its not just math .. its math, science, engineering, medicine, tech .. ie. everything.

We need to ensure we dont outsource thinking itself - yes its great to have a lot of our knowledge encoded in books, and in the weights of LLMs [easier to access ]

Do we even 'have' a technology if it doesn't reside actively in some human minds ?

Some of math is handed down to apprentice mages, and not encoded well in books [ perhaps books dont encode intuition well, Ive had many cases where someone has explained something not in the textbook, a trick they learned from someone else ]

Apprentice mages only become mages by grappling with hard problems, asking questions, going on long detours, discussing/arguing with master mages, trying lots of tough thought experiments - all valuable "training".

Training using the AI might lead to a golden age where more mages learn wider and deeper, and the subject flourishes and more humans understand the tech.

The danger is using the AI makes us lazy - we dont grapple with programming syntax, draw math diagrams slowly by hand, check edge cases, try to prove things ourselves the slow way and build intuition in the process.

Another issue is ownership and access. Already RAM GPUs and soon CPUs are harder to get hold of due to competition with the hyperscalar datacenter buildout. This is an example of economic inequality effectively stealing resources from the mainstream.

Will math remain open or will it be owned by the frontier models ? With Math and science journals Elselvier almost had a stranglehold, bullying universities to pay massive bulk subscriptions - fortunately Arxiv solved some of that. Can I even own a copy of a music track, tv show or movie these days, when there it is so much more profitable for companies to rent it out pay-per-view or monthly ? There is every financial incentive to slurp up the whole of Arxiv, github and every science textbook into a frontier model and rent out access via pay per token. I no longer need to go to stack overflow to look up a simple algo, google can give me a pithy summary, so its likely that the LLMs will steal traffic from github, or github could be drowned in the volume of vibe code. Is there any point buying a textbook or going to university when the AI covers the material ? If no universities then we dont have a physical space for science and tech to be discussed. That activity might go online .. or may disappear altogether - we already have less socializing in person due to the rise of social media.

We have several "alignment" problems : humans arent aligned with each other, frontier models are aligned with profit-making which may differ from the common good, the race is on and so frontier models are more aligned to short term shareholder / VC value than to longterm benefit to humanity as a whole. These mis-alignments may have always been there, but are multiplied by the power and reach of new AI technology.