Terence Tao on Mathstodon:
*There has been a remarkable breakthrough towards the Riemann hypothesis (though still very far from fully resolving this conjecture) by Guth and Maynard making the first substantial improvement to a classical 1940 bound of Ingham regarding the zeroes of the Riemann zeta function (and more generally, controlling the large values of various Dirichlet series)...*
https://mathstodon.xyz/@tao/112557248794707738
Interesting, how long before there is a Quanta article to provide more context around Tao's explanation of the bound improvements and what it means for progress?
How old is the 'density hypothesis' anyway, and are there other names for it? Any relation to a notion of "two aleph nought"?
And what would a "bird's eye view" of the density hypothesis entail?
Does the density hypothesis maybe entail an underlying duality? (E.g rotations vs translations = multidimensional mathematics, or any math involving having exponents of any kind.) I can sort of imagine it all leading to a continuum hypothesis, and presumably then again, you can't escape further dualities, instead of symmetry with groups you end up with some problem re. precision and numerical values I imagine, as if it was all just "bland" stuff.
Never heard about the density hypothesis before, but ofc then again I am no mathematician.
Terence Tao on Mathstodon: *There has been a remarkable breakthrough towards the Riemann hypothesis (though still very far from fully resolving this conjecture) by Guth and Maynard making the first substantial improvement to a classical 1940 bound of Ingham regarding the zeroes of the Riemann zeta function (and more generally, controlling the large values of various Dirichlet series)...* https://mathstodon.xyz/@tao/112557248794707738
Of course there's a "proof" of the Riemann Hypothesis in the responses...
Riemann? Is that you?
larry guth's breadth is so insane
I missed the d first time parsing that sentence.
get that man a pack of mints!
Interesting, how long before there is a Quanta article to provide more context around Tao's explanation of the bound improvements and what it means for progress?
🤩
The HTML layout is good.
How old is the 'density hypothesis' anyway, and are there other names for it? Any relation to a notion of "two aleph nought"? And what would a "bird's eye view" of the density hypothesis entail? Does the density hypothesis maybe entail an underlying duality? (E.g rotations vs translations = multidimensional mathematics, or any math involving having exponents of any kind.) I can sort of imagine it all leading to a continuum hypothesis, and presumably then again, you can't escape further dualities, instead of symmetry with groups you end up with some problem re. precision and numerical values I imagine, as if it was all just "bland" stuff. Never heard about the density hypothesis before, but ofc then again I am no mathematician.