My 2021 book

Landscape of 21st Century Mathematics, Selected Advances, 2001–2020

collects great theorems with elementary statements published in 2001-2020. I now finishing the second edition of this book (draft available on request, e-mail [email protected]), which will cover the period 2001-2025.

I would like this mathoverflow question to complement the book and display the big list of great theorems with elementary statements to be published from 2026 onward.

Here, by "great" I mean on the level of top math journals, such as Annals of Mathematics, Journal of AMS, Acta Mathematica, Forum of Math Pi, or Inventiones mathematicae. I do not require the paper to be published in these journals, just be on the same level (or above). For example, Perelman's proof of the Poincare conjecture exists as arXiv preprint only but is obviously great.

"Elementary statement" means that you can rigorously formulate the result here, starting with only basic undergraduate background. If the main result of the corresponding paper is too technical, but you can present its easier-to-state special case, or elementary corollary, this would be especially interesting. It would be nice if you also provide some background and context, also on elementary level.

I am asking this question now because all top journals just finished the publications of their last issues of 2025. So, all papers not currently published (accepted for publications, under review, just appered in arXiv, etc.) are expected to be published from 2026 onward, and therefore qualify.

It is ok to answer with your own theorems, as soon as they satisfy the requirements. In fact, in cases when the main result is too technical, the author may be in best position to state an elementary reformulation or corollary.