
Sometime Cambridge logic lecturer, now idling in retirement. Also procrastinating at @PeterSmith@mathstodon.xyz
Cambridge
Joined December 2007
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Peter Smith retweeted
Terence Tao made a very powerful point:
“In most cases in pure mathematics, the problems are posed not because we desperately want the solution to these problems in and of themselves, but because we have seen from past experience that human-directed efforts to solve these problems tend to spur further development of the field through the efforts to solve such problems, and then to digest any partial or complete solutions that emerge for further insights.
Prematurely solving the problem by purely AI-powered methods—particularly without full transparency into the solution process—can contaminate this process to the point where it actually becomes a net negative for the progress of mathematics as a whole.”
I’ve been following Terence Tao for like 20 years, and I have always been impressed by the clarity of his thinking.
This clarity stands out even more in this difficult moment, as AI labs turn mathematics into a battleground in their race for supremacy.
In this race, they risk damaging one of humanity’s highest intellectual endeavours.
A reminder for new semester/term
There are now FIVE Rig Red Logic Books free to download.
My (ex-CUP) Intro to Formal Logic, and Gödel's Theorems. The shorter Gödel Without Tears. A Study Guide to Math Logic. And Introducing Category Theory.
logicmatters.net/books/
Three enthusiastic (non-logic) book recommendations -- James Marriott's *The New Dark Ages*, Lettice Cooper's *Fenny*, Kathleen Jamie's *The Overhaul*.
logicmatters.net/blog/recent…
ICYMI, I am beginning slowly to revise the 2022 *Beginning Mathematical Logic* Study Guide.
Here is the third updated chapter -- this one is on proof theory. (Not major revisions, but improved, I hope!)
logicmatters.net/tyl/pdfs/Pr…
A gentle reminder. A PDF of the third edition of my *Introducing Category Theory* can be freely downloaded from logicmatters.net/categories. But there is now also a nice hardback version for libraries, ISBN 106834671X. 1/2
And many do find working from a five hundred page PDF irksome, *much* preferring a physical book. So DO ask your local university library to order to a copy (it certainly won’t dent their budgets much, being listed at just $35, £31.50, etc.). 2/2
Peter Smith retweeted
Martha Nussbaum on Bernard Williams: "Over the years I began to notice that he was never angry (whereas I am angry more or less all the time). Contempt, world-weariness, cynicism, even an irritability linked to the world-weariness, but never just anger, the sense that wrong has been done and that one had better go out and right it. I think his non-angry attitude to tragedy was of a piece with his critique of the Enlightenment: doing good for a bad world did not energize him, because his attitude to the world was at some deep level without hope. The world was a mess, and there was no saving or even improving it. It was childish, naïve, to suggest that improvement was possible. (His liberal politics were difficult to reconcile with this view, and this perhaps explains his increasing withdrawal from politics and even political thinking in later life.) Nietzsche called this attitude amor fati and connected this embracing of necessity with a kind of cheerfulness, the cheerfulness that comes when we abandon the hope of real change. Similarly, what energized Bernard, cheered him up, was a kind of elegant assertion of the hopelessness of things against the good-newsers, a contemptuous yet brilliant scoffing." @BostonReview
Peter Smith retweeted
I've just written a blog post in which I discuss the question of whether current LLMs are better at some kinds of mathematics than others, with an emphasis on "current", given how quickly the situation is developing. Link in next tweet.
I am starting to update the 2022 *Beginning Mathematical Logic* Study Guide (logicmatters.net/tyl)
Here's the first newly revised chapter, a list of recommended (and not-recommended) reading on First Order Logic, logicmatters.net/tyl/pdfs/FO…
Suggestions? Corrections?
ICYMI elsewhere. There's a pbk version of *Introducing Category Theory*, 3rd edn. new today, ISBN 1068346728. Amazon-only print on demand to keep the price minimal. Or you can still download the PDF from logicmatters.net/categories (more info there). Spread the word :)
A new blog post about using AI in proofreading the upcoming revised 2nd edition of my category theory book. Might be of some interest to other maths writers. logicmatters.net/2025/12/28/…
ICYMI elsewhere. There's now a pbk version of *Introducing Category Theory*, 2nd edn., ISBN 1068346701. Amazon-only print on demand to keep the price minimal for a 500pp book. Or you can still download the PDF from logicmatters.net/categories (more info there). Spread the word :)
New online today -- an almost complete draft for a second edition of *Introducing Category Theory*. Cheapo pbk to come in Feb/March (in the meantime, all corrections VERY welcome as my proof-reading is probably terrible!). You can download it from logicmatters.net/categories
The table of contents and the Preface will give you a good idea whether this will be of any interest to you. But if, for example, you are about to start an industrial-strength category theory course, this could provide a gentle warm-up.
Three short-ish blog posts so far on Noson Yanofsky’s new book on Monoidal Category Theory at logicmatters.net/blog










