"He kept Mechanics for 2000 in the dark ages,"
You can blame him for being wrong at first, but somewhere around, oh, 200 years later (very, very conservatively), the people who treated him as an unimpeachable source really ought to be assigned about 100% of the responsibility.
"A bit of mathematics would have helped."
Your use of modern terminology in the previous sentence leads me to think you're not clear on how primitive mathematics is for Aristotle. The calculus you are referencing comes from give-or-take two thousand years in the future, and while you can make a case that physics was "held back" by some very bad understandings, I think if you survey the history of mathematical development that you can't really make that argument for math [1]. Are you personally ready to stand and give an account to the future for failing to understand concepts that will be considered obvious and taught to whatever the equivalent of schoolchildren is in the year 4025 AD? 'Cause I wouldn't take that responsibility on.
[1]: What I mean here is that while mathematicians also had some errors, that just by the nature of math being built up from the ground those errors were never as fundamental as the physics errors because there was always a clear sense of what was well-grounded versus speculation. You have things like the casual assumption of Euclid's parallel postulate being true, but that didn't really "hold back" mathematics in the same way; it prevented the investigation of hyperbolic and spherical geometry but not discovering and/or investigating a new field is radically different than being persistently wrong about an existing one for centuries at a time.
Just to note all those points of Aristotle were corrected by Galileo, before calculus.
One thing that Galileo did more systematically than his precursors was that he found ways to treat time geometrically, as a spatial magnitude, so then he could draw distance-time graphs, and velocity-time graphs, which helped him in coming up with his law of fall (distance in free fall is proportional to the square of the time taken to fall), and then to deduce that the trajectory of a projectile is a parabola
> you're not clear on how primitive mathematics is for Aristotle
Completely agree, and to add some color: Aristotle lived about 100 years after Pythagoras, meaning in his time a²+b²=c² was groundbreaking material.
They didn’t even have access to algebraic notation (IIRC, an innovation of the Islamic Golden Age, a result of cross-pollinating Greek geometry with Indian arithmetic). So the groundbreaking material was that famous diagram of a right triangle with squares constructed on each side.
Interestingly, there is no actual reference to Pythagoras for this discovery until 5 centuries later, by Greek authors Plutarch and Cicero attributing this theorem specifically to Pythagoras.
However, Pythagoras’ Theorem is often linked to the Babylonians. There are implications of the theory on a fragment of a clay tablet from Babylonia in the Plimpton 322, dating back to approximately 1800 BCE.
Question: Why do things move?
Before Aristotle: Um, Zeus’s will I guess. No need to look further.
Aristotle: Great question! I don’t really know. But maybe that’s something we should investigate and reason about so that we can understand how our world works. Hmmm, maybe… like this?
After Aristotle: What he said. No need to look further.
I think he’d have been horrified at the idea that we could stop investigating, and yet.