Could you derive something useful from the data?
“We have to find the connection between the data and the unknown. We may represent our unsolved problem as open space between the data and the unknown, as a gap across which we have to construct a bridge. We can start constructing…
Auxiliary elements
“There are various reasons for introducing auxiliary elements. We are glad when we have succeeded in recollecting a problem related to ours and solved before. It is probable that we can use such a problem but we do not know yet how to use it. For instance, the…
Can you derive the result differently?
“When the solution that we have finally obtained is long and involved, we naturally suspect that there is some clearer and less roundabout solution: Can you derive the result differently? Can you see it at a glance?… Having found a proof,…
i love how every time i have a hard problem i want to solve now, i'll spin up 8 tabs and ask the same question to:
- sonnet 3.7
- sonnet 3.7 thinking
- gpt 4.5
- o3-mini-high
- o1-pro
- o3-deep-research
- gemini 2.0 pro experimental
- grok 3 thinking
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