Alexander Grothendieck’s mathematical work is by far the most important influence on my own. I’m not an obsessive fan who collects everything about him, but I can say that years ago I read some volumes of the samizdat version of Harvests and Sowings (Moissons et semailles), and also the short biography by Philippe Douroux. And heard some anecdotes, mostly second hand, mostly from people who were the students of his former colleagues. Most if not all stories were examples of strange behavior on his part, and the present article is among other things a firehose of such examples. It’s amazing that in his professional days he was so phenomenally creative. I am reminded of Philip K. Dick, another visionary who went mad at the end.
I’ve never seen any of the great pictures this article contains, and the same goes with many names of people and places. On the other hand I know several of the math people who are mentioned in the article, some by reputation, some personally. And if you look him up on wikipedia, Laurent Lafforgue is a kind of mystic too.
I am a total non-mystic by nature, but a few experiments with hallucinogens have given me an idea of the varieties of religious experience, and I find that a mystical quest is a wonderful way to enrich yourr very short stay on this insignificant blue-green planet. That is, if this path suits you. There are many other ways to go.
But if you want to influence others with your own personal discoveries, a very important factor is the quality of your own quest, whatever the path you choose to follow. And this article is yet another facet of the still growing process of enshittification that affects everything that is touched by the current wielders of power in technology. It seems that it’s threatening to engulf just about everything in our lives.
There’s nothing wrong with becoming very rich in computer tech, as a designer of platforms, as a CEO, or whatever. But the current incentive structure which is a product of our present version of capitalism selects and gives enormous power to very small-minded—although extremely driven—people.
What kind of mysticism are you expecting Huawei to harness for the good of mankind?
I want to add that the article contains the best summary of Grothendieck’s work and its place in the greater order of things that I’ve seen written with the purpose of being read by laymen. The author obviously did his homework and contacted the right people. I only want to mention that the sentence “he rarely made use of specific equations” is commonly heard in the relevant subset of the math community, but I disagree. I do believe that he started with simpler examples to build his big theories, like the rest of us, but discarded them at the time he wrote the papers. He had a gift for generating enthusiasm in his high-power research circle (Look up EGA and SGA), and got plenty of help at writeup time.
The headline is misleading. The article knows full well that Grothendieck is not forgotten and itself contains the answer to the question of why he left research mathematics:
Many versions of this story can be found, and they all say the same thing: Grothendieck was such a pacifist that he refused to give any labor to IHÉS as long as it was funded by the military. This is a tough admission for society to make because it leads to the realizations that we needed his insights more than he needed our money, that money can’t buy everything and everybody, and that genius is a real phenomenon.
Also, the author knows nothing of topos theory and embarrasses themselves in the process. A topos (WP, nLab) is a structure which contains everything needed to do mathematics: foundations, logic, objects, a domain of discourse. It turns out that they are quite customizable; there are topoi with/without natural numbers, the Principles of Choice and Excluded Middle, infinitesimals, points, etc. They aren’t esoteric, just difficult to describe formally.
Huawei is getting soft power by picking brilliant researchers all over the world and funding them to work on whatever they want in Huawei’s name. My personal guess is that they don’t care what people do as long as they are famous and it is recognized as good work by the rest of the community. They have an easy time doing this because western countries are chronically under-funding research, far from meeting their commitments in term of GDP percentage, and moving to less and less pleasant research management and bureaucracies to try to hide the lack of support. (As in: concentrate all your money to a few key areas that politicians think are going to deliver breakthrough (for example: AI, quantum computing), and stop funding the rest.) Foreign countries with deep-enough pockets that play the long game can come up, create prestigious research institutes for reasonable amounts of money, and get mathematicians or whatever to work in their name. You can tremendously improve the material working conditions (travel funding, ability to hire students and post-docs, etc.) of a Fields medal for one million euro a year, that’s certainly a good deal.
(Google and Microsoft did exactly the same, hiring famous computer scientists and letting them do whatever they wanted. In several cases they eventually got rid of the teams that were created on this occasion, and people were bitter about it. Maybe China can offer a more permanent situation.)
