Mathematical Development

Question

I have two questions regarding the development of mathematics:

1) Is there an example where in mathematics, a collaboration has led to the discovery of another result? I already know something like the Polymath project, or the Hilbert program and the Hamilton's program.

2) Is there an example of how individual secrecy and lone effort in mathematics has led to a breakthrough discovery without much contact with the math community? The ones I am aware of are like Andrew Wiles, and Ramanujan.

I just want some more examples cause I was quite curious with regards to certain approaches to mathematical development.

Answer 1

In recent time, Gregory Perelman's proof of the Poincare Conjecture wins the Oscars for the best mathematical work done in complete secrecy.

If you go back a few centuries, almost all mathematical work was done in secrecy. For e.g. Newton's invention of calculus was so secret that he did not publish it for several years after inventing it that it led to the controversy with Leibnitz who also invented calculus independently.

Answer 2

An original math that has a specific application can be sent to the patent office. But the patent office will tend not to support something that is original actually because of it as being previously unknown.

But an original math that has a specific application can then be generalized for the purpose of looking for additional applications. Then the additional applications can prove that the original math is fundamental in nature.

Two maths that became well-known and that reached the patent office were the Black Scholes financial application and the RSA cryptography system. But consider that the RSA cryptography system was not patented as an algorithm but patented as an electronic motherboard device. The Black Scholes financial application did use a new technique of calculus that was found in a scientific paper.

Oh, a quick search for a Black Scholes patent only turned-up a modified Black Scholes. The Black Scholes financial application did ultimately win a Nobel Prize in economics.