Monthly Archives: April 2014

Review of Gowers’s Weblog – the blog of Timothy Gowers

Sir William Timothy Gowers is, as you might expect, a British mathematician. As with Aaronson, I won’t repeat his biography here, as the wiki is adequate. I just thought I’d point out one fun little tidbit: Gowers once sang in the King’s College Choir, Cambridge, as a choirboy. That choir is one of the best in the world, and is probably my favorite. In particular, their album O Come All Ye Faithful is one of the truly great Christmas albums.

Gowers’s Weblog is definitely more on the technical side overall, with a few exceptions. However, you will find that Gowers likes to write posts for lots of different ability levels. There are posts accessible to high schoolers, undergraduates, graduates, and research-level Ph.D.’s. Moreover, the posts range over many different kinds of math. You’ll find analysis, combinatorics, logic, algebra, etc., as well as pedagogy. Gowers is not so much a specialist as some, which I think is all to the good. We do not need more specialists these days, but generalists.

Gowers’s style is engaging, while still technical enough to interest the expert. I have linked to several posts of interest. I just thought I would especially point out the Polymath5 tag, which corresponds to the Erdos Discrepancy Problem. This is an attempt to solve a mathematical problem with an highly collaborative effort. Probably it is not the case that any ol’ problem can be solved this way, but there are features of certain kinds of problems which render them vulnerable to this kind of attack. It’s an interesting experiment. Another interesting experiment was Gowers’s proof program for generating proofs of certain kinds of theorems. Yours truly submitted one comment for that experiment.

One criticism I might have is that Gowers does not usually explicitly mention the prerequisites necessary to understand various posts. Aaronson doesn’t do this, either. This unfortunately makes the signal-to-noise ratio lower than it might be. If I have no idea how to start reading a post because it dives into technical details way over my head, then I’m less likely to come back for more. Naturally, it’s impossible to please everyone, and some might find a list of prerequisites for each post tiresome. On blogs, at least, you could use tags to accomplish this. Then it’s there, but not in-your-face.

In conclusion, I would definitely say this blog is worth following, even if its frequency is a bit low. The blog is still alive certainly; posts are dense and efficient, as you’d expect from a Fields-medal-level mathematician.

Review of “Shtetl-Optimized” – the blog of Scott Aaronson.

Shtetl-Optimized, as I’ve mentioned elsewhere, is the blog of Scott Aaronson. And, as I’ve just linked to his wiki page, I don’t feel especially inclined to say much about his biography. Aaronson’s field of research is quantum computation; an exciting new field with possibilities. It lies at the intersection of mathematics, physics, computer science, and electrical engineering.

I have found Shtetl-Optimized to be well-written and informative. His latest post, dated March 22nd, is about Tegmark, his book Our Mathematical Universe, and Tegmark’s idea of the Mathematical Universe Hypothesis. Aaronson’s writing is lively and witty, you’ll find. He writes about both the human-ness of Tegmark’s writing, as well as his disagreement with Tegmark’s fundamental thesis, which is that the universe is not just mathematical, but is itself the mathematics. One of Aaronson’s reasons for finding the Mathematical Universe Hypothesis (MUH) unconvincing is that it is not impressive science – defined as when elegant mathematics lines up with facts as we have experienced them. I think this is exactly right. It does seem unlikely, as well, that anyone could ever devise experiments to test the MUH. This is my issue with all multiverse theories: while theories are definitely a part of science, and important (theories are the goal, after all!), experiment is the life-blood. A theory without experiment exists only in men’s minds, and has dubious predictive power.

Shtetl-Optimized is probably not for the layman, however, as he has no hesitation in getting “technical”. If you are interested in popular science, this blog would stretch you. Perhaps that is what you’re seeking, and if so, you’ve found a good place. It’s like classical music: you get out of this blog what you put into it.