The Breakthrough Prize Foundation, which is funded by the likes of Mark Zuckerberg, Sergey Brin and investor Yuri Milner, just doled out five $3 million awards to cutting edge math projects (which you almost certainly won't understand).

The Breakthrough Prizesâ€”there have been two previously, for life science and fundamental physicsâ€”are designed to raise awareness of math and make it a more compelling career choice for the young. Sure, $15 million will do that, but really anything that makes people stop and think about how crucial math is to the technology that surrounds us is a good thing.

So, what were the prizes awarded for? Well, pause for one moment to realize that "raising awareness" doesn't equal "making accessible," then brace yourself. Ready? So, they went to:

Simon Donaldson, Stony Brook University and Imperial College London, for the new revolutionary invariants of 4-dimensional manifolds and for the study of the relation between stability in algebraic geometry and in global differential geometry, both for bundles and for Fano varieties.

Maxim Kontsevich, Institut des Hautes Études Scientifiques, for work making a deep impact in a vast variety of mathematical disciplines, including algebraic geometry, deformation theory, symplectic topology, homological algebra and dynamical systems.

Jacob Lurie, Harvard University, for his work on the foundations of higher category theory and derived algebraic geometry; for the classification of fully extended topological quantum field theories; and for providing a moduli-theoretic interpretation of elliptic cohomology.

Terence Tao, University of California, Los Angeles, for numerous breakthrough contributions to harmonic analysis, combinatorics, partial differential equations and analytic number theory.

Richard Taylor, Institute for Advanced Study, for numerous breakthrough results in the theory of automorphic forms, including the Taniyama-Weil conjecture, the local Langlands conjecture for general linear groups, and the Sato-Tate conjecture.

If those projects mean much to you, then you are doing very well indeed. These five winners now automatically form part of the committee who will pick the next winners. [Breakthrough Prize Foundation]

*Image by Tom Brown under Creative Commons license*