When things get complicated, math proves it’s literally impossible for one person or thing to be the GOAT at everything.
March 20, 2026
Original Paper
Pareto points in growing dimensions
arXiv · 2603.18698
The Takeaway
In our 3D world, one object can easily 'dominate' another by being smaller, cheaper, and faster all at once. However, this study identifies a phase transition where, as dimensions increase, almost every single point becomes 'optimal' in its own way, making it impossible for anything to be the overall winner across every category.
From the abstract
We consider $n$ independent random points uniformly distributed in the $d_n$-dimensional unit cube and study Pareto points, that is, points that do not coordinatewise dominate any other point. We identify the critical growth rate of $d_n$ at which a phase transition occurs: below this threshold, the number of non-Pareto points diverges in probability, whereas above it there are asymptotically no such points. At criticality, the number of non-Pareto points converges in distribution to a Poisson r