[0636] Hodge Theater

[0636] Hodge Theater

Ye Thuza is, of course, reading Shinichi Mochizuki’s infamous paper on „Inter-universal Teichmüller theory“: [1][2][3][4]. According to Mochizuki, it proves the abc conjecture, one of the most important conjectures in number theory. However, nobody has yet been able to verify his proof because it is so bizarre and complicated that nobody understands it.

I found words such as “Hodge theater” and “Inter-universal Teichmüller theory” incredibly funny, so I just had to make a comic about Mochizuki’s work. The blog posts of mathematicians like Caroline Chen about it are also funny to read:

On MathOverflow, an online math forum, […] Andy Putman, assistant professor at Rice University asked: “Can someone briefly explain the philosophy behind his work and comment on why it might be expected to shed light on questions like the ABC conjecture?” […] Or, in plainer words: I don’t get it. Does anyone?

The problem, as many mathematicians were discovering when they flocked to Mochizuki’s website, was that the proof was impossible to read. The first paper, entitled “Inter-universal Teichmüller Theory I: Construction of Hodge Theaters,” starts out by stating that the goal is “to establish an arithmetic version of Teichmüller theory for number fields equipped with an elliptic curve… by applying the theory of semi-graphs of anabelioids, Frobenioids, the étale theta function, and log-shells.”

This is not just gibberish to the average layman. It was gibberish to the math community as well.

“Looking at it, you feel a bit like you might be reading a paper from the future, or from outer space,” wrote Ellenberg on his blog.

  • Ye Thuza: The F-symmetry is represented in a DΘ-Hodge theater HT by a category equivalent to the Galois category of fiite étale coverings of X.
  • Ye Thuza: On the other hand, each of the labels referred to above is represented in a DΘ-Hodge theater HT by a D-prime-strip.
  • Ye Thuza: That’s enough inter-universal Teichmüller theory for today. Now sleep tight.
  • Yuna: Unfair! Just when it started to get exciting!
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