NavList:

Alex E., in the zeppelin thread, you wrote:
"This info is obtained from Google AI (which I do not find very reliable in general)."

A BRIEF A.I.+MATH SIDEBAR:
Like you, I find that Google AI is not reliable. The "public-facing" free Google AI is mediocre and suffers from many of the issues that were common to most AI chatbots in the first year (it's actually hard to believe that we're coming up on the third anniversary of the boom in AI use ...the craziness began on 30 Nov 2022). I suggest to anyone experimenting with AI: try different products. The current version of ChatGPT is really quite impressive. An experiment that you, Alex, as a mathematician and a mathematics teacher might try: ask ChatGPT to give you a ten-page introduction to some abstract mathematics topic (and for any other NavList reader following along, you might try replacing the suggested topic below with "spherical trigonometry" or similar). It's important to write a "prompt" for ChatGPT that lets it know what sort of introduction you want. How do I know what prompt to write? I asked ChatGPT how to write the prompt. Here's its suggestion for a prompt:

Write a graduate-level introductory essay on Algebraic Topology and Homology Theory suitable for first-year mathematics graduate students. Structure it with clear sections:

• Motivation and historical background – why topology needed algebraic tools.
• Core ideas – topological spaces, continuous maps, and the notion of invariants up to homeomorphism.
• Homology theory – intuitive idea of “counting holes,” formal definition via chains, boundaries, and cycles.
• Key theorems and examples – fundamental groups, simplicial and singular homology, simple computations.
• Connections and outlook – relation to cohomology, differential forms, category theory, modern applications.

Write in formal academic prose with clear mathematical precision but no symbol-heavy proofs. Include brief illustrative examples and emphasize geometric intuition.

Try dropping that in at https://chatgpt.com. It can do much more, but quite often the other "tools" need very specific instructions since they're adjuncts to the chatbot's "brainy" capabilities. For example, you might add to your prompt "Use inline LaTeX for formulas, but also include at the end of your response a fenced 'code block' labeled latex that lists all equations and symbols in raw LaTeX form for easy copying." But if you try something like this, expect problems. This is the part where the end-users (that's us) have to deal with the chatbots' fundamental "blindness". They --the chatbots-- don't see the output that they create. They send instructions to another layer of the system, and it's up to end-users to explain "that didn't quite work"... 

Frank Reed