hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final
((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3, has jacobian determinant -2, and sends (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0)
🚨 Erling Haaland refuses to throw Sørloth under the bus after Norway's defeat to England. 🇳🇴
🗣️ Erling Haaland:
Alexander Sørloth is a great player and, more importantly, a very good friend of mine. Football is a game of decisions, and sometimes you make the right one, sometimes you don't.
People watching from home have time to slow everything down and analyse every angle, but on the pitch you have a split second to make a decision. That's football.
I'll never blame him for that moment because we've all been in those situations. Every player has made a decision they wish they could take back.
I'm proud of what we've achieved as a team. Reaching the World Cup quarter-finals was something very few people believed we could do before the tournament started.
We gave our country something to be proud of. We fought for every badge, every shirt and every supporter who believed in us.
Losing to England wasn't because of one pass or one missed opportunity. We created chances throughout the game. We had moments where we could have scored, and they had moments where they punished us.
That's football. Sometimes you win, sometimes you lose, but you never point fingers at one teammate. We win together, and we lose together.
I'll always stand by Alexander, just as I know he'd stand by me. That's what being teammates is all about.
We leave this tournament disappointed, but also proud. This is only the beginning for Norway, and we'll come back stronger.
The "look and say sequence" {L[n]} goes 1, 11, 21, 1211, 111221, 312211, 13112221, ...
[Conway 1986]: Writing d[n] for the number of digits in L[n], the limit of the ratio d[n+1]/d[n] exists, and is an algebraic integer of degree 71.
Following the amazing reaction to the Marble Curriculum yesterday, we've decided to make it open source 🛰️👇
Everything a child learns in primary school. 1,590 concepts. 3,221 connections across 8 subjects, from Math and Science to Computing and Life Skills. Anchored in the US and UK curriculums, standard by standard (NGSS, Common Core, DfE).
What you will find in the repo: every concept as structured JSON with its age band and the evidence a child must show to master it. Every prerequisite link marked hard or soft, with a written rationale. It's a true DAG you can compute learning paths on. Open license, you can build whatever you want with it.
Now is a unique time in history to be building in education. Getting AI and kids education right is likely one of the hardest and most important problems to crack over the next decade and we need as many smart and creative minds behind it.
We think a common solid basis, accessible to all and that can be built upon, is critical to move fast. That's why we're making this curriculum open source.
It's not perfect but we know it's a robust basis, and we believe that sharing it openly is the fastest way to progress in this field. If you're building in education, share this around you and tell us in comments if you find this useful and if you want to contribute.
We'll keep working and investing on it @withmarbleapp. Credit goes to @guillaume_boni for building this. I just made it look pretty.
Links below 👇
แอบหวังว่าจะได้เจอใครสักคนในชีวิตจริง แล้วค่อยๆ ทำความรู้จักกัน someone in real life ใครสักคนที่ชอบตอนเราหน้าสด ตอนเห็นเราทำตัวแปลกๆ ตอนที่เราไม่ได้ดูดี อยากถูกรักแบบเจ้าใจง่ายว่าเพราะเป็นเราเฉยๆเขาถึงรัก
3 blacks attack a drunk white kid in Birmingham, the female police officer comes in to protect the violent blacks and arrest the white kid
Absolutely disgusting the way white people are treated in England (@KnockoutAudit)