Giving advice seems like our lecturing: we teach to learn a particular subject ourselves. The knowledge we pass to students not interested in research should be custom-fitted to no more than 9 people in a classroom. A comment about math olympiads: it has come to my attention that grading practices discourage partial solutions. This is fine for the production of people like Perelman, who seems satisfied with one big result. However, if a proof is considered as a pseudo-object, then by the anthropic principle it is impossible to produce a sequence of them to satisfy higher needs.

Giving advice seems like our lecturing: we teach to learn a particular subject ourselves. The knowledge we pass to students not interested in research should be custom-fitted to no more than 9 people in a classroom. A comment about math olympiads: it has come to my attention that grading practices discourage partial solutions. This is fine for the production of people like Perelman, who seems satisfied with one big result. However, if a proof is considered as a pseudo-object, then by the anthropic principle it is impossible to produce a sequence of them to satisfy higher needs.

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