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" "Mathematics is not just a language. Mathematics is a language plus reasoning. It's like a language plus logic. Mathematics is a tool for reasoning. It's, in fact, a big collection of the results of some person's careful thought and reasoning. By mathematics, it is possible to connect one statement to another.
Richard Phillips Feynman (May 11, 1918 – February 15, 1988) was an American theoretical physicist. He is known for the work he did in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of the superfluidity of supercooled liquid helium, and in particle physics, for which he proposed the parton model. For his contributions to the development of quantum electrodynamics, Feynman received the Nobel Prize in Physics in 1965 jointly with Julian Schwinger and Shin'ichirō Tomonaga. Feynman developed a widely used pictorial representation scheme for the mathematical expressions describing the behavior of subatomic particles, which later became known as Feynman diagrams. During his lifetime, Feynman became one of the best-known scientists in the world.
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I returned to civilization shortly after that and went to Cornell to teach, and my first impression was a very strange one. I can't understand it any more, but I felt very strongly then. I sat in a restaurant in New York, for example, and I looked out at the buildings and I began to think, you know, about how much the radius of the Hiroshima bomb damage was and so forth... How far from here was 34th street?... All those buildings, all smashed — and so on. And I would go along and I would see people building a bridge, or they'd be making a new road, and I thought, they're crazy, they just don't understand, they don't understand. Why are they making new things? It's so useless.
But, fortunately, it's been useless for almost forty years now, hasn't it? So I've been wrong about it being useless making bridges and I'm glad those other people had the sense to go ahead.
[T]he Mayan[s]... had a scheme for predicting... when Venus was a morning... or . ...[T]hey had a rule for... making corrections and... had a very good way of predicting when Venus was coming up. ...Suppose that the professors (the priests in those days) ...were giving a lecture ...to explain ... these wonderful predictions ...He would say, "What we're doing is counting the days, just like you're putting nuts in a pod." ...[The students] did not know a quick and tricky way to add 365 x 8. ...These students were learning ...the laws of arithmetic. Something... to us now, because we have public, free, general education, almost everybody has to... learn... by a tricky scheme... The waitress, just an ordinary person, in two minutes does that. How..? ...She's ...counting ...415 pennies ...then ...287 more ...and telling you how many pennies you would have got if you counted ...beginning to the end. But it's highly educated and very trained to... do that... quickly. ...In the 14th century [it was] mathematicians... who could do that.
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The chance is high that the truth lies in the fashionable direction. But, on the off-chance that it is in another direction — a direction obvious from an unfashionable view of field theory — who will find it? Only someone who has sacrificed himself by teaching himself quantum electrodynamics from a peculiar and unfashionable point of view; one that he may have to invent for himself.