>>> How is this different from a human using an algorithm they have memorized ...

>> Humans identify which "algorithm they have memorized" to use beforehand, due to the problem to be solved being defined by other humans ...

> This doesn't make any sense at all. Was this supposed to be a gotcha?

No, it was meant to be an explanation as to the difference between "memorization" and "understanding." In this context, people pick the algorithm they determine applicable and then the question of memorization is relevant.

> An LLM is trained on problems defined by other humans, and identifies which algorithm it must use based on pattern recognition.

Funny that you make this argument here, where when I wrote elsewhere in this thread:

  [LLMs] are statistical token generators whose results are
  dependent upon their training data set and involve a
  degree of randomness.

  Nothing more.

  ...

  It is pattern recognition, a task in which ANNs excel.

  During conversation, we are statistical token generators 
  whose results are dependent upon our training set. 
  Seriously, write that definition out rigorously. It 
  encompasses virtually everything. It is totally 
  meaningless. So to say "nothing more" is effectively also a 
  tautology.
  
  This argument was asinine in 2024. It is insane to be 
  saying these things in 2026. Where have you been?

  ...

  It absolutely understands how to do math, by whatever
  reasonable definition you want to provide to the word
  "understand".

Are LLMs ANNs? Which themselves are pattern recognition algorithms (hint: they are)?

OR (setting aside the ad hominems you kindly provided)

Do LLMs possess "understanding" of concepts such as abstract mathematics (defined and interpreted by humans) and we, as simple humans, nothing more than statistical token generators as you assert?

Because it cannot be both.