You misunderstand cryptocurrency, I'm afraid. You don't actually mine Bitcoins; rather, they are awarded for your mining efforts. Mining is required to add transaction blocks to the blockchain, and it's a means to limiting the number of added blocks per minute. There are other ways of achieving that apart from solving an absolutely abstract, arbitrary mathematical puzzle, and there are other types of cryptocurrency which don't require mining at all (see Ripple, for example). In fact, so many altcoins are using mining because Bitcoin, the first and original one, used it. But it's just so happened, and there was absolutely no way of knowing this 20 years ago.