That’s what you’ll see if you scroll down the list of winners of the 2016 PROSE Awards, also known as the *American Publishers Awards for Professional and Scholarly Excellence*.

It’s nearly true, but not quite, that I learned that *MWA* had been chosen when I saw this on the book’s Amazon page:

Scroll down to the bottom of the Amazon page (for which I hope I will never provide a link) and you’ll see the book described as “disorganized” and “snobby.” I had never heard of the PROSE Awards before last week, and I don’t know what they entail (apart from a “special luncheon ceremony” to which I hope my publisher was invited, because they won awards in several categories). So not only do I not know whether or not congratulations are in order (I haven’t received any); I can’t even judge whether or not the award confirms or contradicts the suspicion that *MWA* is a book of, by, and for disorganized snobs. Maybe some readers can help me out?

As far as organization is concerned, I can assure you that *MWA* is in fact highly organized, though its structure is not conventional. Packing information from a variety of sources, normally only consulted by snobs, into a small volume, while simultaneously avoiding an infinite regress of cross-referencing and maintaining the illusion that the prose flows naturally, is a combinatorial problem no less challenging, though on a smaller scale, than guaranteeing that the dependency graphs of the Stacks Project are simply connected. When the challenge became too taxing I only managed to solve it, imperfectly no doubt, by retreating to an isolated environment, and with the help of a combination of natural stimulants.

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Shecky RWell-deserved and Congratulations! (in order or not!)

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mathematicswithoutapologiesPost authorThank you very much! (Does that make you a snob?)

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John SidlesAlthough I don’t often comment on this weblog, I do read

Mathematics Without Apologies(both the weblog and the book) with great enjoyment and attentiveness. Indeed, my personal copy ofMWA(the book) has already received more marginal notes (140 notes to day) than any other book that I have ever read, on any topic … and upon readingMWAagain (as I plan to) many more annotations will no doubt be added. Readers who considerMWAto “disorganized” are invited to read it more carefully!LikeLike

mathematicswithoutapologiesPost authorThat’s very flattering… and I certainly do appreciate your support!

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John SidlesComplexity theorist Scott Aaronson’s weblog

Shtetl Optimizedgraciously hosted a comment (link here) that touched uponMWA‘s thematic resonance with another 2016 Prose winner, Peter Sterling and Simon Laughlin’sPrinciples of Neural Design. Needless to say, these works can be appreciated in more than one way; theMWAnotion of a “relaxed field” provides (as it seems to me) a particularly valuable way.LikeLike

mathematicswithoutapologiesPost author“Post-rationalist?” I’ll have to think about that.

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John SidlesIn the context of computer science/complexity theory, Google’s

AlphaGoprogram is a paradimatic “post-rational” cognitive construct, in the sense that logical reasons as to “why a move is good” cannot readily be discerned in AlphaGo’s computational processes, and indeed did not enter in Google’s design and tuning of AlphaGo.It is natural to wonder about the degree to which humans learn how to

domathematics by post-rational “tuning” processes that are similar to those of Google’s AlphaGo.LikeLike

David Roberts[the below comment turned out a long longer than I intended, and strays from topic – sorry!]

May I take issue with your use of the phrase “simply connected” wrt a dependency graph, esp. the Stacks Project? I don’t know if you are aware of the area of ‘directed homotopy’, but that is where dependency graphs sit: they are not plain unadorned graphs in any case. The Stacks Project dependency graph will never be simply connected in the usual (undirected) sense, and nor should it be. But one should hope it does not have any *directed* loops.

In any case: all dictionaries have directed loops, and we find them no less useful. The language of mathematics with its layered and precise definitions gets a whole lot more like ordinary language down near the foundations. I watched part of a YouTube recording of a talk on ‘meaning explanations’, which is a careful philosophical construction as to why type theory is meaningful and why it captures what we mean when we talk mathematics using its language. It was something you would enjoy, methinks; full of phrases like “To know M => M’ is to know that M’ is the value of M.”

In the post-rigorous mathematics that Terry Tao speaks of (and this is somewhere where the nLab roughly operates, if I may bring it up) one is not playing Bourbaki, or Russell and Whitehead, or EGA. It can be done, but that is going on at a more subconscious level, or perhaps after the main results are plausible to the point of wanting to get the proof down. Voevodsky spoke of working in a formally _inconsistent_ framework just to get ideas thrashed out, then making sure afterwards in a more formal setting that no contradictions were accidentally used.

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mathematicswithoutapologiesPost authorI see your point, but the dependency graphs I’ve seen on the Stacks Project really are trees. This is because a single tag can appear as several vertices. See for example Tag 09TT, the (always useful) Lemma 81.9.2. Northwest on the dependency graph you’ll see two nodes labelled 041J side by side. The same tag occurs one generation closer to the target.

I am looking forward to an explanation by a professional philosopher of Terry Tao’s notion of post-rigorous mathematics, and in what sense it is both post-rigorous and mathematics. It’s an important notion, though the word “post-rigorous” may conjure up a misleading picture.

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David RobertsSorry, forgot to give the link to the video: https://www.youtube.com/watch?v=xMAqniX2Paw (titled: LambdaConf 2015 – Type Theory and its Meaning Explanations Jon Sterling)

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