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

## 4 comments:

Also I have a blog at

njwildberger.wordpress.com

where I will be discussing, among other things, foundational problems with modern mathematics. These are much more serious, prevalent and problematic than most mathematicians realize. It means big opportunities for new thinking!

Take a look at "

A Comparison of Rational and Classical Trigonometry"By Michael Gilsdorf

http://web.maths.unsw.edu.au/~norman/papers/TrigComparison.pdf

in which Gilsdorf shows that Rational Trigonometry is NOT simpler than Classical Trigonometry.

I find it interesting that when this comparison first made its appearance on MathForum, Wildberger promised to comment on it but failed to do so. That was back in February 2007.

http://mathforum.org/kb/message.jspa?messageID=4492575

Norman Wildberger has placed numerous hours of math videos on youtube and elsewhere. I have found his videos to be extremely good from the standpoint of teaching and content; and he provides a fresh, enlightening, and original approach to learning serious math topics. He does state his opinion on several areas -- including critique of standard teaching methods. It is okay to be critical of his approach because it is so original, nonstandard, and unique; however, to suggest that he is a "crackpot" is very inaccurate and takes away from the output of what appears to be a very capable mathematician. Use of ad hominem arguments makes one realize the depth of the politics that exists in math circles; which has left an ugly mark in its recent history, (e.g., http://en.wikipedia.org/wiki/Manifold_Destiny). Why not praise a guy with such self motivated high quality output. He does have a Ph.D. from Yale, he taught math at Stanford, and he currently is a math professor in Australia. Come on now...

"...example that even in a field as cut-and-dry as math is perceived to be, there is room for a variety of opinion"

You should read up on the foundations of math...it is worse than a cat fight amongst women! Some names...Hilbert, Godel, Turning, Chaitin, Weyl. Especially Hermann Weyl. He seemed to straddle the various views in a reasonably fair manner. Wildberger reminds me of one of Weyl's influences L. E. J. Brouwer.

Best wishes,

Don

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