MathPhys

Paul Erdős, a great Hungarian mathematician of the 20th century was famous of proposing cash prizes for his math problems. He never owned anything (everything he had could be put into a small suitcase). He thought possession is evil. He gave away his money to poor students and for his cash prizes pay-out. There were only two things he was addicted to: math and meth (with prescription, after his wife passed he suffered from depression). Worried about his addiction to meth, Ron Graham, Erdős’ colleague and boss at AT&T Bell Lab, offered him \$500 if Erdős can stop taking meth for a month. Erdős accepted the offer and he actually managed to stop taking meth for a month. After getting \$500 from Graham, he started taking meth again. Erdős reportedly said something like this: “I couldn’t do math during that time. Every time I looked at a piece of paper, nothing came out of it.”

There is another mathematician who proposed cash prizes for his math problems. His name is Michel Talagrand. He is a well known French mathematician in probability. His rule is funny. Only the first person who solves gets the prize. You don’t have to be the one who solved the problem to claim the prize. You can still receive the prize if you purchased solution, but at half the prize money. Also he asks to submit solutions before he becomes senile because he won’t pay if he can’t understand solution :). The largest prize is \$5000 one. Unfortunately, someone (actually two people) solved it and they together received the money. There are three more problems left. Each has \$1000 prize.

Mathematicians don’t tackle difficult problems for money or fame. But some cash prizes can surely add a little more fun and excitement. Although not a cash prize, Arthur Besse, a pseudonym for a group of French differential geometers, offers a nice meal at a Michelin-starred restaurant in exchange for a new example of compact Ricci-flat manifolds (they are very difficult to find).

I like “real and good” mathematicians. (Regrettably, I am not one of them. I am not a real mathematician because I am not working on serious mathematics problems. Of course, if one is not a real mathematician, he can’t be a good mathematician.) They are not just smart but humble (No offense but you can hardly find someone among “real and good” mathematicians like those arrogant a$$holes, who act like they know everything, among hep-th people. Make no mistake, there are also so many hep-th people whom I respect and admire greatly.), humorous, have interesting personal characters, and certainly know how to have fun.

Are you up for going after math bounties? Go at them!

Let me begin with the following declaration: “Not anyone can do mathematics” or “Mathematics is not for everybody.” Who should be doing mathematics then? Some people might say smart people. Being smart is certainly helpful to do mathematics. Someone being smart is a necessary condition to be a mathematician but not a sufficient condition. In other words, being smart does not necessarily mean that one can be a mathematician. As seen from math’s many difficult problems that have haunted the smartest mathematicians, one can’t be too smart in the world of mathematics. The awe-striking depth and difficulty of mathematics make any smart person who studies it humble. But then such depth and difficulty are also the reasons that make mathematics so attractive to people who love doing mathematics. Yes, to love doing mathematics is the first and the foremost qualification to be a mathematician. You may not be so smart but you can still be a mathematician as long as you love doing mathematics. You may be slower than some of others but you can eventually encounter a glimpse of the true beauty of Mother Nature if you are patient and persistent. Being a mathematician is comparable to being an artist. Being a mathematician means that you are just fascinated with the beauty of Mother Nature, even a glimpse of it, and you have insatiable desire to quest after the hidden beautiful structures of Mother Nature.

If you wonder what mathematics is useful for, what the purpose of doing mathematics is, or why one must do mathematics, while they are quite legitimate questions by laypeople, you are already disqualified to be a mathematician. Mathematics is really for people who love doing it not because it is useful but because it is beautiful.

The other day I was reading a blog article by Andrei Martyanov and he said in there: “One cannot fight physics and math, it’s impossible.” The article was not about math or physics and he is neither a mathematician nor a physicist, but what he said rings so true to me. I think it should be a guiding principle for mathematicians and physicists. I would add one more to that though: Occam’s razor. When stumble upon a seemingly improbable or inexplicable phenomenon, even some serious scientists often accept a possibility of answers, such as God, outside the realm of science. Pythagoras did it with the existence of irrational numbers. While examining his famous so-called Pythagoras theorem regarding right triangles, he evidently discovered the number $\sqrt{2}$ which is the hypotenuse of the right triangle with both the lengths of base and height equal to 1. (At that time Greeks believed that there are only rational numbers because they are beautiful as rightful creation of God.) After failing many attempts to write the weird (no not really) number as a rational number, Pythagoras finally has given it up and told his pupils that God made a mistake and ordered them not to reveal this to anyone outside of his school. (Anyone who disobey this would’ve been killed.) It turns out God (metaphorically speaking) created way more irrational numbers than rational numbers. Apparently, the notion of beauty for God was different from that for Greeks. Newton did it also with precession of the perihelion of Mercury. When Newton realized that the precession of Mercury’s orbit could not be explained by his law of universal gravitation, he concluded that it is God’s domain. But he was wrong. It had nothing to do with God. Humanity just had to wait until another theory of Gravitation, Einstein’s general theory of relativity came along, which finally could nicely explain the precession of Mercury’s orbit. If Nature obeys the laws of mathematics and physics, so should any phenomenon that occurs in it. In the Chinese TV series Three-Body (adapted from the novel The Three-Body Problem by Liu Cixin), some of the elite theoretical physicists committed suicides because they were in despair over the thought that physics doesn’t exist anymore after stumbling upon improbable/inexplicable phenomena that defy the laws of physics. Those phenomena, however, turned out to have been created by a highly advanced alien civilization to dismantle Earth’s scientific community because it could pause a threat to their plan of invading Earth. (Sorry for the spoiler.) Under the pretense of this having happened in real life, if those unfortunate theoretical physicists were to stick to the guiding principle that one cannot fight physics and math, they would’ve been still alive.