It was based on solving a maths equation.
True.
There's a big and very obvious difference between "scientific research" and "mathematics".
Ehhhhh
Nobody was out there putting clocks on satellites
Technically true, but they were definitely doing experiments. The inconsistencies in Maxwell's electrodynamics and previous physics were the hot topic of late 19th century physics. To the point where various people thought resolving them would put the finishing touches on physics. Even the popular account includes the Michealson-Morely experiment.
Einstein himself says in "On the Electrodynamics of Moving Bodies" (i.e. the special relativity paper):
It is known that Maxwell’s electrodynamics—as usually understood at the
present time—when applied to moving bodies, leads to asymmetries which do
not appear to be inherent in the phenomena. Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the
magnet, whereas the customary view draws a sharp distinction between the two
cases in which either the one or the other of these bodies is in motion. ...
Examples of this sort, together with the unsuccessful attempts to discover
any motion of the earth relatively to the “light medium,” suggest that the
phenomena of electrodynamics as well as of mechanics possess no properties
corresponding to the idea of absolute rest. They suggest rather that, as has
already been shown to the first order of small quantities, the same laws of
electrodynamics and optics will be valid for all frames of reference for which the
equations of mechanics hold good.
There were a whole bunch of relevant experiments. Lorentz reviews many of them in "On the influence of the earth's motion on luminiferous phenomena”, published in 1886.
Anyway, the author's point is not that AI can't think because it can't find the consequences of equations. Regular old numerical simulations and logic engines are pretty good at that, no AI required. His point is that AI can't think because it cannot generate ideas out of thin air, presumably the "pure reason" of ancient greek philosophy, and he uses Einstein as an example.