> In 1902, Henri Poincaré published a collection of essays titled Science and Hypothesis, which included: detailed philosophical discussions on the relativity of space and time; the conventionality of distant simultaneity; the conjecture that a violation of the relativity principle can never be detected; the possible non-existence of the aether, together with some arguments supporting the aether; and many remarks on non-Euclidean vs. Euclidean geometry.
https://en.wikipedia.org/wiki/History_of_special_relativity
Now, if I had to pick a major idea that seemed to drop fully-formed from the mind of a genius with little precedent to have guided him, I might personally point to Galois theory (https://en.wikipedia.org/wiki/Galois_theory). (Ironically, though, I'm not as familiar with the mathematical history of that time and I may be totally wrong!)
As for general relativity, he spent several years working to learn differential geometry (which was well developed mathematics at the time, but looked like abstract nonsense to most physicists). I’m not sure how he was turned on to this theory being applicable to gravity, but my guess is that it was motivated by some symmetry ideas. (It always come down to symmetry.)
> Critique of absolute time and space of Newtonian physics was already well underway
> Many of the phenomena that relativity would later explain under a consistent framework already had independent quasi-explanations hinting at the more universal theory.
Your argument really makes the claim that since there are others pursuing similar directions that this means it is in distribution. I'll use a classic statistics style framing. Suppose we have a bag with n red balls and p blue balls. Someone walks over and says "look, I have a green ball" and someone else walks over and says "I have a purple one" and someone else comes over and says "I have a pink one!". None of those balls were from the bag we have. There are still n+p balls in our bag, they are still all red or blue despite there being n+p+3 balls that we know of.
> I am not a [...] physicist
I only believe that (1) if it hadn't been Einstein, it would very soon have been someone else using very similar concepts and evidence, (2) "completely novel idea" is a stricter criterion than "not in distribution," and (3) better examples of completely novel ideas from history exist as a benchmark for this sort of things.
> Without a formal study of physics it is really hard to differentiate these kinds of propositions. It can be very hard even with that education. So be careful to not overly abstract and simplify concepts. It'll only deprive you of a lot of beauty and innovation.
I agree, but with the caveat that I think ancestor worship is also an impediment to understanding our intellectual and cultural heritage. Either all of human creativity deserves to be treated sacredly, or none of it does.
> The quintic was almost proven to have no general solutions by radicals by Paolo Ruffini in 1799, whose key insight was to use permutation groups, not just a single permutation.
Thing is, I am usually the kind of person who defends the idea of a lone genius. But I also believe there is a continuous spectrum, no gaps, from the village idiot to Einstein and beyond.
Let me introduce, just for fun, not for the sake of any argument, another idea from math which I think it came really out of the blue, to the degree that it's still considered an open problem to write an exposition about it, since you cannot smoothly link it to anything else: forcing.
https://en.wikipedia.org/wiki/Prat%C4%ABtyasamutp%C4%81da https://iep.utm.edu/processp/
Edit: but even it likely relied on his prior experience with nondualistic Hinduisms, of course.
General relativity was a completely novel idea. Einstein took a purely mathematical object (now known as the Einstein tensor), and realized that since its coveriant derivative was zero, it could be equated (apart fron a constant factor) to a conserved physical object, the energy momentum tensor (except for a constant factor). It didn't just fall out of Riemannian geometry and what was known about physics at the time.
Special relativity was the work of several scientists as well as Einstein, but it was also a completely novel idea - just not the idea of one person working alone.
I don't know why anyone disputes that people can sometimes come up with completely novel ideas out of the blue. This is how science moves forward. It's very easy to look back on a breakthrough and think it looks obvious (because you know the trick that was used), but it's important to remember that the discoverer didn't have the benefit of hindsight that you have.
I'm not sure about GR, but I know that it is built on the foundations of differential geometry, which Einstein definitely didn't invent (I think that's the source of his "I assure you whatever your difficulties in mathematics are, that mine are much greater" quote because he was struggling to understand Hilbert's math).
And really Cauchy, Hilbert, and those kinds of mathematicians I'd put above Einstein in building entirely new worlds of mathematics...
Source: https://www.newtonproject.ox.ac.uk/view/texts/normalized/THE...
"Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore."
:)