🚨AGORA: PsyOpera, novo álbum de Grimes, está programado para ser lançado no dia 22 de Janeiro de 2027.
Grimes vai lançar singles a cada semana até o lançamento do álbum!!!
the love i have for F5ve is so strong it pains me that i can’t see them live and that they don’t have a bajillion songs to stream. everytime they show up on my phone i smile from ear to ear they are so perfect..
the whole timeline, from the equations to today:
1822: navier writes the equations down.
1845: stokes gets them right, and his name on them.
1934: leray shows weak solutions exist forever, and leaves smoothness open.
2000: clay puts $1m on that gap. fefferman writes the official statement, four options.
2014: luo and hou watch 3d euler blow up in numerics.
2016: tao proves blowup for an averaged navier-stokes.
2021: elgindi proves euler blowup for rough data.
2023 to 2026: córdoba and martínez-zoroa build forced blowups, with a rough force.
then this year:
aug 15: buckmaster and alpöge get smooth-forced blowup for boussinesq and euler, with claude and codex.
aug 22: lean checks it.
aug 28: per wired, openai starts training its math model.
sep 1: per axios, openai's run starts, after researchers hear rumors.
sep 3: buckmaster emails openai to say what they have.
sep 6, sunday: bubeck says openai had the final solution that morning. buckmaster says he was told on the afternoon call.
sep 8, 4am: buckmaster and alpöge post three papers and the lean repo. buckmaster posts his statement.
sep 8, 17:20 utc: openai posts "we're sharing a solution to the navier-stokes millennium prize problem."
https://t.co/MOmY67RLGM
Some thoughts on the Navier-Stokes news from a professor of aerospace engineering:
1) take a deep breath
2) posts indicating we "solved Navier-Stokes" are incorrect and overblown. A very specific mathematical proof involving a niche scenario for Navier-Stokes has *potentially* been shown (that a perfectly smooth incompressible initial condition with finite energy could produce a singularity--note the assumptions here piled on to an equation set that already involves some assumptions).
3) there is no general closed form solution for N-S and that's not what this news is about
4) this is more of a mathematical curiosity than anything else and could matter a lot to mathematicians but basically changes nothing in the way N-S are used in practice
5) there are already very useful exact solutions to Navier-Stokes that greatly simplify the equation set with the right boundary conditions/geometry like laminar flow through a pipe or a 2D Taylor-Green vortex
6) in aerospace, we already treat N-S as an approximation in many instances and are well aware of its limitations. we don't outright solve these equations anyway and regularly chop off terms or simplify parts (at the expense of accuracy) to make them easier to deal with.
7) to be honest I have never found this specific problem to be particularly interesting because we know a core assumption of N-S is a "continuum" fluid where you ignore molecules and assume hydrodynamic scales >>> molecular scales. We know a real fluid cannot have infinite velocity or energy. But clearly you can push equations outside of their bound of validity and make them produce funky results and singularities.
So it just occurred to me that 10,000 agents over 88 hours is roughly 100 years of working time
That means an above phd level mathematics agent was able to solve the problem in 100 years which sounds… really realistic?
When 5 Just Stop Oil protesters seeking to save our planet organised protests to block the M25 they’re sentenced to 5 & 4 years in prison for conspiracy to cause a public nuisance. So what happens when the new Blackshirts block roads & intimidate people? https://t.co/g5EV10XA0c
Man came from the 4th division of Brazil for €8m as an 18 year old, joined us when we were at our lowest point and went on to score 68 goals for the club and provide 38 assists. Multiple goals at Anfield, multiple big goals against Man City, goals against Bayern, Real Madrid, you name it. That equalizer against City will never be forgotten in the road to our first league title in 22 years. Champions league top scorer in a season we made our 2nd final in club history. Took and scored the penalty in the final under immense pressure. And in the end of it all, he gets us a £50m+ profit becoming our record sale. Phenomenal professional with a top work ethic - never created any troubles even once. If it were upto him, he would’ve signed a lifetime contract. He is one of us and will be remembered here forever.
🚨 Another one!
Didn’t those Extinction Rebellion protesters argue the travel disruption we could be facing in a few years would be worse than anything they were causing.
Are we ready to admit they had a point yet?
hounded to death by an unrelenting and under regulated media. in any normal society this would give rise to serious questions about the conduct of journalists and platforms and would lead to change. will be waiting a long time i fear.
I'm devastated for the family and friends of Jason Arday.
He faced an unacceptable public hounding and campaign of abuse. I know many Londoners will be angry and upset this evening.
Jason Arday was the victim of a pernicious public shaming that other people in his position simply wouldn’t have faced.
His death was a tragedy, but once again it should be a wake up call for all of us.