> Why does it need to be beautiful?

"Beauty", IMO, signifies the idea that you're doing `something` for its own the sake where "its own sake" approximate the idea of getting/being closer to (or in proximity of) `something`/`anything`/`someone` you find "beautiful".

> Once you proved it it's true and you can use its consequences in math, sciences and engineerings (sic).

The expression "you can use its consequences in ..." suggests that the action is a "just a means" to "something else". However, not everyone is interested in the idea of "something else"; they're interested in the idea itself (in a broad sense) as that's one of the main reason they got started/involved in the first place.

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We all do things as "just a means" to "something else". However, there must be an "end" to this chain of "something else"; otherwise, how do you find any "meaning" (or sense of fulfillment) in this whole enterprise (or chain of "something else"s)?