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Sizable article - write down a few highlights about the Langlands program. > Mathematics has received a rare gift, in the form of a mammoth 350-page paper post
by rohanphadte 5y ago
Sizable article - write down a few highlights about the Langlands program.
> Mathematics has received a rare gift, in the form of a mammoth 350-page paper posted in February that will change the way researchers around the world investigate some of the field’s deepest questions.
> The work is a collaboration between Laurent Fargues of the Institute of Mathematics of Jussieu in Paris and Peter Scholze of the University of Bonn.
> It opens a new front in the long-running “Langlands program,” which seeks to link disparate branches of mathematics — like calculus and geometry — to answer some of the most fundamental questions about numbers.
> The Langlands program is a sprawling research vision that begins with a simple concern: finding solutions to polynomial equations like x2 − 2 = 0 and x4 − 10x2 + 22 = 0.
> “The Langlands program is a network of conjectures that touch upon almost every area of pure mathematics,” said Caraiani.
- db48x 5y agoThat’s “x² − 2 = 0” and “x⁴ − 10x² + 22”. We should all take more care to transcribe exponents correctly when copying between media. (Actually, we should go back in time and prevent anyone from inventing superscripts and subscripts entirely, but that is a longer–term goal.)
- Aerroon 5y agoThis has been bothering me since I basically started using computers: why are default inputs for computers so bad for writing math? Computers are basically bathed in the field of mathematics and yet writing math with a computer is quite an unpleasant experience. Why?
- darig 5y agoBecause you didn't manufacture the keyboard you think you want? Enjoy your 3 customers. The rest of us aren't bother to learn the alt codes.
- yetihehe 5y agoToo many years of inadequate display technologies (text only) plus some powerful notations which could describe math to computers in other ways (using functions like sqrt() and pow()). Also mathematicians like to invent typographically hard to use symbols, which would need to be widely implemented first before they can publish their research, so programmers only make specialised packages for mathematicians instead of system-wide support.
- nabla9 5y agoBecause Don Knuth only invented digital typesetting he had time to only write TeX and Metafont. Had he also done the same for display managers, we would be fine.
- db48x 5y agoThe notation is far too complex and ambiguous, with too much reuse of notation to mean different things in different subfields. For example, superscript numbers are used for exponents, and subscripts are for indices, right? Well except for certain cases where vectors are indexed by superscripted numbers instead. Mathematicians should have been taught to use Scheme syntax instead.
- deleted 5y ago[deleted]