I think language and symbology is at the core of why they are so impenetrable.
One major sin is taking new concepts and ideas and putting the primary discoverer's name on them. Such names yield no clue as to the interpretation or application of the idea itself.
Another problem is the symbols used in certain mathematical texts. Everyone who uses them treats them like they're universally understood, but in reality the syntax and meaning of the symbols can and frequently are recycled and reused across disciplines and even theories in the same discipline. You have to be close to the 'in-group'. Like reading other people's code where operators have been overloaded, it's like learning a new language every time you want to dig into a cool new maths paper.
I don't actually have any good solutions to these problems. I would guess there are lots of lessons to be learned from the history of Chinese characters, though. They have thousands of unambiguous symbols which _can_ be learned by non-natives and which _do_ give an appreciable degree of cross-lingual intelligibility among languages that use them.
I was extremely frustrated with my machine learning class because of this. The notation used was hazy. Also if you ask me, probability theory should just be squashed and the ideas reformulated with new more consistent syntax / symbols, because the entire thing is so damn inconsistent and disorganized at present.
>Also if you ask me, probability theory should just be squashed and the ideas reformulated with new more consistent syntax / symbols, because the entire thing is so damn inconsistent and disorganized at present.
How do you mean? Probability doesn't even have that much complicated symbolism... although I do wish we would teach in probability courses how to translate between random-variable "distributed according to" notation and actual density functions. As in, I wish I knew how to do that.
One major sin is taking new concepts and ideas and putting the primary discoverer's name on them. Such names yield no clue as to the interpretation or application of the idea itself.
Another problem is the symbols used in certain mathematical texts. Everyone who uses them treats them like they're universally understood, but in reality the syntax and meaning of the symbols can and frequently are recycled and reused across disciplines and even theories in the same discipline. You have to be close to the 'in-group'. Like reading other people's code where operators have been overloaded, it's like learning a new language every time you want to dig into a cool new maths paper.
I don't actually have any good solutions to these problems. I would guess there are lots of lessons to be learned from the history of Chinese characters, though. They have thousands of unambiguous symbols which _can_ be learned by non-natives and which _do_ give an appreciable degree of cross-lingual intelligibility among languages that use them.