This post, what will most likely become a string of posts or a heavily back-edited post, is a correction of some previous views that I took on (with respect to math and teaching) without either 1) really knowing anything about what I was thinking about (yes this does indeed seem possible… not even wrong?) and 2) believing certain notions because I assumed that an “expert” was expounding on them. I hope to correct these notions in my brain and what a better place to start than the warm private world of a blog/website.
I am reading a beautiful book by David Ruelle at IHES:
he Mathematician’s Brain poses a provocative question about the world’s most brilliant yet eccentric mathematical minds: were they brilliant because of their eccentricities or in spite of them? In this thought-provoking and entertaining book, David Ruelle, the well-known mathematical physicist who helped create chaos theory, gives us a rare insider’s account of the celebrated mathematicians he has known-their quirks, oddities, personal tragedies, bad behavior, descents into madness, tragic ends, and the sublime, inexpressible beauty of their most breathtaking mathematical discoveries.
Consider the case of British mathematician Alan Turing. Credited with cracking the German Enigma code during World War II and conceiving of the modern computer, he was convicted of “gross indecency” for a homosexual affair and died in 1954 after eating a cyanide-laced apple–his death was ruled a suicide, though rumors of assassination still linger. Ruelle holds nothing back in his revealing and deeply personal reflections on Turing and other fellow mathematicians, including Alexander Grothendieck, René Thom, Bernhard Riemann, and Felix Klein. But this book is more than a mathematical tell-all. Each chapter examines an important mathematical idea and the visionary minds behind it. Ruelle meaningfully explores the philosophical issues raised by each, offering insights into the truly unique and creative ways mathematicians think and showing how the mathematical setting is most favorable for asking philosophical questions about meaning, beauty, and the nature of reality.
Here’s a review in Nature, mine will undoubtedly be of a lesser pedigree but I will give it “the old collage try,” if any will endure it.
Tidbit: Donal O’Shea (along with Harriet Pollatse) also has some interesting ideas about mathematical prerequsites, read about it in this article on the AMS site.
For an interesting perspective on many of the same issues check out “On proof and progress in mathematics” by William P. Thurston. The paper touches on natural language, symbols (Mathese), the visual system and many other topics also found in Ruelle’s book.
“The product of mathematics is clarity and understanding. … The real satisfaction from mathematics is in learning from others and sharing with others. … The question of who is the first person to ever set foot on some square meter of land is really secondary.”
Aaaand, maybe I was a bit premature on that whole last post thing… this might be a more appropriate one as I am moving on to other blogs (phutureshock). Jesus, it’s hard to say these days…