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Stream: community: events

Topic: INTERNATIONAL DAY OF MATHS & π DAY 2026

John Baez (Mar 14 2026 at 17:16):

A message from the first mathematician pope:

Pay attention to the moral dimension of emerging technologies, Pope Leo XIV urged in a message sent on Friday to mark the International Day of Mathematics.

In the message, sent to Professor Betül Tanbay, Chair of the International Day of Mathematics, and signed by Cardinal Secretary of State Pietro Parolin, the Pope offered cordial greetings to all those taking part in the webinar on the theme “Mathematics and Hope.”

In the context of the manifold challenges facing the human family, "not least rapid technological development with all its potential for good or evil," the Pope encouraged participants to consider how mathematicians can be hopeful signs to the wider world.

"Manifold challenges". :laughing:

Use of algorithms in AI

In this regard, Pope Leo suggested that an especially fruitful area of research is the use of algorithms, particularly in artificial intelligence.

“Such a task,” he said, “requires not just intellectual effort and ingenuity but an integral growth of the whole person, in order to encompass the moral dimension of these emerging technologies.”

Humanizing the digital sphere

Recalling his own time as a teacher of mathematics and physics, Pope Leo XIV reiterated that having a great deal of knowledge is not enough if we do not know who we are or what the meaning of life is.

Oh-oh, then I'm in trouble.

Federica Pasqualone 🦅 (Mar 14 2026 at 17:40):

It seems he likes geometry :stuck_out_tongue_closed_eyes:

Federica Pasqualone 🦅 (Mar 14 2026 at 17:43):

Well, I was having a conversation with an Indian colleague a couple of days ago, about all this AI business and our role. It seems Harvard university tested AI on hard problems with poor results. AI cannot replace the human intellect, our capabilities of moral intuition, meaning-making, surfacing the invisible ... (just food for thoughts :thought: )

Federica Pasqualone 🦅 (Mar 14 2026 at 17:44):

At least, that's my humble opinion.

Jean-Baptiste Vienney (Mar 14 2026 at 17:58):

I agree with you. To me LLMs are mainly improved search engines. They are better to find the information you need, although sometimes what they provide you is bullshit :sweat_smile:. For instance I can take a picture of some plant and it tells me what plant it is and how often I should water it. I think it would be more difficult with Google.

Jean-Baptiste Vienney (Mar 14 2026 at 17:59):

I love the ability of LLMs to identify plants :potted_plant:

Jean-Baptiste Vienney (Mar 14 2026 at 18:01):

I can also use them to estimate the cost of living in some country. It can help you making some imprecise budget

Federica Pasqualone 🦅 (Mar 14 2026 at 18:04):

There are all sort of applications in business actually! It sounds it's doing great there!

Jean-Baptiste Vienney (Mar 14 2026 at 18:05):

It makes sense when you see how much money is invested in them by companies. But I hope it will lead to improvements for customers rather than just companies making more money

Federica Pasqualone 🦅 (Mar 14 2026 at 18:07):

But yeah empathy, emotions, care and love for each other ... we are not just made of logic (fortunately!) :thought:

Jean-Baptiste Vienney (Mar 14 2026 at 18:11):

Sure! And we can also say that LLMs are not even better at logic than ourselves :sweat_smile:

John Baez (Mar 14 2026 at 22:30):

Someone gave me a free subscription to Claude, so I decided to test it out. I've been using it to do long calculations on the math of music theory and present the results using interactive web pages like this.

I've also been using it to learn math. Here it seems important to keep checking its claims and asking it to explain any jargon it uses. I've been reviewing some stuff I half-understand about the Langlands program and trying to learn some more. It seems very useful.

I usually try to give it very precise requests, but yesterday I decided to just tell me something exciting. I could see it going through various topics I'd talked about... octonions, tuning systems.... and eventually it said this:

The three distance theorem (Steinhaus conjecture, proved in the 1950s by Sós, Świerczkowski, and Surányi independently): take any irrational $\alpha$ and place the points $\{\alpha\}, \{2\alpha\}, \ldots, \{N\alpha\}$ on the circle $\mathbb{R}/\mathbb{Z}$ . The gaps between consecutive points take on at most 3 distinct lengths. And when there are exactly 3 lengths, one of them is the sum of the other two.

The reason I think this might excite you: it's a theorem about 1-dimensional Diophantine approximation on the circle, and the three lengths are governed by the continued fraction expansion of $\alpha$ . The transition from 3 lengths to 2 happens exactly when $N$ is a denominator of a convergent of $\alpha$ .

All this makes sense to me. I checked the main claim in an example that's important in music theory - and it works, and indeed explains a lot of stuff.

@ww has been using Claude more seriously. Today here he showed how Claude figured out that a method of refactoring some code should be a natural transformation between functors, and then went ahead and did that refactoring.

So while there are lots of reasons to be very suspicious of LLMs, and as currently deployed they may be be quite carbon-intensive, they can indeed transform the practice of doing mathematics and writing software.

Jean-Baptiste Vienney (Mar 15 2026 at 02:01):

That’s exciting! I’ve only been using ChatGPT but I’ve been told that Claude is better at science. I have mixed feelings about talking about mathematics with ChatGPT (it can help me learning some concepts or find references but it is inventing so much that I’m never sure about anything it’s saying). Since you say it helps you learn things, now I definitely want to try Claude

John Baez (Mar 15 2026 at 04:28):

I find Claude Opus a lot better than Claude Sonnet, and it's possible you may only have access to Claude Sonnet unless you have a subscription - I'm not sure.

Federica Pasqualone 🦅 (Mar 15 2026 at 07:43):

Interesting! Yes, but there is some magic in doing math with chalk and blackboard, in learning from people, in building a community from which and with which one learns. I know, I am very old-fashioned - or maybe is because of my obsession with leadership, but I love humans better! :innocent: