You're right. But all of those things are things you can do something about, because you've heard of them.
Just saying there's a lot of things in the math world that if you didn't put down a stake early on, you won't know that you don't know them.
Just saying there's a lot of things in the math world that if you didn't put down a stake early on, you won't know that you don't know them.
But this is true of many (all?) fields, not just quantitative. For example, recently I've been learning ancient Hebrew and one of the things I learned early on was that it (like Arabic) has a "dual number" which is in a similar grammatical category to English singular and plural, but implies the things usually come in pairs, like hands and eyes. It uses this construct to refer to "the heavens" in Genesis, which immediately raises the question of why ancient Hebrew cosmology identified "the heavens" as dual in number.
There's something I didn't even know I didn't know until I started into the field.
English and Germanic have vestiges of dual number, it's pretty interesting. Like the word "both", it seems like a weird thing to have in a language that normally is single/plural. I came across it because I was reading about languages at one point, but all I used to get there was just ordinary reading. Yes, I didn't hear about it until I heard about it, but I also wasn't prevented from learning this little tidbit from a lack of supporting knowledge. By contrast, there are areas of math that would take me years to even understand what the research questions are.
Hahahaha you clearly don’t know how much you don’t know about art, music, philosophy, ummm psychology.
Sorry to be a bit mean but come on man .... :).
I’m not denying that math isn’t special in certain ways. It is.
And you could even make arguments about the mathematical nature of music.
But man, to be a serious classical musician or serious jazz musician you have to study and practice your entire life since childhood. Just to have a running.
You wanna get good? Achieve mastery and knowledge? Compose work in dialogue with the great work of the past? Would take you years just to get started.
Or Picasso. His father? A painter. He was literally born into it.
I encourage you to read some good biographies of some artists.
Or even a biography on say, Winston Churchill. Or Lincoln. True political / leadership skill takes a lifetime of study and acquiring experience.
To pick more examples of obviously challenging and cavernous non-math stuff, have you read any Thomas Pynchon, Don deLilo, or David Foster Wallace? Or James Joyce or Samuel Beckett?
Or Homer, for gods sakes. Or the Bible, the Koran, the Old Testament, the Tao Te Ching?
Allow for creative, rational thought which is less precise but more complex than pure logic or math (ie allow for human fucking language), and you get what is maybe the deepest cavern there is.
You underestimate both the time and effort needed to gain a real understanding of literature and art, and, to create it on a high level. And all the fields of human experience which we are unable to completely describe our understanding of via mathematics.
As someone else said, math is hard because it is easy. Humanities are easy because they are hard.