An infinite amount of math exists, with greatly increasing difficulties. But overcoming those difficulties can be quite satisfying, even if I expect to never know the entirety of math.
The fact that math is difficult actually makes the world a better place. E.g. because the discrete logarithm problem is difficult, HTTPS works. https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange Look at the part with the paint for a simple example. Without math being difficult, online banking would not work.
I doubt history is very useful without probability and statistics. E.g. maybe event A can lead to events B or C, but how often, and how certain can we be about how often? Also probabilities for intersections, unions, and complements show be done.
Mathematics is boolean logic applied to definitions. To communicate correctly, boolean logic must be applied to the definitions of the words in the language. Math is not only about numbers, math is also about symbols and words. As for PE, to optimize performance, one should record performance and analyse it via my history argument.
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