Chemistry -- "wet bench" chemistry -- had to wait for physical technology to catch up, in order that compounds could be prepared in anything like pure form; and the insistence on *NON* mathematical constructs such as phlogiston, as well as difficulties with non-reversibility of reactions involving organic compounds, significantly delayed the progress of chemistry.
And even Mendeleyev laid out the periodic table by associating various chemical characteristics of the elements, well in advance of either modern atomic theory, quantum mechanics, or knowledge of the Aufbau principle. Purely empirical.
The reason I said that scientific proof is weaker than mathematical, is Feynman's famous quote: "It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong."
Evidence of this is given by Relativity, which is purely mathematical in essence -- people like to trumpet how Relativity was "proven" by experimental measurements of the precession of the perihelion of Mercury.
But in reality, the first couple of measurements were taken as *dis*proof of Relativity: it was only after the setup and results were re-checked that the current conclusion was reached.
Or, for that matter, look at the large number of variations in fundamental particle physics / cosmology: String Theory, SuperSymmetry, Loop Quantum Gravity, Hawking's declaration of a variable event horizon for black holes and the idea of "firewalls".
All due to paucity of data.
I never mentioned the social sciences; you did.