You could also say that the purpose of maths is falsifiable philosophy.
replyCalculus (e.g. differentiation), for example, is mind-blowing when taking it seriously, and not only useful.
The idea of "speed at an infinitely short moment", for example, is philosophy!
"Falsifiability" is generally understood in terms of physical observations. Mathematics is ultimately tautological: they are true or false by their own definition, without reference to the physical world.
replyIt just so happens that certain kinds of mathematics are unreasonably effective in drawing parallels to the physical world, but as far as mathematicians are concerned those mathematics are neither better nor worse than those that do not correspond to anything tangible.
> those mathematics are neither better nor worse than those that do not correspond to anything tangible.
replyA sweeping generalization. I certainly know professional mathematicians who disagree.
Also: many consider “inter-connectedness”, not “tangible” to be a sign that a topic is interesting. That is, it touches branches of mathematics aside from its own.
For GH Hardy, the more useless the maths is, the better and more beautiful it is.
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