Imagine how much you could accomplish if you used that time to for example learn a new language.
I disagree. The best way to learn a language is by playing. Reading compelling stories, making puns and jokes, flirting with the natives, having some fun!
And I hold the same opinion with mathematics. You can learn to attack some classes of solved problems without having fun, but to be a mathematician you have to follow your sense of aesthetics. Now this is highly sophisticated fun, the kind that takes years to develop. But once you achieve it, it is bottomless, requires nothing but a little free time and it is so useful that our entire civilization runs on it!
I disagree. The best way to learn a language is by playing. Reading compelling stories, making puns and jokes, flirting with the natives, having some fun!
And I hold the same opinion with mathematics. You can learn to attack some classes of solved problems without having fun, but to be a mathematician you have to follow your sense of aesthetics. Now this is highly sophisticated fun, the kind that takes years to develop. But once you achieve it, it is bottomless, requires nothing but a little free time and it is so useful that our entire civilization runs on it!