As a result, he recognized that techniques for studying PDEs could apply to the Collatz conjecture. Courtesy of UCLAįor Tao, this goal had the same flavor as investigating whether you always eventually get the same number (1) from the Collatz process no matter what number you feed in. Terence Tao, inspired by a comment on his blog, made some of the biggest progress in decades on the Collatz conjecture. “I didn’t reply, but it did get me thinking about the problem again,” Tao said. The commenter suggested trying to solve the Collatz conjecture for “almost all” numbers, rather than trying to solve it completely. Then this past August an anonymous reader left a comment on Tao’s blog. Over the years, he’s made a few attempts at solving the Collatz conjecture, to no avail. Every year, he tries his luck for a day or two on one of math’s famous unsolved problems. “You could get obsessed with these big famous problems that are way beyond anyone’s ability to touch, and you can waste a lot of time.”īut Tao doesn’t entirely resist the great temptations of his field. “It’s actually an occupational hazard when you’re a mathematician,” he said. He’s used to solving problems, not chasing pipe dreams. In 2006 he won the Fields Medal, math’s highest honor, and he is widely regarded as one of the top mathematicians of his generation. Tao doesn’t normally spend time on impossible problems. “Now I know lots more about the problem, and I’d say it’s still impossible,” Lagarias said. He’s amassed a library of papers related to the problem, and in 2010 he published some of them as a book titled The Ultimate Challenge: The 3x + 1 Problem. For decades he has served as the unofficial curator of all things Collatz. Lagarias first became intrigued by the conjecture as a student at least 40 years ago. The futility of these efforts has led many mathematicians to conclude that the conjecture is simply beyond the reach of current understanding-and that they’re better off spending their research time elsewhere. “We really don’t understand the Collatz question well at all, so there hasn’t been much significant work on it,” said Kannan Soundararajan, a mathematician at Stanford University who has worked on the conjecture. Other results have similarly picked at the problem without coming close to addressing the core concern. From 1994 until Tao’s result this year, Ivan Korec held the record for showing just how much smaller these numbers get. In the 1970s, mathematicians showed that almost all Collatz sequences-the list of numbers you get as you repeat the process-eventually reach a number that’s smaller than where you started-weak evidence, but evidence nonetheless, that almost all Collatz sequences incline toward 1. It’s very tempting to try,” said Marc Chamberland, a mathematician at Grinnell College who produced a popular YouTube video on the problem called “ The Simplest Impossible Problem.” “The problems we deal with these days both in mathematics and in science are a lot more complex and require collaboration,” Professor Tao said.“You just need to know multiplying by 3 and dividing by 2 and you can start playing around with it right away. Today his focus is on collaboration – he has worked with more than 30 others on key discoveries that expand the limits of human understanding. Professor Tao completed his PhD at Princeton in the US, became UCLA’s youngest-ever full professor at the age of 24 and the youngest-ever winner of the Fields Medal at age 31. “I used to spend an hour each week with one lecturer talking maths with him, it was great.” “I formed some good friendships at Flinders, particularly with the lecturers,” Professor Tao said. He remains one of the youngest students ever to enrol at Flinders, graduating with a masters degree at the age of 16. A true child genius, he enrolled at school at the age of five and was writing computer programs by the age of six. Professor Tao is one of the world’s leading mathematicians. “It’s the one area of my work that is relatively easy to explain and it’s nice to be able to say there is one thing I have done that can actually save lives,” Professor Tao said. However, the application of an algorithm Professor Tao developed with Professor Emmanuel Candes and Associate Professor Justin Romberg reduced the machine’s data processing time dramatically, enabling lung MRIs to be taken in just 10 seconds instead of two minutes. People requiring an MRI scan of their lungs need to hold their breath while the scan is conducted, making scans life threatening for some patients.
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