Bourgain's Problem Resolved!

June 6, 2025
By Aathreya Kadambi

Today I was reminded by a mentor of the importance of interacting with scientific and mathematical communities that we are interested in. I was inspired by them to take my relationship with research on a more livelihood level and to start reading and blogging more about magazines and general articles.

Already, I’m having a lot of fun and feel like I’m gaining a lot of inspiration! Today I read an article in the Scientific American by Max Springer about a preprint from the end of last year by Boaz Klartag and Joseph Lehec which resolves the Bourgain slicing problem. Klartag told Scientific American: “If you believe in this so-called curse of dimensionality, you might just give up,” but that he and Lehec “belong to a different school of thought.” The curse of dimensionality seemed to me to be a widely accepted phenomenon and fact of life in the data science space, so a bold defiance of it seems cool and inspirational.

Taking a closer look at the preprint, the authors mention that the key technique involved in resolving Bourgain’s problem is the idea of stochastic localization. I was intrigued by the use of probability measures in this seemingly geometric problem, the same ideology that made me enjoy reading about optimal transport. I plan to make a sketch about it on Orange Juice, so I’ll update this post when that’s done! Until then, check out the awesome article by Max Springer, as well as the preprint by Klartag and Lehec!