(Just some thoughts while I read Mathematics and the Unexpected and Innumeracy: Mathematical Illiteracy and its consequence. Maybe some more detailed post later.)

Nature is too complicated for us to model with finite equations. All mathematical models are wrong.

Do not expect to find (new) simple mathematical models which are useful in real world problems. If they do exist, the chances are that they had been discovered, or they are not so useful.

Do not expect to find relations (simple or complicated) in the small scale , or in a quantitative manner. The only choice is to find relations in the whole picture: a large scale relation in a qualitative manner is more feasible.

Do not cook up mathematical models for the problem without testing it with a large amount of data, or having a good theory to explain why it must be like that. Finding out meaning among seemingly meaningless data is surely a big deal, but to resist the temptation of cooking up an artificial meaning is no less important.

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