A basic rule of mathematical life: if the universe hands you a hard problem, try to solve an easier instead, and hope the simple version is close enough to the original problem that the universe doesn’t object.
Ellenberg describes a common mathematical strategy: replace a difficult problem with a simpler one that can be understood or solved more easily. The simplified version does not need to reproduce every detail of the original situation. Its value depends on whether it preserves enough of the important structure to provide a useful answer.
The quotation also reflects a broader approach to reasoning. Complex problems are often approached through models, assumptions and approximations rather than by representing reality in full detail. This can make analysis possible, but it also requires judgement about what can safely be left out. The phrase about the universe not objecting points to that limitation: a simplification is useful only when the differences between the model and the original problem are small enough not to undermine the result.
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Jordan Ellenberg
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