Tim Chow

In the comments to this post, David MacIver provides an alternative, registration-free link to Tim Chow’s You Could Have Invented Spectral Sequences.

I poked around Tim Chow‘s site, and found two other interesting articles (in the form of old sci.math.research posts):

  • Forcing for Dummies. Forcing is the technique invented by Paul Cohen to prove the independence of the Continuum Hypothesis.
  • What is Class Field Theory? Class field theory describes the extensions of a field with abelian Galois group.

3 thoughts on “Tim Chow

  1. Tim Chow’s “Forcing for Dummies” article is definitely a good read, and I think that’s actually how I first encountered his website (via a link from Tom Forster’s homepage). I confess however that I’ve not found it to be overwhelmingly useful in my ongoing attempts to actually understand forcing.

    The problem seems to be that forcing consists of some reasonably well motivated ideas, and an awful lot of mathematical voodoo. All the introductory explanations you get of this nature, no matter how clear their explanation of the motivations, don’t give you a great deal of insight into how the voodoo works. This is certainly the stumbling block I’ve found – I simply couldn’t wrap my head around the details of why a forcing argument works or how it is carried out. I don’t think this is entirely the result of me being stupid.

    I’ve been intermittently alternating between ignoring the subject and half heartedly fiddling around with it for about a year now and I think I’m finally at the point where I believe that I will understand it. Interestingly, the method of forcing that seems to make more sense is much more poorly motivated than the traditional method. I’ve been working on Dales and Woodin’s exposition of Boolean valued models. It’s extremely hard work, as you have to deal with some very difficult and not that clearly motivated mathematics, but the difference seems to be that it’s very hard but nonetheless comprehensible mathematics as opposed to simply black magic. I certainly recommend their exposition of the subject, but given that I own almost every book Dales has published and the main point of the book is almost directly linked to one of my major interests, my opinion may be somewhat biased.

    On a related note, having discussed Forcing a bit with some respectable logicians and set theorists at the last cameleon meeting in Cambridge I was relieved to hear that they more or less shared my views on the subject. They generally understood it better than I do of course, but they’re clever doctors and professors with PhDs and 10+ years of research to their name while I’m just a lowly graduate.

    Anyway, I’m sure I had a point somewhere in there.

    Merry Christmas,

  2. I confess I don’t tend to respond very well to the categorical approach. The Boolean valued models approach is increasingly appealing to me – I’m an analyst by default, so the notion of being able to reduce the problem to little more than Boolean algebra combinatorics is very nice.

    That being said, I would like to learn about the topos theoretic side of things, so I will probably take a look at that book when I have the chance. Thanks.

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