Michel Talagrand: Advice to Young Mathematicians (2024) [video]

This one really stuck for me: "focus on something special, then expand from there".

I have time and again fell victim to fulfill all the prerequisites before I begin to attempt to understand a topic. This is a mistake I have made repeatedly. I now understand why this is tempting to do and why it is a mistake.

It is tempting to do so because you feel things will come easier to you if you fulfill the prerequisites first. But the problem is that there is just not enough time. AND, it actually may not be even necessary.

It is a mistake to do so because you are wasting time and ultimately it may not be necessary after all.

Even in a field such as pure mathematics (I have an MS in pure Math), it is okay to skim through some of the background material and understand it intuitively or even non-rigorously, while focusing on what you want to actually learn.

It took me a while to learn that and I am glad it is being repeated here by such an accomplished professor.

Not a Mathematician myself, but I totally agree with him regarding the benefits of choosing Mathematics as the career.

My father is a Mathematician with small fame. He was obsessed with Mathematics when he was a kid. In fact, Mathematics was the single thing that helped him to move through the political turmoil during his first 30 years of life.

I'll also quote a paragraph from Cixin Liu's "Ball lighting". It's related.

> "Of course I know!" Dad took another half glass of wine, then turned to me, "Actually, son, living a wonderful life is not difficult. Listen to Dad: choose a universally recognized world problem, preferably a mathematical one that only requires a piece of paper and a pencil, like the Goldbach Conjecture or Fermat's Last Theorem, or a pure natural philosophy problem that doesn't even need paper and pencil, like the origin of the universe. Dedicate yourself entirely to it, focus solely on the process, not the outcome. In the unconscious focus, a lifetime will pass. What people often refer to as a 'pursuit' is just this. Or, conversely, make earning money your sole goal, always thinking about how to make money without considering what to do with it. By the time you die, you can, like Grandet, hold a pile of gold coins and say, 'Ah, so warm...' Therefore, the key to a wonderful life is what you can become passionate about. For example, me—" Dad pointed to the small watercolor paintings placed all around the room. They were all very traditional in technique, well-painted but lacking any real inspiration. The paintings reflected the electric light from outside the window, like a group of flickering screens, "I became passionate about painting, even though I know I can't become Van Gogh."

The video is by the mathematician Michel Talagrand.

https://en.wikipedia.org/wiki/Michel_Talagrand

A surprising tip from his personal page.

"If you are desperate to get my books and your library can't afford them, try to type the words "library genesis" in a search engine. I disagree with piracy, but this site saved me many trips to the library, which unfortunately does not carry electronic versions of older books."

http://michel.talagrand.net/

Reminds me a bit of Feynman, and his advice on working "fun" topics that aren't necessarily high-impact or important, but feel interesting to you - as they increase your self-confidence and joy.

The example he used from his own work escapes me, but he had spent years working on topics quite unrelated to quantum mechanics, just out of pure interest and curiosity.