Polytropy

My title alludes to some notes for the layperson that I rediscovered recently. I have reviewed and edited them, and they are below, in the following sections (linked to by the titles after the three main bullets; other links are to Wikipedia).

• “Quasicrystals,” based on an email of mine sent to a group of alumni of St John’s College on October 8, 2011. This was my contribution to a thread in which somebody said that
  • Dan Schechtman (whom she called Danny) was a worthy recipient of that year’s Nobel Prize in Chemistry for the discovery of quasicrystals, but
  • John Cahn deserved credit, even the prize itself, as the real discoverer.

  My wife and I had recently moved to Istanbul, and the Istanbul Model Theory Seminar had just got going. The Nobel Prize and quasicrystals had been mentioned there too.

• “Free Groups,” based on an email of October 10, 2011. I tried to describe free groups to somebody who expressed interest, but who also called himself the world’s worst mathematician.
• “Topology” – a draft of an attempt to describe that subject. In graduate school, I got excited about the definition of a topological space when I first encountered it. Here I try to motivate the definition by abstracting from the properties of the Cartesian plane as a metric space. I give the example of the Zariski topology on the same plane. I start to talk about the topology derived from the Gromov–Hausdorff metric on the space of groups with n generators, but then I stop.

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