I thought my comments were clear and I was hoping for a clear response. Your response referring to conformation with an algorithm is not clear to me.
Mathematical reasoning has certainly demonstrated its usefulness to scientists, especially physicists, who try to understand how the world
"works." A "problem" with seeing mathematics as "science" is that mathematics is really a mind game (admittedly a very elegant one) like Chess or Go. The physical world (including everything from subatomic particles to galaxies and living and non-living things) is what it is. We humans, who can think about stuff, try to make sense of the physical world. We use all sorts of strategies to make sense of it. One of these strategies is to find "laws" that describe (and can predict) what we percieve and experience of the physical world.
Equations are nice when you can find them, like F=ma, but Darwin and Wallace's hypothesis about biological evolution by natural selection is an example of a profound "non-mathematical" insight into the way the world works. The fact is that mathematics gives not a whit about the physical world. There are plenty of "valid" mathematical formulations that may or may not be found by "scientists" to be useful in describing this or that aspect of
the world as we experience it.
Nick



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