Unfortunately this sentiment is mirrored among most programmers who claim to be interested in mathematics. Mathematics is fascinating and useful and doing it makes you smarter and better at problem solving. But a lot of programmers think they want to do mathematics, and they either don’t know what “doing mathematics” means, or they don’t really mean they want to do mathematics. ​ Honestly, it sounds ridiculously obvious to say it directly like this, but the fact remains that people feel like they can understand the content of mathematics without being able to write or read proofs. ​ So read on, and welcome to the community. ​ I honestly do believe that the struggle and confusion builds mathematical character, just as the arduous bug-hunt builds programming character. ​ I’m talking, of course, about the four basics: direct implication, proof by contradiction, contrapositive, and induction. These are the loops, if statements, pointers, and structs of rigorous argument, and there is simply no way to understand the mathematics without a native fluency in this language. ​ And so it stands for mathematics: without others doing mathematics with you, its very hard to identify your issues and see how to fix them. ​ And finally, find others who are interested in seriously learning some mathematics, and work on exercises (perhaps a weekly set) with them.

It's my fault, sorry. In the early days of Swift, we had a closure syntax that was very similar to traditional Javascript, func (arg: Type, arg: Type) -> Return { ... }. While this is nice and regular syntax, it is of course also very bulky and awkward if you're trying to support expressive functional APIs, such as map/filter on collections, or if you want libraries to be able to provide closure-based APIs that feel like extensions of the language. Our earliest adopters at Apple complained about...