Please see the embold phrases below. I'm just a laywoman, and I'm just seeking simple answers. I last took math when I was 17.
I read Has the standard of mathematical proofs changed over time?, but how did the standards of mathematical proof change "in the millennia separating Euclid from Hilbert"? I don't understand how they can change, when logic is forevermore permanent and objective.
Why are "standards of mathematical proof" "still not quite settled"?
RATIONALITY IN FLUX
Economic analyses have been based on Plato’s notion of a skillful weigher: To evaluate a plan, one first assigns utilities to every type of pain or pleasure that may result from the plan, at every point in time; then weights the utilities by probabilities to take account of uncertainty; and, finally, evaluates the plan in terms of such a weighted sum. My arguments indicate the need for a broader standard of rationality. Why should the tandard not change? Even standards of mathematical proof changed in the millennia separating Euclid from Hilbert, and they are still not quite settled. [Emphasis mine] I see no reason why Plato’s standard of rationality—or its modern economic versions, for that matter—should not also change in the face of increased knowledge of decision making, especially knowledge about choice construction and context-dependent social goals.
Paul Slovic, The Irrational Economist (2010), p 70.