Terence Tao on Nostr: At the graduate level, I have found that students are often reluctant to deviate from ...

At the graduate level, I have found that students are often reluctant to deviate from their assigned problem, or from the proof technique selected from the paper in the literature they were reading. It can take some time to distinguish between difficulties that are artefacts of their chosen method, and difficulties that are genuinely part of the original problem, which is important if one needs to how to resolve the difficulty.

For instance, recently one of my students was analyzing a configuration of slabs in Euclidean space by subdividing the space into cubes, and performing various Fourier-analytic arguments on each cube (following a previous paper in two dimensions on the subject). The student had encountered technical issues involving the faces and corners of the cube, especially if the slabs involved were somehow aligned with those faces. But the cubes had nothing to do with the original problem; they were just a convenient localizing device, and any alignment with the cubes being used to decompose would be purely coincidental. So I advised the student to either switch to a different type of localization method (e.g., a smoother or more randomized cutoff), or else just pretend for now that these boundary issues could be resolved in principle and continue the argument to locate the more essential difficulties of the problem.
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