Hong Wang, Joshua number
The “amazing” advance solves a barrier to many other mathematical issues. It seemed “impossible”, but it was the lack of counter-exposes that eventually solved the problem.
The greatest advance of the 21st century in the “needle problem”. This is how you describe it. But there are those who go further: “This work is perhaps the greatest advance of mathematics in the present century,” says mathematician Nets Katz.
The problem, first formulated in 1917 by Sōichi Kakeya, is easy to state (just not so much to explain): How many shapes can have a needle while turning 360 degrees?
The mathematicians considered the issue of an infinitely thin needle and found that the area the smallest way to turn it was zero, even with a definite length.
An issue that became known as Kakeya’s conjecture asks if the dimension of the form drawn by the needle maneuvers would always be the same as that of the space in which it moves. This issue has been proven for a 2D needle, but so far it had never been for 3D needle cases.
Until now. Mathematicians Joshua Zahl and Hong Wang proved in a new The volume through which the needle moves must also be 3D.
“We shouldn’t be enthusiastic too, because many mathematicians, at the time of their life, thought they had solved a serious problem,” says Zahl. “In the past, I thought I might have resolved Kakeya’s conjecture for one afternoon and then I realized that it was just an impossible dream.”
“Impossible” was the word in which even the researcher himself believed. But together, the team eventually came to a conclusion… walking back instead of “forward”.
They started by creating imaginary counter-exples. But they found that all these counter-exposes contradicted theories previously proven. Now, If counter-exemplos are not possible, the conjecture has to be true.
“In my analysis subcampo, it is certainAnd the biggest advance in the last 10 years“Comments the mathematician Terrence Tao. “This conjecture is part of a whole family of problems that seemed impossible.” In addition, he adds, “They took much more profit from this method, is frightening“.
According to Katz, this new proof “Solve a problem completely which was attacked by a variety of techniques by several of the main figures in the area, most of which only obtained modest partial results. ”
Tao says that now there are several “unlocked” problems: “I predict years and years of activity throughout this tree of more difficult problems in Numbers Theory, Partial, combinatory differential equations, and so on, which were considered hopeless and now seem very difficult. ”
