About Alessandro Linzi
Math, AI and what it means to understand
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In 1733 a Jesuit priest named Girolamo Saccheri published a book with a wonderfully confident title: Euclid Vindicated from Every Blemish . He wanted to prove the parallel postulate by assuming it was false and deriving a contradiction. He kept deriving, page after page, and what he built along the way was hyperbolic geometry. He just refused to believe it. In the end he declared the results "repu...
What Theories Can't Do, and What Minds Can
Oct 20, 2026
11 views
This week I kept coming back to one idea: doing math is like going to the gym. I posted that on X on Thursday, and it got more response than anything I've written there so far. I think that's because most of us already feel it. Nobody gets stronger by watching someone else lift. Von Neumann supposedly said that in mathematics you don't understand things, you just get used to them. I used to read t...
The Gym and the Library
Oct 17, 2026
8 views
Math is a human activity. The first thing I do when I encounter a new piece of mathematics is note the name of the person who first created it. Then I go learn about them. Not as a side curiosity. As the main method. I learn their career, their constraints, the problems that obsessed them, the way they thought, the life they lived. I practice cognitive perspective-taking until I can roughly see th...
Math and Mathematicians
Jul 24, 2026
37 views