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An anecdote that I shared about rolling around on the floor back in 2000 to solve a math problem, both in my #Masterclass at https://www.masterclass.com/classes/terence-tao-teaches-mathematical-thinking/chapters/transforming-problems , and on #MathOverflow at https://mathoverflow.net/a/38882/766 , as well as the #NewYorkTimes https://www.nytimes.com/2015/07/26/magazine/the-singular-mind-of-terry-tao.html , has for some reason recently gone viral on various social media. Just for the record, I wanted to add some mathematical background behind the story, which eventually led to my paper https://arxiv.org/abs/math/0010068 . At the time, I was trying to construct solutions to an equation known as the wave maps equation on the sphere: the solution was like a solution to the wave equation, except being forced to take values in a sphere rather than in a vector space.

I was trying to solve the equation iteratively, breaking up the solution to a low frequency base solution and a high frequency correction. As a first approximation, the low frequency base could also be assumed to stay on the sphere and solve the wave maps equation, so the main problem was to work out what the high frequency correction was doing.

Because the high frequency correction also had to keep the solution on the sphere, one could assume as a first approximation that the high frequency correction was tangent to the low frequency base. So, at any given point in space and time, the low frequency base solution was located on some point on the sphere, and the high frequency correction basically lived on the tangent plane to the sphere at that point. But because the base solution evolved (slowly) in space and time, this tangent space kept rotating around the sphere.

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