Hello Jbrenner,
Hume was better known in his time as an economist and historian. He was an empiricist of the enlightenment. His most recognized and controversial contribution to philosophy was his questioning of induction as an infallible source of fact.
He reasoned that with the exception of math, if you could not prove something empirically one could not be certain. To prove that something existed, one needed to provide evidence through observation, but induction from observation was limited, e.g., one cannot say that all swans are white, just because one has never observed a black swan.

I believe Rand's primary problem with Hume was that he was an influence on Kant. Kant, of course, took things too far in another direction, questioning the validity of observation and emphasized the influence of one's mind on the world as observed. He did not trust anyone to observe reality faithfully. He undercut man's conceptual and cognitive capacity. He undercut the faculty of reason.

"If you observe that ever since Hume and Kant (mainly Kant, because Hume was merely the Bertrand Russell of his time) philosophy has been striving to prove that man’s mind is impotent, that there’s no such thing as reality and we wouldn’t be able to perceive it if there were—you will realize the magnitude of the treason involved." Ayn Rand, Return of the Primitive, The Anti-Industrial Revolution, A R Lexicon

Good to see you are still fighting the good fight,
OA

Knowledge advances by the use of proposition and experiment, thinking and observation.
Human ideas are verified or falsified by recourse to human senses, these are not infallible.

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.
Richard Feynman, Cornell University Lecture, 1964

From what I've read, it was Hume's contention that one should not be restricted by past conclusions when investigating the future that influenced and encouraged Einstein to continue pursuing a logical path that was out of step with the accepted view of physics at the time. Einstein was at first highly skeptical of what he was discovering, and almost dropped what led him to the discovery of relativity, primarily because he was ridiculed and berated by other scholars who "knew better."

I think Einstein would be laughing and sympathetic with the new generation of scholars who contend that Einstein might not have gotten relativity entirely right, as he would feel empathy for the abuse many of them take.

After Einstein arrived in the US at Princeton he made no additional major advances in physics, but seeing that Quantum Mechanics did not follow the principles of General Relativity, he spent the rest of his life trying to find a way to refute how things operate at an atomic level different than at the macro level. He said "God does not play games," but in the sense of QM he certainly does. Einstein's contribution to science is huge, but it all happened in Germany, long before his arrival in the US. He still had a huge impact on society, but not in Physics, e.g., when asked if we should build a nuclear device.. The finding of Gravitation Waves validates sort of the last thing of Einstein postulated. Einstein made great contribution to physics, but got stuck on QM. He just couldn't bring the two together (theory of Everything) and in some ways we are still trying to do the same. I think that it is pretty well accepted that he wasted his time going up a blind alley, we should be careful not to do the same.

To me the most important part of the letter was:

"Hume writes: 'The chief objection against all abstract reasoning is derived from the ideas of Space and Time. Ideas in everyday life may appear clear and intelligible, but when they pass through the scrutiny of the profound Sciences... they seem full of absurdity and contradiction.'"

Which would be in accord with Hume. I will paraphrase Einstein for his belief that empiricism is the means to gain knowledge of objective reality (yes Einstein even used that term in the EPR paper). He said something like, it is time to bring the ideas of space and time down from the 'a priori' .

I am reading a fiction book right now, Split Second, by Douglas E Richards. It covers a lot of physics by Einstein and it is mind boggling! Block universes, space time, etc. It is fascinating reading and I have an immense appreciation of Einstein's mind! (I have never had any experience with physics before).

Reason and evidence.

Yep...

Now that the Higgs field has been proven to create mass by slowing down Quarks causing resistance to acceleration and giving energy to the gluons that flit back and forth at the Sub atomic level.

Maybe bending of time-space that we perceive as gravity can now be integrated with the Higgs field and how it crates mass. Should one of you do this please give credit for your inspiration coming from my writings. :)