Archive for Fields medal

Nature tidbits [6 Aug 2026]

Posted in Books, pictures, University life with tags , , , , , , , , , , , , , , , , , , , , , , , , , on October 7, 2026 by xi'an

The 6 August issue of Nature arrived after my return from Japan, but it took me a while to catch up, the more because its cover story, Bloom service, about fertilising the oceans with iron as a carbon sink did not appeal much to the geoengineering sceptic in me. Nice pun though. Flotsam of interest for me:

  • an article on GPT-4 (and open-weight models) predicting the outcomes of 70 preregistered US survey experiments, 469 effects and 119,330 participants in total. The predicted treatment effects are highly correlated with the observed ones, about as well as pooled human forecasters do, including studies published after the training cutoff. But the predicted effect sizes are systematically too large, which is not a minor detail for a field still recovering from its replication crisis! Plus a survey of 460 social scientists about using LLMs for pilot testing, and a web app to “forecast” your own experiment’s effect before running it. (I wonder what a prior elicited this way would look like.)
  • a paper on membership inference attacks on medical AI models, showing that patients who differ from the majority are the easiest to identify as part of the training data, which I already discussed here. This fits the long-known issue with differential privacy and outliers.
  • a story on the four 2026 Fields Medals, announced at the ICM in Philadelphia, in fields far, far away:
    • Yu Deng (Chicago), for his work on PDEs, including a rigorous derivation of the Boltzmann equation from hard-sphere dynamics (with Zaher Hani and Xiao Ma), wave kinetic equations, and probabilistic approaches to nonlinear Schrödinger equations.
    • John Pardon (Stony Brook), for symplectic topology and enumerative geometry. He started as an undergraduate by answering a question of Gromov on knot distortion.
    • Jacob Tsimerman (Toronto), for extending techniques within arithmetic and complex algebraic geometry and solving conjectures in this field.
    • Hong Wang (NYU and IHES in Bures-sur-Yvette, almost a colleague!), for Fourier restriction, progress on Falconer’s conjecture and, with Joshua Zahl, the resolution of the Kakeya conjecture in three dimensions.
  • a feature on the scientific papers most cited in patents.
  • a news item on a Science paper by Blasi, Hamilton, Gray and Bowern, estimating that humanity may have spoken tens of thousands of languages between 3,000 and 1,000 years ago. The paper suggests a shift away from nomadic life triggered this diversity before it collapsed. I wonder at how deep the statistical linguistics inferring this rich past from the surviving sample goes. In a sense, the finding is not that surprising, given how isolated small prehistoric communities were, and how quickly a language drifts apart without contact. (I would also like to check how much the estimate depends on the assumed birth-and-death rates of languages, since the lost ones leave no trace to calibrate against…)
  • an editorial on the White House’s “new golden age for science” plan. It argues that such a golden age needs open borders and funding for the social sciences, public health and the humanities, not only AI and engineering. Alas, the now usual Trump.2.0 fare, with an AI funding roll-out in the news pages.
  • an emergency call by WHO director-general Tedros Adhanom Ghebreyesus on why the WHO has never been more needed, and news that the first volunteer received an Ebola vaccine three months into the current outbreak.
  • a forecast that the coming El Niño should be the largest (by a mind-blowing margin) on record, pushing 2027 temperatures to new highs. And already having severe impact on tropical weather.
  • a scary comment on the risks of nuclear-powered merchant ships, in the very issue dated on the anniversary of Hiroshima…

AIs rushing to the proofs

Posted in Books, Kids, University life with tags , , , , , , , , , , , , , , on June 23, 2026 by xi'an

A “Feature” article in Nature (21 May 2026) and a long article in the New York Time (June 8, 2026) are both covering the sudden intrusion of AIs in proving or disproving mathematical conjectures… Genuine, hard, conjectures likes Erdös problems. Specialised AIs like Alethia, Math Inc., AlphaProof are hacking at existing open problems and a benchmark collection of problems whose solutions are not available (yet) called First Proof has been recently gathered, solved by OpenAI,  and is soon to be extended. In an earlier interview with Nature (27 April 2026), Terry Tao acknowledges the tectonic shift represented by this intrusion and how a mathematician’s skill need evolve. (This is also the starting point of the NYT story. ) A side issue of this is that reviewing the proofs thus produced by an AI may prove inhumane if it reaches hundreds of pages, which also relates to the un-academic (?) tendency of AIs companies to over-blow the results produced by their machines. For the times they are a-Changin…

The Guardian on [and on and on] Grothendieck

Posted in Books, Kids, Mountains, University life with tags , , , , , , , , , , , , , on September 11, 2024 by xi'an

A very looong piece in The Guardian of 31 August relates the life and achievements of Grothendieck in a highly romanticized way, hinting at hidden secrets contained in the tens of thousands of pages he wrote during his 26 years of retirement in Lasserre, Pyrénées… (Even when acknowledging that Grothendieck’s life and personality are providing enough fodder for a whole series of novels!)

“Grothendieck’s genius defied his attempts at erasing his own renown. He lurks in the background of one of Cormac McCarthy’s final novels, Stella Maris, as an éminence grise who leads on its psychically disturbed mathematician protagonist.”

With very little about maths, apart the mumbo-jumbo usually associated with non-specialists trying to convey the unique ability of a researcher with images and allegories aplenty! The only factual information is that Huawei sees worth in Grothendieck’s concept of topos (within his general theory of categories) toward future AIs and that they hired French 2002 Fields medalist Laurent Lafforgue to explore this subject (besides not mentioning Huawei creating an algebraic geometry chair at the IHÉS, the very place Grothendieck resigned from due to IHÉS receiving military funds).

“Applied to AI, toposes could allow computers to move beyond the data associated with, say, an apple; the geometric coordinates of how it appears in images, for example, or tagging metadata. Then AI could begin to identify objects more like we do – through a deeper “semantic” understanding of what an apple is. But practical application to create the next generation of “thinking” AI is, according to Lafforgue, some way off.”

The author of the Guardian piece, Phil Hoad, is also very reserved about the ultimate purpose of Huawei in funding this research (and the new Centre Lagrange in the centre of Paris), for its obscure links with the Chinese Government and the Chinese military, a concern also expressed by some French mathematicians who signed a tribune in 2021 calling for a boycott of the Centre… But leaving open the door open on whether or not the unexplored thousands of pages blackened by Grothendieck could contain mathematical gems, rather than esoteric ramblings aggravated by his complete shunning of society. Which sounds quite unlikely.

law of small numbers

Posted in Statistics with tags , , , , , , , on June 22, 2022 by xi'an

secrets of the surface

Posted in Statistics with tags , , , , on October 30, 2020 by xi'an