… A mathematician is not a man who can readily manipulate figures; often he cannot. He is not even a man who can readily perform the transformations of equations by the use of calculus. He is primarily an individual who is skilled in the use of symbolic logic on a high plane, and especially he is a man of intuitive judgment in the choice of the manipulative processes he employs.
All else he should be able to turn over to his mechanism, just as confidently as he turns over the propelling of his car to the intricate mechanism under the hood. …
from As we may think – Vannevar Bush.
You'll find much better pages on mathematics at Imperial, at mathworld (where I am a very minor contributor), in Eric's Treasure Trove or among Gregory Chaitin's papers; integer sequences in Sloane's database; better teaching materials at Cut the Knot; St. Andrews covers the history of mathematics.
Colin Wright writes and blogs about mathematics, somewhat more orthodoxly than me, among other things. Volker Runde collects mathematical jokes. Ben Orlin illustrates mathematics with bad drawings, and reminds us that other subjects are just as worthy. If all the mathematicians you've ever heard of were men, check out the #MathGals T-shirts and Power in Numbers: The Rebel Women of Mathematics by Dr. Talithia Williams.
Please read my caveat and apologia about these pages before trying to tell me how to keep them. On the other hand, if you can see how to fit all these fragments together, or want to point me to somewhere which covers related material or does its page-design well, I'll be delighted to hear about it: and when you notice my mistakes (or catch me using a term in a way which conflicts with that of some pertinent orthodoxy – thanks Jeremy ;^) please tell me about them. The odds on my fixing them are then greatly improved. My e-mail address is firstname.lastname@example.org.
Back in the '90s I started writing mathematics in plain text, since that was the only thing that worked in all browsers. In devising denotations that are easy to type on a keyboard with few characters outside the ASCII repertoire, I leant heavily on the accumulated wisdom of programming language designers, notably those in the tradition of Ponder (design, type system) and Haskell. By the time browsers could display orthodox notation well, I'd written plenty of pages in a plain text notation that I like better than orthodoxy's; and I don't like what one has to type in the source file to get the orthodox appearance. So I still write in plain text.
In practice I use Vivaldi as my review browser, so those using other browsers might run into problems at times (although this is fairly unlikely these days); let me know if that happens, so I have some chance of fixing it. I also (since 2006/Summer) use the W3C's validator to help me make my pages conform to relevant specifications, which should ease cross-browser compatibility.
The primary sub-sections of this ramshackle assembly of writings about mathematics are:
Here are some hook-in points to bits and pieces I've written, many of which could use some further sorting out and tidy-up:
Meanwhile, if your borwser supports images, here's a preview of a pictorial proof of Pythagoras' theorem.
While there is some structure to my site, it's a bit haphazard and, all things considered, if I were starting afresh today I'd do it all differently. I mix discussion and proof rather sloppily: I want to include the proof in the discussion, but sometimes end up just proceeding from proof to proof. It might be better to have a network of pages devoted to formal definitions and proofs, that are referenced from a related network of discussions and explanations, that explore why the questions addressed are of interest and how we come by the approaches that resolve them. Ben Orlin has a nice essay on this that prompted some interesting discussion (see its comments section).
Activity on this section of my site, as on the rest, is somewhat sporadic. My thoughts of the moment index includes yearly diaries of activity, sketching what I've been up to.Maintained by Eddy.