Even if you don't do skiddy tricks (but do a lot of miles) knowing the arithmetic leads into all sorts of interesting thinking about prime numbers - and, indeed

Even if you don't do skiddy tricks (but do a lot of miles) knowing the arithmetic leads into all sorts of interesting thinking about prime numbers - and, indeed, figuring out optimum gears ratios for (personal perference for) particular gear inches. Added to which, to minimise chain wear how big can we go at the front without hitting the chainstays/still making kerb jumps plus we want the number of links in the chain to be relatively prime as well. Agreed re brakes, on a bike having a decent front brake is all that matters (irrespective of age)- if stopping quickly, the back wheel is generally waving about in the air anyway so whether its leg-braked or other makes no difference (except fixed riders will still be pedalling, force of habit and all that).