There is an object that is called Fargues-Fontaine curve, which is so groundbraking that it might help solving three of the million-dollar Millennium Prize problems: the Riemann hypothesis, the Birch and Swinnerton-Dyer conjecture and the Hodge conjecture.
If you ever known a mathematician then you must have heard about how one day s/he’ll solve the Reimann hypothesis for a good ole’ million bucks. But what is at stake is much more connected to a breaktrough in number theory which in turn leads to – well first at least – to a set of novel encryption cracking methodology.
The aforementioned curve is something at the center of the Langlands program, itself named after the renowned math visionary, Robert Langlands. The program is an attempt to solve calculations not by algebra but by the analysis of automorphic form objects. Now “It’s remarkable that these objects of a very different nature somehow communicate with each other,” Ana Caraiani of Imperial College London quoted as saying.
In laymen’s terms it means that the wide gap of the clean logic of the algebra and the equally clean logic of geometry might be tightened one day with the help of the third field of the mathematics that is analysis.
In other context, it is yet another promising opportunity to compute something big for a very long time for a lot of peanuts that frankly noone understands but many will want to have. Just as the original Fargues-Fontaine curve was machine computed for a sum equal to the GDP of some African countries, the Langlands program – which is “a kind of grand unified theory of mathematics” will cost a fortune without anyone ever understanding what it is all about. Or as the Wikipedia entry puts out: “To a lay reader or even nonspecialst mathematician, abstractions within the Langlands program can be somewhat impenetrable” and that “The Langlands program is notorious for being hard to explain to non-experts. Perhaps only 1% or so of professional, university-employed, research mathematicians have a decent gasp of what it is“.
Wow. I wanna be part of the fundraiser team for the next-gen Reverse Temporal Engineering AI that will compute it. Word on the street is that it will be called Infinidim Enterprises Guide Mark I