>>14277224Let me explain what I think about it.
The method of testing hypothesis (falsifiability, following Popper) is the "corrective" part of science, but really no one has a theory of how conjectures are born, and that's exactly where the similarities between the mathematician, the philosopher and the scientist and any creative machine emerge. Perhaps it's useful to put "invention" (music, engineering, etc (also, note that in some sense art itself is a form of psychological engineering, as one tries to manipulate the experiences of another person when performing/creating art. I believe this idea is due to Alfred Gell, the anthropologist)) and "discovery" (science, mathematics) as separate cases, but I won't go into this division further now.
Take then only science and mathematics. The process of creation of conjectures involves what we could call an emergence of forms in the mind of the scientist or mathematician. I believe that's why disciplines like physics, in which phenomena are "exact" and amenable to reductionist analysis, have theoretical and experimental scientists each doing their thing. The theoretical scientist will essentially think as a mathematician, he will analyze the behavior of (theoretical, aka abstract) objects/concepts through different perspectives in order to synthesize the different aspects of that object/concept into a cohesive whole.
Also, when I compare the mathematician to the scientist, I'm not suggesting that the scientist should be "distant from reality". Quite the contrary... see
https://mathshistory.st-andrews.ac.uk/Extras/Von_Neumann_Part_1, an article Von Neumann wrote on this topic.