Lafforgue claims that Huawei is interested in applications of topos theory, and more broadly category theory, to AI and what not. Maybe he is right because brilliant researchers manage to convince themselves and Huawei intermediate managers of potential applications. Maybe he is delusional and Huawei does not give a damn about industrial applications as long as they get recognition out of it.
Check the employment of Rust core active devs ;)
Rust is something that makes sense as a part of a sound long-term business strategy. It’s a bit too early to tell, but being one step ahead of other companies in Rust may be strongly beneficial in order for the company to build better products and have larger impact. It is a good opportunity for visibility, soft power, but it also directly gives power/leverage to the companies that develop the language. (I view this as a similar investment to being an active participant to the Javascript evolution process, in particular its standardization bodies. Or wasm, etc.) The situation with topos theory is very different, because it is, in terms of practical applications, completely useless just like most contemporary mathematics; I don’t think that anyone in the field expects any kind of industrial applications of topos theory in the next 30 years. Of course we never know, but let’s say it is not more likely than many other sub-fields of mathematics. This is interesting and valuable fundamental research but, from an industrial perspective, a vanity project.
(There is another sub-field of category called “applied category theory” which is more interested in the relation to applications, and may have applications in the future, for example by helping design modelling languages for open systems. Industrial impact is still much farther ahead than most companies would tolerate, and this is not the same sub-field that is being discussed in the article and by Lafforgue.)
I had to wait for ideas to stop colliding in my head before I wrote a reply. You can guess that something was on my mind and that the article triggered me. Typical of such situations, I did a certain amount of projection too. BTW I’ll never remotely approach JD Vance’s level in this category of behavior. When there are Paralympics for psychological projection Vance will be given an honorary eternal gold medal that will forbid competition, to allow mere mortals to compete.
I maintain that my snark with respect to mysticism was and is and will forever be justified. But boy did it ever hit the wrong target. Lafforgue happened to be there, while some much needed context was definitely not. Many thanks to @gasche for the update, it allowed me to skip research on the circumstances of that fellowhip.
You see, I happen to be one of those who intend to use topos theory in real-world situations. And if I was offered a pile of money to do what I want with toposes, no strings attached, I’d think seriously about it. I’d only make sure of the provenance of the money before saying yesyesyes. So congrats to Laurent. Maybe some time from now we’ll compare notes. The Chinese are known for questionable business practices, but this current wave of hiring scientific celebrities is just good business sense. It should be seen as fair competition. It wouldn’t have happened if the powers of foresight of current Western tech (and automobile) bigwigs hadn’t shriveled to their current sub-dismal level.
I recently had an exchange of PMs on a social network, with a guy who’s reputed in the topos set, among other specialized mathematical circles. I told him I remembered some conversation we had, naming others who were there and he didn’t remember me at all then. Could be different now, I mentioned plenty of people he knew who would help him if he ever felt like knowing my name. I have to say I enjoy my Zelig status in the topos community.
I haven’t seen Olivia in easily 20 years. If she ever reads these lines she’ll either identify me instantly… or be puzzled for some while, see example above. I once had nice conversation with Pierre Cartier during a bus ride on the excursion afternoon of a conference and he surely wouldn’t have remembered me after a year, let alone 20. RIP Pierre. And last year I had several chats with Georges Maltsiniotsis. OK I can stop the name dropping, adding more people is now pointless.
BUT I’ve never met Laurent Lafforgue. I know he’s a serious Catholic, but I have no idea if that has any bearing in his topos-theoretic research.
AND I know deep down inside that if you want to have insights about reality, just don’t rely on mysticism to leapfrog into a higher realm that will hand you nuggets of wisdom you can then spend translating for the benefit of mankind at your leisure, when you’re back on the ground. If you want to apply topos theory to reality, start from the bottom and look at the world around you, the world of shapes and smells and interaction and communication between organisms of all kinds and sizes. Keep the laws of physics in mind, and perhaps most importantly cultivate a Darwinian frame of mind. Darwin was a bottom-up guy if there ever was.
BTW during his ecological phase Grothendieck was very much against physics, if my memory serves me well.
@milosgajdos I intend to buy that book, thanks for the tip.
There is a wonderful book I really enjoyed reading a while back that contains a chapter about him (Grothendieck) [1].
[1] https://www.amazon.co.uk/When-Cease-Understand-World-INTERNATIONAL/dp/1782276149