#Dennis #Gaitsgory has dedicated the past 30 years to proving the #geometric #Langlands #conjecture.
Over the decades, he and his collaborators have built an extensive body of work, forming the foundation of the new proof.
Although the geometric Langlands program is highly abstract, it forges deep connections between different mathematical structures
and has the potential to drive breakthroughs in theoretical physics, number theory, and even quantum computing.
The #Breakthrough #Prize was established in 2012 by Sergey Brin (Google), Mark Zuckerberg (Facebook), and others to recognize outstanding researchers for their groundbreaking discoveries.
It is awarded in the fields of life sciences, physics, and mathematics.
In 2016, the Breakthrough Prize in Life Sciences was awarded to #Svante #Pääbo from the Max Planck Institute for Evolutionary Anthropology in Leipzig,
and in 2022, to #Anthony #Hyman from the Max Planck Institute for Molecular Cell Biology and Genetics in Dresden.
https://www.mpg.de/24476145/breakthrough-prize-mathematics-2025?c=2249

#conjecture : an opinion, or judgment, formed on defective or presumptive evidence

- French: conjecture

- German: die Vermutung

- Italian: congettura

- Portuguese: conjetura

- Spanish: conjetura

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33-year-old mathematician Wang Hong from the Courant Institute of Mathematical Sciences (CIMS-NYU) has proved the century-old Kakeya conjecture in three dimensions with collaborator Joshua Zahl!

The problem is rooted in the question: what's the smallest area that an infinitely thin needle can sweep out if it has to be turned to point in every possible direction?

News:
[1] https://www.scmp.com/news/china/science/article/3300958/chinese-maths-star-wang-hong-solves-infamous-geometry-problem
[2] https://english.jagran.com/world/chinese-student-wang-hong-cracked-an-impossible-geometry-puzzle-that-stumped-mathematicians-for-over-a-century-10221886

2023 piece from Quanta Magazine on their earlier progress on the problem:
https://www.quantamagazine.org/new-proof-threads-the-needle-on-a-sticky-geometry-problem-20230711/

@tao
#WangHong #CIMS #NYU #JoshuaZahl #Kakeya #KakeyaConjecture #ThreeDimensions #Needle #Geometry #QuantaMagazine #Conjecture #AdvancingMaths #Maths #Mathematics #CenturyOld #Tao #TerenceTao

#Poincare on #Intuition in #Mathematics

Very interesting paper by Henri Poincaré on 'Intuition and Logic in Mathematics' from 1905.

In this piece he presents intuition not just as a psychological trait, but as a critical component of mathematical creativity and innovation.

https://mathshistory.st-andrews.ac.uk/Extras/Poincare_Intuition/

Fermat conjectured that for \(n\) a non-negative integer, all numbers of the form \(2^{2^n}+1\) are prime.

Was there ever a worse conjecture in maths than that?

#Maths #Math
#MathsEd #MathEd
#MathsChat #MathChat
#Fermat #Conjecture
#Primes #FermatPrimes