The future of "math" is not just solving, but communicating what was solved, and why that solving is important. "Math" as a discipline is only ever been half created, they abandoned explaining themselves like it was beneath them. Well, now in "Math 1.0 finally whole" they will be explaining what they did to the rest of us. If you can't explain you are not really there.
That's what math has always been about, even if not everyone is necessarily as talented a communicator as someone like Thurston -- who was himself an exponent of computational tools in math research:
>I think of mathematics as having a large component of psychology, because of its strong dependence on human minds. Dehumanized mathematics would be more like computer code, which is very different. Mathematical ideas, even simple ideas, are often hard to transplant from mind to mind....Translation in the direction conceptual -> concrete and symbolic is much easier than translation in the reverse direction, and symbolic forms often replaces the conceptual forms of understanding....
This is an entitled take. The usefulness of a thing has nothing to do with how easily communicable it is. That is the whole premise of specialization and becoming an expert. People go in-depth on things so they can say “trust me on this” and so you don’t have to. You are advocating for a tyranny of the illiterate.
Also, this reads like you didn’t like math classes. That sucks, but it’s no basis for societal organization
I am advocating for effective communications, it is not as if knowledge once understood remains difficult. To communicate and convey understanding is good, and to withhold understanding is tyranny.
> 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.
communicating results clearly is just as important for specialists/experts. A reaction by many mathematicians to the OpenAI dump (and many LLM breakthroughs) is simultaneously
1. if this is true, it is interesting, and
2. the exposition of this is a huge pile of slop.
This requires mathematicians to have to clean up the slop for it to be useful. It has happened for most LLM-generated proofs in the last few months. Anthropic explicitly payed two top complexity theorists to do it for the 3SUM and APSP breakthrough.
They didn't do this because those complexity theorists are advocating for a tyranny of the illiterate lmao
