Comment by essai57
4 hours ago
> it is not as if knowledge once understood remains difficult
What do you mean by this? Once a person has understood something, it may no longer be difficult for them, but it can certainly still be difficult for those who have not understood it yet. And we humans know of no way of transmitting understanding to another person without having that person exert some effort.
I don't know where you get the impression that mathematicians at large are withholding understanding. In fact, many mathematicians share their lecture notes freely online, share their articles freely on arxiv etc.
If your complaint is that these texts are written in the language of the field and thereby not accessible for laymen: This is the case for any advanced knowledge, because it builds on more basic knowledge that a person must first acquire. That is not withholding knowledge.
It is not "they are withholding information", it is more an issue of, and this is not just formal mathematics, not enough emphasis on communicating to be understood, and the education that we all receive not really including how to communicate our specializations to anyone but a peer or a boss.
These formal educations we receive are half baked. We cannot use them without other specialists, specialists we specialists ourselves probably cannot afford. We cannot discuss what we do with anyone but other specialists of our same color and stripe, the same star shape on our bellies. We're not being taught how to communicate, not really, not in general, not in a manner that enables us to function without some corporate apparatus extracting the maximum while always offering statistically less than the market average.
What I meant by knowledge not remaining difficult once understood is that there is a collective consciousness hurdle that we as a society can move on. Once how to express difficult ideas and controversial question and answer exchanges become better understood in general, and once how to handle situations that currently cannot even be discussed due to the emotions they stir become less emotional storms and become logical frameworks people can discuss in abstract, then we become a more functional society than we are now.