Also - does he actually "have money"?

Tesla and SpaceX don't make a profit or pay dividends. My guess is he finances his entire life from taking on debt which is secured against his stock.

So how exactly are people like him supposed to just give money away? What happens to the stock he owns then? Would he forgo control of his companies?

How would he pay taxes on that income anyway?

Lots of questions the billionaires-shouldn't-exist crowd have no concept of.

Bingo! Balance is key.

Farmers working under communist rule in China who started private farming caused agricultural productivity to skyrocket and the number of starving people to drop [1]. Say what you will about human greed, but aligning a behavior you want with a natural economic incentive is a powerful tool.

On the flipside, some industries like healthcare don't belong in such a ruthless system, because "voting with your wallet" is sometimes equivalent to "voting with your life". Other industries like scientific research have too long a lag time for the the companies to stay afloat, or for the decision makers to benefit from the decision. These industries are the ones that frequently need help from government, nonprofit, donors, etc.

[1]: https://reaction.life/chinese-capitalist-growth-happened-spi...

What giant advances has Elon Musk made in maths/science?

As long as the intention is to actually create wealth for the society as a whole as opposed to just making yourself rich, I don't see a problem to what Elon does.