You don’t need to understand everything in every field and I doubt very many people do.
When Einstein was working on general relativity, he had a lot of help from friends and colleagues who pointed him towards the math he needed. He didn’t learn differential geometry until he was already deep into general relativity.
Find a level of abstraction that you’re comfortable with and learn to be okay with black boxes at the lower level, and only dig into those boxes when what’s inside them actually matters.
I think an important lesson for any grad student is to learn to read through the bullshit in papers and try and understand what the authors actually did.
It helps a lot that in CS you can often see the code that the authors published along with the paper. Just staring at formulae doesn't mean much, because for all you know the author just hammed up the equations to get their paper into a top conference. That's not to say that the equations are excessive, or the authors are being misleading, but I think there is definitely an expectation in some fields that putting equations in makes your paper look clever even if they're broadly unecessary.
It's also wildly different depending on the field. If you look at variational methods in computer vision, images are [continuous] mappings from some domain onto the reals (I : Ω->R3 for colour). Does that change the fact that an image in memory is just a bunch of numbers in a grid? Not really, but it's bloody confusing the first time you see it.
This doesn't help with understanding the maths, but at some point you have to give up and say "This guy proved it, and someone else peer reviewed it, so I can use it to solve my problem". It's perfectly OK to stand on other people's work and still make creative contributions to your field, that's the point of research.
>I think an important lesson for any grad student is to learn to read through the bullshit in papers and try and understand what the authors actually did.
We actively work to make our writing hard to understand in this field. I do this all the time myself. I don't really need this complex looking equation to make my point. But if I don't have it in there a reviewer will think my writing is not academic enough. So there you have it. Once you go in realizing this is the case everywhere, it becomes a lot easier to understand academic papers.
I get your point but I wish this wasn't the case with most research. I, like the author, am not a math guy but have been reading tons of ML papers recently. I usually skip the formal definition parts and get to the 'juicy' implementation parts.
That's hard as I haven't read too many. The recent deepmind papers (the ones about imagination) were good. The papers were pretty standard but they came along with explanatory blogpost[1] and some videos covered them too[2][3][4]. This supplementary content is what made them accessible for me.
Quite possibly. I suppose I read "when Einstein was working he got help with the math" - so "he also got help (from his wife and others) when working on special relativity" might be more accurate.
In particular, Einstein worked with Marcel Grossman: https://en.wikipedia.org/wiki/Marcel_Grossmann who did most of the calculating and verifying of intuitive ideas that Einstein came up with.
When Einstein was working on general relativity, he had a lot of help from friends and colleagues who pointed him towards the math he needed. He didn’t learn differential geometry until he was already deep into general relativity.
Find a level of abstraction that you’re comfortable with and learn to be okay with black boxes at the lower level, and only dig into those boxes when what’s inside them actually matters.