting for themselves the level of rigor? Are rigorous-minded graduate students so awash in problems that they truly resent the offerings of the so-called theoretical mathematicians?
As far as I know, there has never been a surplus of originality in mathematics or in physics. Is it useful to criticize the manner of expression of original ideas on the grounds that the community is slow to absorb, evaluate and/or pursue them?