At its best, writings about advanced mathematics describe it as a mysterious, magical realm, tangentially linked to the world in which we live. Only a few strange, obsessive souls have the wherewithal to gain entrance to this realm, and even fewer return bearing with them a precious truth. Or purportive truth, because the vast majority of us -- and even a majority of trained mathematicians -- must take these claims of mathematical revelation on faith.If you look at it that way, Math outran ordinary cognitive capabilities 100s of years ago. Even people with doctoral degrees in the sciences rarely have any clue about 20th century mathematics. Mathematics advanced in the 20th century as much as Physics, Biology, and a lot of other subjects, but the public is unaware.
These thoughts are brought to mind by "Elusive Proof, Elusive Prover: A New Mathematical Mystery" an article by Dennis Overbye in the Science Times. ...
Several experts have amplified Perelman?s rather short, cryptic writings into 1,000 pages of detailed argumentation, which other mathematicians are trying to evaluate. Is the proof proven? No one can say for sure yet. We must await the verdict of the cognoscenti.
This episode bolsters my conviction that mathematics is outrunning the cognitive capacities of ordinary and even extraordinary humans.
It might seem like the newspaper is dependent on the verdict of the cognoscenti, but Math is more transparent and open than just about any other intellectual activity. Perelman did not need any special status or credentials to post his work; the public got it at the same time that the experts did; there is no proprietary experimental data that is being held back or anything like that; and no one has to take anyone's word for anything.
If you want to know whether the Koreans really cloned dogs or whether the latest antidepressant is really better than Prozac, you have to trust those who claimed to do the experiments. But no one has to trust Perelman for anything. His work stands for itself.