A conversation about mathematics inspired by a hat. Presented by Katie Steckles and Peter Rowlett.
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Way back at the end of last year I put out a call to mathematicians I know: hop on Skype and chat to me for a while about the work you’re doing at the moment. The first person to answer was David Roberts, a pure mathematician from Adelaide.
We had a fascinating talk about one thread of David’s current work, which involves all sorts of objects I know no more about than their names. I had intended to release this as a podcast, but the quality of my recording was very poor and it turns out I’m terrible at audio editing, so instead here’s a transcription. Assume all mistakes are mine, not David’s.
If you’ve ever wanted to know what it’s like to work in the far reaches of really abstract maths, this is an excellent glimpse of it.
DR: I’m David Roberts, I’m a pure mathematician, currently between jobs. I work – as far as research goes – generally on geometry and category theory, and the interplay between those two. And also a little bit of logic stuff, which I thought I’d talk about.
Why should I worry about dying? It’s not going to happen in my lifetime!
Raymond Smullyan, This Book Needs No Title (1986)
This week, the mathematical community has lost not one but two of its most beloved practitioners. Earlier this week, Swedish statistician Hans Rosling passed away aged 68, and today it’s been announced that author and logician Raymond Smullyan has also died, aged 97.
Good news, logic fans! The Open Logic Project is a project to write an open-source textbook on logic. And if you read it, you’ll find tautologies like the last sentence completely thrilling.
The book is aimed at a non-mathematical audience, mainly computer science and philosophy students, so it assumes very little knowledge of the basics. The project was instigated by Richard Zach, who’s Professor of Philosophy at the University of Calgary. The rest of the project team consists of Aldo Antonelli, Andy Arana, Jeremy Avigad, Gillian Russell, Nicole Wyatt, Audrey Yap, and Richard Zach. They’re aiming to cover first-order logic, sequent calculus, soundness and completeness theorems, computability theory, and incompleteness. If things go well, they want to add material about model theory, computability and Turing machines (that’s already in progress), and some stuff on philosophy of language and mathematics.
A high-quality textbook for free would be pretty good on its own, but what’s really nifty is that the source code has been set up so the book is configurable to your tastes: you can say what kind of notation you’d like, and even adapt theorems and lemmas to use different proof systems.
The Open Logic Project official website
Get the source code and contribute on GitHub
@OpenLogicProj on Twitter
C: $K_A m; \\ K_B d.$
A: $\neg K_A d; \\ m \vDash \neg K_B m.$
B: $d \not\vDash K_B m; \\ (K_A(\neg K_B m)) \vDash K_B (m,d).$
A: $m \wedge K_B(m,d) \vDash K_A (m,d).$
Albert, Bernard and Cheryl have had a busy week. They’re the stars of #thatlogicproblem, a question from a Singapore maths test that was posted to Facebook by a TV presenter and quickly sent the internet deduction-crazy.
First of all: no, it’s not meant to be answered by an average Singaporean student. It’s a hard question from a schools Olympiad test.
In case you weren’t already excited enough about Matt Parker’s Domino Computer (see: Math/Maths Episode 112, and articles on this website), the Manchester Science Festival blog has posted an official press release about the event, including photos of the domino assembly team lying around on the floor (none of us are professional models, but we did our best for the camera), and quotes from Matt about how important domino computers are.
Top marks go to sometime Aperiodical author Paul, for looking super-bored in the group photo. I’m sure he was thinking about hard maths.