Mad Teddy's website - mathematics: introduction and menu

Mad Teddy's web-pages

Mathematical stuff

Crystallized thought

Even as a little kid, I was always fascinated by shapes and patterns. When I was in kindergarten, there were big coloured dots on the wall arranged into patterns akin to those you see on a dice, with the appropriate numerals writ large next to them. The layout of the dots struck a chord in me somewhere.

All through primary school, I found that I was able to latch on easily to arithmetic, or "sums" as the subject was called (by the kids, at least!). Most of the kids didn't like "sums", but I enjoyed it and viewed it as a challenge. Even then, I realized I was not like most other kids in that regard, and it was a source of puzzlement to me why they found it so hard and frustrating. I always scored high in arithmetic tests, and I learned to recognize the look of distaste, humiliation and resentment on the faces of the kids who didn't.

By high school, it became a real problem. Being clever at maths didn't help a person to form friendships easily. You had to watch your back and choose your company rather carefully.

At matric. college (a term which has fallen into disfavour in these supposedly egalitarian times - terms like "senior secondary college" are de rigueur these days), one was among one's peers, some of whom actually gave one some friendly competition. I remember my days at matric. with fondness.

So, maths was always very much my favourite subject, followed fairly closely by chemistry. (You may be surprised, in the light of other pages in this website, to learn that I struggled with physics - even though I really did want to understand. It was only much later, even after finishing at university, that the pieces finally began to click comfortably into place.)

By the way - I found this on the net, and I just had to have it on this page:

Biologists think they are Chemists,
Chemists think they are Physicists,
Physicists think they are Gods,
And God thinks he is a Mathematician.

University was a shock. I did a Bachelor of Science (B.Sc.) degree, with a major in pure mathematics. It wasn't plain sailing.

I'd never really had to study in school; just doing my basic homework was enough. Hence I didn't know how to study when I started uni; and I found that I had a serious problem, because to survive at uni you just have to study.

I did eventually figure it out, but only after some years of painful failure, during which I very nearly lost interest in maths and science altogether. But, ultimately, I survived, with my enthusiasm intact and rejuvenated. So now here I am, hoping to share my joy in knowledge with any person who'd like to read these pages.

If, through this website, I can encourage anyone who has struggled - or is still struggling - with maths and/or science, I shall feel that it's all been well worth the effort.

UPDATE, Wednesday, 28th October 2009: If you'd like to read more details about my experiences as a student - and beyond - described in the light of something I only came to understand a bit over a year ago, you may like to visit my On the spectrum page, which I posted in early July this year.

So: what sort of thing will you find here?

In 1941, a book called "What is Mathematics?", by two eminent New York mathematicians, Richard Courant and Herbert Robbins, was published by Oxford University Press. (I have a copy of the ninth printing, 1958.)

It's a valiant attempt to convey to the interested lay-person some idea of the essence of what mathematical thought is about. Does it succeed?

Another book, "Mathematics for the Million" by Lancelot Hogben, originally published in 1937 by W.W.Norton and Company (I have the 1993 paperback edition), attempts something similar. Albert Einstein said of this book:

"It makes alive the contents of the elements of mathematics."

H.G.Wells said:

"A great book, a book of first-class importance."

Were Einstein and Wells right?

Yet another book, published in 1998, is "What is Mathematics, Really?" by Reuben Hersh. I haven't read it; but from reviews I've seen, I gather that Hersh to some extent takes issue with Courant and Robbins. Apparently, he emphasizes the human aspect of how mathematics has developed over hundreds or even thousands of years, which he apparently thinks is not given due attention by other writers. Is he right?

As far as I'm concerned, they're all right. The point is, mathematics comprises an enormous body of knowledge, and has been (and still is being) developed by all sorts of people over time - some of them, very odd and eccentric characters indeed. There's room for disagreement and debate. It's healthy - bring it on!

I'm proud to call myself odd and eccentric. I certainly don't claim to be an eminent mathematician like any of the authors mentioned above; but I definitely am an interested participant, and pleased to have an opportunity via this modern medium to add my contribution to whatever makes maths more interesting, understandable, and enjoyable - to the fellow nerd and the lay-person alike.

I'm not attempting to compete with Courant, Robbins, Hogben, Hersh, or any other excellent author in the field. (Fat chance!) Here, you'll find no more than mathematical "bits'n'pieces"; but they are presented with enthusiasm. I'm just hoping to tickle your fancy and whet your appetite, so that you may be inspired to dig further into the subject yourself. If I can achieve that, I'm happy!




A divisive issue

A taste of topology

Polyhedra: frozen music for the eyes

Some mathematically-based computer graphics

Quaternions: an old (and new!) look at four dimensions

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