Dear Professor Graham White, Reading your email made me happy in more than one respect, one of which is that which you suggest emphasizing, i.e., the conceptual and the geometrical side of mathematics dating back to ancient Greece (in the words of Professor F. William Lawvere): https://conceptualmathematics.wordpress.com/2012/09/23/comfortable-with-sheh... I just thought you might find it of some interest. Thanking you, Yours respectfully, posina P.S. Early this morning, I asked the shopkeeper, who gave me a bill of Rs. 6009, for a 1 rupee candy, so that I can pay a round figure of Rs. 7000 (happy to be in your good company ;) On Mon, Jun 1, 2026 at 2:31 PM Graham White via Categories <categories-list@categories.org.au> wrote:
This is very depressing. I've always been on the geometrical, conceptual side of mathematics (and I've never really been any good at numerical calculation). And the geometrical side of mathematics goes very far back, to ancient Greece at least. Could we not try to emphasize this?
Graham White London
On Mon, 1 Jun 2026, 08:20 peklund via Categories, <categories-list@categories.org.au> wrote:
Why do we have this development?
Decades ago the famous categorists were still young or at least younger and still working. Today we have a new generation of categorists teaching category theory and sharing memories of times when now the oldies were younger, and when everybody felt self-confident and proud about being part of the CT community.
Young students now, unfortunately for CT, have more options to feel self-confident and proud.
Category theory is useful, always was. Bernays and Gödel never saw that, but never mind (until the PS). CT is useful in math. CT is useful in computer science. CT is useful in real applications, but that was never acknowledged.
Are we ourselves to blaim for not having transformed CT to something that lives and survives through times. Has it been too introvert?
Just wondering.
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Is there a silverlining? What can we do?
CT in CS has often been seen as a good example where CT comes into play. And it does, still today. But I cannot see it has improved, so CT in CS may decline similarly in a decade or two. I may be wrong, I hope I'm wrong, but I say so since I was recently at the Types 2026 conference in Gothenburg. I haven't been at those for a while and now I wanted to see if there is something new in CT in CS. I didn't see anything, I should to say, but thanks to a plenary (by Emily Riehl) there was at least a plea for CT (teaching) to remain in CS (teaching).
Of course, there are CS teachers who can teach CT, but many of them are also not interested in real applications at all. Very few if any can explain why we need CT.
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"Real applications", what's that?
I was nominated to professor in 1995, and from start I recognized my three tasks, i.e., tasks we recognize as our three tasks in universities. One, we teach. Two we do research. And it is in that order! Three, we cooperate with the surrounding society. We are obliged to do one and two, and CT teachers often do not have the luxury and time of doing two. Not even CT professors.
Take CT people and take math people in general. Is there a difference between how they at average engage in the third task (ignoring the situation about how much time they have for such engagements)?
Am I right or am I right?
If I'm right, what happens before a meeting between a categorist professor and, say, a medical professor. Will the medical professor be curious to know something about CT "before" the meeting? No. Will the CT professor be curious to know something about the medical domain to be discussed "before" the meeting? Should be, but in most cases will not. So what happens after the meeting? The medical professor go backs to office and continues research in, say, cardiology. The CT professor goes back to office and continues to remember the good old days when we didn't even think about talking to professors in other disciplines.
Am I wrong or am I wrong?
If I'm wrong, then there is hope, otherwise not.
And whenever we might go "real", do remember that we must "FIRST find the problem, THEN design a solution", not the other way around ("FIRST design a solution, THEN find a problem where the solution comes into play").
I rest my case.
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Best,
Patrik Eklund
PS CT became CT some less than a century ago. Suppose CT had become CT some decades before, say, even before Hilbert wrote his foundations of geometry. In that case, CT had been around by the time Bernays was recruited to Göttingen, and I bet Gödel's ideas would never have reached publication in 1931. Hilbert's and Bernays' two volumes on the foundation of mathematics might even have been preceded by another two volumes on the foundation of the foundation of mathematics. Who knows. I bet Mac Lane never thought about it that way. Otherwise he would have called Bernays and said "Hey, we really need to talk!". But I don't see that in Bernays correspondence, so here we are, 75 years later, still not talking to each other.
On 2026-05-31 16:29, Steven Vickers via Categories wrote:
Hi Peter,
I'm sad to hear of the decline of category theory in the Maths Faculty.
All the same, I know there are people in the Computer Lab who would be be qualified to teach it at pt III level, and they would be on the University payroll. Is that route not possible for some reason?
To me it's a sign of how category theory has developed into a piece of applied maths, just not in the DAMTP sense. At Birmingham too, nobody in the School of Maths really does category theory.
All the best,
Steve.
________________________________ From: P.T. Johnstone via Categories <categories-list@categories.org.au> Sent: Friday, May 29, 2026 10:11 AM To: Marino Gran via Categories <categories-list@categories.org.au> Cc: P.T. Johnstone <ptj1000@cam.ac.uk> Subject: [categories] Category Theory under threat in Cambridge
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As many subscribers to this list will know, I have continued to lecture a course on Category Theory in Part III of the Mathematical Tripos in Cambridge every year since Martin Hyland and I retired (there being no-one on the current Faculty who is able to do it). I'm quite proud of the fact that I didn't even miss a year as a result of Covid!
I have now been informed that Cambridge University has a new policy of not allowing people who are not on the University payroll to teach examinable courses, which if implemented strictly means that Category Theory will cease to be an option in Part III from next year.
I know that there are many people on this list who first encountered categories through Martin's or my Part III lectures. If you feel, as I do, that the suppression of this option is a disgrace to Cambridge, I'd be grateful if you could write to the Head of DPMMS, Ivan Smith (is200@cam.ac.uk) and tell him so.
Peter Johnstone
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