Vivek just gave me a documentary film on the history of mathematics. The whole history of mathematics can be said to be the whole problem of the human mind. For two thousand years or more in the West and for five to ten thousand years in the East, mathematicians have been trying to find the ultimate science.
One thing is certain in their eyes, that only mathematics can become the ultimate science, for the simple reason that there are no mathematical things around you. It is a pure science. You don’t see mathematical objects: this is a mathematical chair and that is a mathematical house.
Mathematics is just a pure ideological game. It consists not of things but ideas. And because ideas are properties of your mind, you can refine them to their ultimate purity. So it has been an accepted thing that mathematics can become the purest science possible. But there have been problems. Those mathematicians were not aware that your mind itself is the problem, and the mind is going to create a science which will have no problems, no contradictions, no paradoxes.
You can play the game. You can make a great edifice but whenever you look at the base, you will know that at the very base the ultimate problem remains unsolved. For example, Euclid’s geometry…. I could not go much into it for the simple reason that I could not agree with the basic hypotheses.
My teacher of geometry simply told me, “Your problem has nothing to do with me. Find Euclid – get out of the class. Find Euclid and settle things with him. I am a poor teacher, I just get my salary; I have nothing to do with his fundamental axioms. Whatever is written in the book, I teach. I am not interested at all whether his fundamental hypotheses are right or wrong. You get out.
He wouldn’t allow me in the class. I said, “But how can you go on teaching year after year knowing that the basic points are absurd?”
He said, “I never knew; it is you who is hammering on my mind that they are absurd. I have never bothered; I am not a scientist nor a mathematician, just a poor teacher. And I never wanted to be a teacher, I wanted to be an inspector, but they didn’t choose me. I tried to be an inspector, but they didn’t choose me. I tried other jobs; everywhere no vacancy. It is just out of compulsion that I am a teacher here.
“Don’t torture me. Your problem is with Euclid – don’t bring me in. If you want to read what is written in the book, I am ready. But if you tell me that the fundamentals are wrong….”
I said, “I cannot go on unless I am certain about the base, because this is dangerous: the foundation of the house is missing and you tell me to go on up in a skyscraper. I cannot move a single inch. First I have to be certain about the foundation, whether the foundation is there which can support this skyscraper. You are going to fall – that is your business – but I am not going to fall with you. If you want to commit suicide, do it.”
He said, “This is strange! With Euclid, nobody commits suicide. What are you talking about?”