Tessellations aren’t just eye-catching patterns—they can be used to crack complex mathematical problems. By repeatedly ...

Physicists have transformed a decades-old technique for simplifying quantum equations into a reusable, user-friendly "conversion table" that works on a laptop and returns results within hours. When ...

Abstract: In this paper, we study upper and lower bounds on the error exponents for joint source-channel coding with decoder side-information. The results in the ...

This article picked by a teacher with suggested questions is part of the Financial Times free schools access programme. Details/registration here. Read our full range of US High School economics picks ...

Roula Khalaf, Editor of the FT, selects her favourite stories in this weekly newsletter. HSBC and JPMorgan both have a problem with their “return to office” strategies. Having downsized their real ...

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Equipment used to train and run generative AI models could produce up to 5 million tons of e-waste by 2030, a relatively small but significant fraction of the global total. Generative AI could account ...

I can now drop the parentheses but don't forget I still am squaring whatever the result is so it's 6 squared and I add that 7. the next thing we do after parentheses is exponents 6 squared is 6 times ...