The Inimitable Dr. Wildberger ?

Well, this is sort of interesting (to me at least)…

Quite awhile back I came across a link to Aussie Dr. Norman J. Wildberger's math videos on YouTube and looked briefly at a couple of them. They seemed interesting, and with better production values than most math videos, especially Khan Academy-type clips, so I went ahead and put a link to them in my right-hand column thinking at some point I'd get back for a closer look.
I even went so far as to list them among 10 favorite math sites in a post I did on such, even though I hadn't explored them very fully.
Well, lo-and-behold the other night I was reading some commentary on a forum and saw Dr. Wildberger's name briefly arise more-or-less in the context of crackpot math, so figured I ought do some more checking.

In googling around the Web I found a fascinating array of opinions on Dr. Wildberger (who IS a fully-credentialed, professional mathematician and university professor). He was written off as a crackpot by several, and as simply misguided by many more, but also praised by a few (even if they don't completely agree with him); and some even calling his work "important," "exciting," "groundbreaking," and the like. It's not often in math that one sees such a wide divergence of opinions on a body of work.

Anyway, someone who doesn't mince words much about "crackpots" is Mark Chu-Carroll of "Good Math, Bad Math" blog, so I clicked over there and searched his site for "Wildberger" to see what I might find… bingo! sure enough Mark had done a post on him back in 2007:

http://scientopia.org/blogs/goodmath/2007/10/15/dirty-rotten-infinite-sets-and-the-foundations-of-math/#more-529

It is a very long post followed by a very long list of interesting and heavy comments (it concentrates a lot on set theory, and contains more than one can digest in a single sitting! -- I wouldn't even attempt a summary), but what is fascinating is to see Mark simultaneously roundly denouncing much of Wildberger's approach, but also, noting a few good, interesting, or agreeable points here and there; indeed he admits that Wildberger is worth a look (somewhat backhandedly Mark writes that Wildberger "...isn't the typical wankish crackpottery, but rather a deep and interesting bit of crackpottery" ;-).

Wildberger strongly believes that the foundations of math and math teaching are both problematic. I think I was initially attracted to him in part because he claims to be re-building mathematics on a more "intuitive" (easier-to-understand) basis. Through high school I thought algebra, geometry, and even early calculus were somewhat intuitive, but that trigonometry was NOT intuitive at all, so someone who claims to make trig intuitive (as Wildberger claims) catches my attention.
Anyway, I'm in no position to judge Dr. Wildberger's novel work (and still hope to find time to view more of his videos), but simply use him as an example that even in a field as cut-and-dry as math is perceived to be, there is room for a variety of opinion (although the negative opinion seems to far outweigh the positive in this case).

If you wish to explore more...:

Professor Wildberger's personal website is here:

http://web.maths.unsw.edu.au/~norman/

His YouTube videos here:

http://www.youtube.com/user/njwildberger/videos

A Wikipedia page entry for his notion of "Rational Trigonometry":

http://en.wikipedia.org/wiki/Rational_trigonometry

and his book on same, "Divine Proportions,"  is here:

http://www.amazon.com/Divine-Proportions-Rational-Trigonometry-Universal/dp/097574920X