KGFM 20, 21: Woodin on the transfinite, Wigderson on P vs NP

And so, finally, to the last two papers in KGFM. I can be brief, though the papers aren’t. The first is Hugh Woodin’s ‘The Transfinite Universe’. This inevitably mentions Gödel’s constructible universe L a few times, but otherwise the connection to the ostensible theme of this volume is frankly pretty tenuous. And for those who can’t already tell their Reinhardt cardinals from the supercompacts, I imagine this will be far too breathless a tour at too stratospheric a level to be at all useful. Set-theory enthusiasts will want to read this paper, Woodin being who he is, but this seems to be very much for a minority audience.

By contrast, the last paper does make a real effort both to elucidate what is going on in one corner of modern mathematics for a wider audience, and to connect it to Gödel. Avi Wigderson writes on computational complexity, the P ≠ NP conjecture and Gödel’s now well-known letter to von Neumann in 1956. This paper no doubt will be tougher for many than the author intends: but if you already know just a bit about P vs NP, this paper should be accessible and will show just how prescient Gödel’s insights here were. Which isn’t a bad note to end the volume on.

So how should I sum up these posts on KGFM? Life is short, and books are far too many. Readers, then, should be rather grateful when a reviewer can say “(mostly) don’t bother”. Do look at Feferman’s nice paper preprinted here. If you want to know about Gödel’s cosmological model (and already know a bit of relativity theory) then read Rindler’s paper. If you know just a little about computational complexity then try Wigderson’s piece for the Gödel connection. And perhaps I was earlier a bit harsh on Juliette Kennedy’s paper — it is on my short list of things to look at again before writing an official review for Phil. Math. But overall, this is indeed a pretty disappointing collection.

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