I have often wondered whether there has ever come a point in your research,

when you were confronted with an explicit real function $f(x_1,x_2,\ldots,x_n)$ and an explicitly defined compact set $S\subset\mathbb{R}^n$,

you checked on a computer that the function is likely to be non-negative on that entire set,

but you had enormous difficulty proving it?

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Sorry if this question appears too "soft". I am not at research-level yet, having just completed my undergraduate degree.