[reedf1]

'Calculating' an integral, is usually done by applying a series of sort of abstract mathematical tricks. There is usually no deeper meaning applied to the solving. If you have profound intuition you can guess the solution to an integral, by 'inspection'.

What part here is the knowing or understanding? Does solving an integral symbolically provide more knowledge than numerically or otherwise?

Understanding the underlying functions themselves and the areas they sweep; has substitution or by-parts, actually provided you with this?

[svnt]

Parent says “I taught my 5yo how to” — this means their 5yo learned a process.

OP says “I taught LLM how to see” and this should mean the LLM (which is capable of being taught/learning) internalized how to. It did not, it was given a tool that does seeing and tells it what things are.

People are very interested in getting good local LLMs with vision integrated, and so they want to read about it. Next to nobody would click on the honest “I enabled an LLM to use a Google service to identify objects in images”, which is what OP actually did.

[dpoloncsak]

I can second this...Been trying to get local LLMs to play through Pokemon Emerald (with virtually 0 success).

I'm under the impression I'm being hampered by a separation of 'brain' and 'eyes', as I have yet to find a reasoning + vision local model that fits on my Mac, and played with two instances of qwen (vision and reasoning) to try to solve, but no real breakthroughs yet. The requirements I've given myself are fully local models, and no reading data from the ROM that the human player cannot be aware of.

I was hoping OP was able to retro-fit vision onto blind models, not just offload it to a cloud model. It's still an interesting write-up, but I for sure got click-baited

[gus_massa]

[I teach Math in the first year of the university in Argentina. We have a few Calculus courses, with different levels according to the degree.]

In 1D, substitution by linear functions like "t=3x+1" is very insightful. It's a pity that sometimes we don't have time to analyze it more deeply. Other substitutions may be insightful or not. Some tricks like "t=sin(x)" has a nice geometrical interpretation, but it's never explained, we don't teach it anyway now.

Integration by parts is not very insightful until you get to the 3rd or 4th year and learn Solovev spaces or advanced Electrodynamics. I'd like to drop it, but other courses require it and I'd be fired.

In some cases, parity and other symmetries are interesting, but those tricks are mostly teach in Physics than in Math.

Also, in the second year we get 2D or 3D integrals, that have a lot of interesting variable changes. Also, things like the Gauss theorem and it's relation with conservation laws.