A fractal spectrum of tales
- Our first month in the University Council
A month has passed since the new University Council (UC) was installed, and I think it’s time to look back on what has happened so far, and what seems to lie ahead. When I enlisted I promised myself to help improve the transparency of the discussions and keep an open channel with anybody that could be interested.
This first month has been a whirlwind of activity, training, and initial discussions. Much of our work so far has focused on preparation: only now I start to see how crucial is to build a good foundation of knowledge and trust for the decisions and actions to come.
5 min read - Oct 6, 2025 - A Different Way Forward
There is a different way forward. Artificial intelligence doesn’t have to be what it is today. We don’t need to accept the logic of unprecedented scale and consumption to achieve advancement and progress. So much of what our society actually needs—better health care and education, clean air and clean water, a faster transition away from fossil fuels—can be assisted and advanced with, and sometimes even necessitates, significantly smaller AI models and a diversity of other approaches. AI alone won’t be enough, either: We’ll also need more social cohesion and global cooperation, some of the very things being challenged by the existing vision of AI development.
1 min read - Oct 4, 2025 - UnAI Education?
I think an update on my previous blog post on generative AI in education is in order. The discussion has been evolving, I am starting to see early signs of polarization, and a mix of denial and overly enthusiastic adoption. Ethical considerations, which had been largely ignored for a good while, are finally getting an increasingly relevant role if not in the decision making, at least in the reflections from many academics. And experimentation is picking up, starting to provide some clarity on the ups and downs of the current revolution.
7 min read - Oct 1, 2025 - AI in Education - Some food for thought
What are we supposed to do about Generative AI in (mathematical) education?
Many of us have been wrestling with it over the past few months. I certainly don’t have a definitive answer, but it’s a topic that demands we share what we’re thinking and what we’re seeing. If anything, it may bring a felt and needed opportunity to finally be able to rethink and reshape the way our education is organized. We discussed this in less uncertain times both in It’s Not Just Numbers and various episodes of Degrees of Freedom, our podcasts on mathematics and education respectively.
7 min read - Jul 29, 2025 - Riemann rearrangement theorem in the browser
One of the first exercises when studying convergence of infinite series asks to show that $\sum_{n=1}^{\infty} \frac{1}{n}$ is divergent while $\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n}$ is convergent. In more technical terms, $\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n}$ is a conditionally convergent series.
This is in contrast to absolutely convergent series, that is, infinite sums $\sum_{n=1}^{\infty} a_n$ such that $\sum_{n=1}^{\infty} |a_n|$ is also convergent.
What is peculiar about conditionally convergent series, is that it is possible to rearrange the terms in the sequence so that the sum of the rearrangement converges to any arbitrary number. This is called Riemann’s rearrangement theorem.
2 min read - Dec 14, 2024 - Running LLMs Locally With Ollama
In my previous post, I explored various ways to run Large Language Models locally. Since that post, I have been pointed to try another powerful tool for this purpose: Ollama. This open-source project makes it incredibly easy to run LLMs on your local machine, offering a great balance between simplicity and flexibility.
While it does not seem as flexible as the
llmpython library I presented in the other post and it can scare some users with its command-line interface, I was impressed by its ease of use and the wide range of models it supports. I am not overselling this, its simplicity is staggering: you can get started with just a few commands.
4 min read - Jul 26, 2024 - Running LLMs locally
Large Language Models (LLMs) are powerful tools for generating human-like text responses. You might be familiar with them through services like ChatGPT, Anthropic Claude, Google Gemini, and Perplexity AI, Nowadays people are using them for editing purposes, writing, brainstorming, and even for generating code snippets. When used responsibly and critically as a tool to assist human creativity, they can be very helpful.
Recently, I spent some time playing with these models and I found them fascinating. However, due to privacy concerns and their high environmental costs, I don’t feel comfortable using cloud-based services. This post is an account of my experience with running LLMs locally on my machines. This can be quite straightforward, and if you have 8-16GB of RAM and a decent GPU, you can run these models on your own computer without significant issues.
7 min read - Jul 24, 2024 - A brief introduction to git, with an eye towards mathematicians
This is a followup to my previous post on git from 11 years ago. I’ve been using git for a while now and I’ve learned a few things since then, that I think are worth sharing.
I am not going to explain in detail what git is, how to install it and how it works; there are plenty of resources for that. It will be enough for our purposes to know that
gitis a version control system that allows you to keep track of changes in your files and collaborate with others.
12 min read - Feb 29, 2024 - Giving Good Maths Talks
The upcoming block I have to coordinate a course on giving good talks. This also meant looking for good extra material for the students to reflect on what it means to give a good talk, what to be aware of and what tips can help to do a good job. Here is a collection of the resources I liked so far:
- MAA has a curated list of resources on giving mathematics talks which includes plenty of examples of good mathematics presentations
- There is an essay by John McCarthy on how to give a good colloquium talk with a response blog post on how to give a good 20min talk
- On the blog of the AMS there is a nice post on preparing a conference presentation, from what it means to many resources on how it can be done
- What characterizes a good presentation? There is a nice summary from an analogous course at MIT
- Terence Tao has a famous blog post on giving talks
- Jordan Ellenberg has a post with tips on giving talks that links an interesting pdf on the same topic
- A nice essay on giving talks by Bryna Kra
Let me know on twitter or mastodon (links on the left bar) if you have other suggestions!
1 min read - Apr 7, 2023 - Panel discussion on the Future of Higher Education
Recently I was invited to participate to a panel discussion as part of a symposium on the future of higher education hosted by our faculty for the launch of the Centre for Learning and Teaching.
I joined other four incredible panelists and we have been given in advance five quite broad (and though) questions on some important aspects of (high) education. I want report here my contribution, with some extra commentary at the end.
6 min read - Mar 27, 2023