# The 10 Hardest Math Problems That Remain Unsolved

A weekend post. Who knows might be able to solve one of these.

1. The Collatz Conjecture

Earlier this month, news broke of progress on this 82-year-old question, thanks to prolific mathematician Terence Tao. And while the story of Tao’s breakthrough is good news, the problem isn’t fully solved.

A refresher on the Collatz Conjecture: It’s all about that function f(n), shown above, which takes even numbers and cuts them in half, while odd numbers get tripled and then added to 1. Take any natural number, apply f, then apply f again and again. You eventually land on 1, for every number we’ve ever checked. The Conjecture is that this is true for all natural numbers.

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# The Hilarious (and Terrifying?) Ways Algorithms Have Outsmarted Their Creators

AI has started surprising us. Should we be scared or excited?

As the paper notes in its discussion—and you may already be thinking—these amusing stories also reflect the potential for evolutionary algorithms or neural networks to stumble upon solutions to problems that are outside-the-box in dangerous ways. They’re a funnier version of the classic AI nightmare where computers tasked with creating peace on Earth decide the most efficient solution is to exterminate the human race.

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Eric Limer — Popular Mechanics

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# A ‘Rogue One’ Writer Reveals How the Film Originally Ended

I saw Rogue One last week and was blown away by the ending. Looks like even the writers of the movie had doubts about Disney accepting the ending where everyone dies.

We always felt that it was the right thing to do, that these characters make the ultimate sacrifice. It wasn’t that way in my original script, but again, we never felt that we would get away with it. K-2 always died, but Jyn survived in the very first version of the movie that we developed, and then it was Gareth who kept pushing for it, saying, “I feel like they need to die. They need to die.” Eventually he convinced [Disney and Lucasfilm].

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Matt Miller – Popular Mechanics

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