Be careful! Simon Peyton Jones is a friend of mine! The problem with a number of these folks is that they're trying to reduce *too much* of math to a single idea or representation. While it's important to see how far these ideas can be pushed, the true beauty of math IMHO is the ability to look at the same thing from many different angles & many different representations. For example, I'm so upset with the usual discussions of Galois Theory, that I'm contemplating writing a small paper about representing all polynomials by means of square matrices -- i.e., p(x) is represented by a matrix M, such that |M-x*I|=p(x). Most people cringe at using a representation that uses O(n^2) elements for O(n) data, but since we're mathematicians, insight is more important than efficiency, nicht wahr? Perhaps such a paper has already been written; please let me know if you're aware of such a paper. At 05:43 AM 8/3/2017, Fred Lunnon wrote:
Wildberger does himself no favours with the professional community, because he takes no interest in situating his self-invented methods in the broader scheme of established mathematics. I have a good deal of sympathy with his attitude, as it happens; but there does come a point where one must down tools and make an effort to get connected, or else risk wasting further time and temper re-inventing the wheel.
My impression of "Divine Proportions" for example was that it went some of the way towards rediscovering Clifford algebra; but given how that has failed to gain acceptance over the past 144 years, maybe a fresh approach might be no bad thing!
His exuberance and blackboard technique in the video were wondrous to behold. [ I was reminded of another supercharged eccentric, Simon Peyton Jones on Haskell programming --- https://www.youtube.com/watch?v=6COvD8oynmI --- and several more ... ]
WFL