Math Homework Help
Around the year 2000, when the Clay Foundation prizes for the solutions to each of the seven selected famous problems became known, I met my old friend Arthur Jaffe, who was then president of the foundation, and asked him, "Why is all this being done? Because this (the promise of million-dollar prizes) is showbiz style, this vulgarization of scientific life.
Really, I thought, is it not clear that the very "monetization" of the solution of scientific problems, rather than scientific interest, will not add enthusiasm to a mathematician who already deals with the Riemann hypothesis or the Poincaré problem, and will not attract some serious mathematician to one of these problems, if he has never dealt with them and is not a specialist in these fields?
To this, Arthur replied forcefully and knowingly, "You don't understand anything about American life. If an official, a businessman, a housewife sees that you can make a million by doing math seriously, they will not prevent their children, if they want to go into math, from going into medicine, law, and other "money" professions. Yes, and other rich people will be more willing to donate to mathematics the money we lack. At the time, this answer partly convinced me. Since then, however, I have had no better understanding of American life, and my understanding of Russian life has become much worse.
And now one of the seven problems, the Poincaré problem, has been solved. Let's return to the same question: was the idea of millions useful for mathematics? I will say in advance that I did go back to my original opinion.
First of all, I think that the number of people involved in the Poincaré problem, and probably the other seven problems, has hardly changed since the announcement of the prizes. The one who solved it, G.Y. Perelman, was doing it even before that. The Clay Foundation had nothing to do with it. And other mathematicians who are still claiming to solve it, of whom I have heard, probably did it before, too. And it is ridiculous to think that any non-specialist (even mathematicians), having heard about the award, and having therefore decided to tackle the problem, has any chance of solving a problem of this level. If so, the acceleration of progress in mathematics from financial incentives has not happened.
But, of course, the very solution of the problem and the method of solving it is a giant success, but this again is irrelevant to our question. As for the greater interest of the general public in mathematics, there does seem to have been "progress. Not a single newspaper or television company has avoided sensational news. From August 20, when the first article appeared in The New York Times (Polit.ru - August 25, 2006 and August 27, 2006) and The New Yorker until early September, passions have not subsided.
How many journalists have turned to our institute, to mathematicians they know and those they do not know, with requests for interviews, inquiring about what this problem is, what it will mean for their everyday life! Now, at least the name of A. Poincaré and, of course, the name of G.Y. Perelman became known to everyone, and people interested in science could learn at least something about the problem itself. That's true, and that would have been good. But, still, what are people most interested in? What questions most often resonate in this polyphony?
And can all this hype really increase the public interest in mathematics and get young people into mathematics, as the organizers of the prizes had planned? I am not so sure. One has to realize that those who have been in love with science since their youth do not need additional injections. And those who looks at the choice of profession and life paths in the first place on what opportunities open for a normal life, important, of course, is not an incentive in the form of a million for an inaccessible task, but something else entirely.
Let's look at the apparently unintended consequences of this venture.