A mathematical breakthrough made this year is so complex that other mathematicians struggled to understand it, but it has already led to progress in other areas of maths.
In May, at Yale University and his colleagues published a series of five papers, totalling more than 1000 pages, that proved the geometric Langlands conjecture, in a culmination of decades of work. The problem is actually a simpler formulation of an even grander mathematical project, the Langlands programme, which seeks to make connections between two mathematical fields called number theory and harmonic analysis.
But even this simpler version is fiendishly difficult to understand. at the University of Chicago, who helped formulate the conjecture, told 快猫短视频 earlier this year that it is 鈥渋mpossible to explain the significance of the result to non-mathematicians. To tell the truth, explaining this to mathematicians is also very hard, almost impossible.鈥�
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The papers have been pored over by the mathematical community in the months since they were published, and many researchers have come to appreciate the magnitude of the work, says Raskin.
鈥淭here鈥檚 some people who are really excited about it and glad that this got done,鈥� he says. 鈥淚 heard from a researcher trying to draw from our work recently that there was a very astute thing, deep in one of these long papers, that did exactly what he needed for a different project.鈥�
But not everyone has seen its usefulness, especially researchers who are more focused on the traditional number theory side of the Langlands programme, says Raskin. 鈥淭here are other people who think it鈥檚 a huge, abstract waste of human effort,鈥� he says, adding that at a talk he gave recently, 鈥渟omeone kind of playfully at the end asked, 鈥榳hat鈥檚 the point?鈥欌��
