Who was the first philosopher to describe what we now call curve fitting or approximation?
Pierre Duhem discusses this a bit in Aim & Structure of Physical Theory, pt. 2, ch. 3 "Mathematical Deduction & Physical Theory", pp. 132-43, § 4 of which is the "Mathematics of Approximation":
a mathematical deduction is of no use to the physicist so long as it is limited to asserting that a given rigorously true proposition has for its consequence the rigorous accuracy of some such other proposition. To be useful to the physicist, it must still be proved that the second proposition remains approximately exact when the first is only approximately true.
What does it mean to be "approximately true"? Isn't something either true or false?
this “mathematics of approximation” is not a simpler and cruder form of mathematics. On the contrary, it is a more thorough and more refined form of mathematics, requiring the solution of problems at times enormously difficult, sometimes even transcending the methods at the disposal of algebra today.
This describes what machine learning (=sophisticated curve-fitting) is.
Certainly philosophers before Duhem (✝1916) have discussed this, but who was the first?
Cf. "Duhem's Bull"
See my related question: "Are mathematical suppositions of physical theories determined uniquely according to Aristotle and Plato?"
another very related question: "If nature is inherently imprecise, how is it so easy for us to conceptualize mathematical certainties?"