Any thoughts on Lakatos’ more science-general “The Methodology of Scientific Research Programmes”? It’s on my reading list.

]]>Another thing to consider is perhaps combinatorics, which is very useful for understanding the underlying ideas behind probability (in a discrete setting, but it’s a good intuition pump), as well as ideas surrounding graphs, and decision trees, and soforth.

]]>If I want to read an interesting reflection on proofs and progress in mathematics, I read Thurston or Gromov or Langlands, or someone similar.

]]>I’ve got some of the materials posted at http://www.ma.utexas.edu/users/mks/360M05/360M05home.html.

]]>I’m sure you’re right, but I suffer from Polya-phobia because way back when I did math team, the coaches were always pushing Polya and How to Solve It, and I associated this with other irritating attitudes they had, such as not wanting to use calculus or analytic geometry, or being opposed to applications.

]]>Congratulations on your NYTimes piece

]]>Are there books on more empirical branches of science that do something similar by focusing on the productivity of error if it’s incorporated in a larger process of reflection?

]]>1. I can get to new articles from the blog list of (for example)

http://observationalepidemiology.blogspot.com/ long before they appear on your home page

2. Comments in the Recent Comments list cannot be accessed for posts that do appear for a day or so. ]]>

Victor Miller

]]>Yes, this is annoying me too. I’ll talk with the sysadmin on Monday.

]]>I disagree. I don’t think the book is about “sloppy definitions” at all. Mathematical definitions are, by their nature, as precise as they need to be. As the theory is expanded, the definitions become more specific. And I think the general point of the interplay between proofs and refutations is very relevant to modern mathematics.

]]>By the time I picked it up, I’d already done abstract algebra and several graduate level math classes in logic and set theory. So maybe I was already too familiar with what it meant to present a proof. Or maybe I’d have enough dialectic after reading *Gödel, Escher, Bach* in high school (as much as that book influenced me to specialize in logic and computation, I wouldn’t recommend rereading favorite childhood pop books after obtaining a graduate-level understanding of the material).

@Joshua Pritikin: Computers are helpful for some proofs (finite simple groups, four color problem, etc.), but they’ve hardly replaced mathematicians.

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