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Absolutely correct! Especially the reference to the topic of mathematics! Where I would disagree with you, however, is the topic of shares and investing are not a hobby. For me, it is a hobby because I deal with things with which I have zero contact in the private and professional environment.

Whether that's armaments, chip development, AI or pharmaceuticals, or even macroeconomic developments. Without the stock market, I might learn something about the areas from a documentary now and then, but that's it thanks to that. That's why it can definitely be a hobby in my eyes. The best example of this is probably also crypto and the blockchain.
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@Mister_ultra then dealing with the companies is your hobby.