Math used to be a young person game, but it now requires so much knowledge just to get to the frontiers of human knowledge, not to speak of making a dent into uncharted territory, that results are being obtained later and later in life. When mathematicians have had time to accrue sufficient knowledge while still being sharp enough to make the intellectual leap. The sad part is that as the trend continues we may reach…
I haven't spent much time thinking about this but were Einstein's contributions a combination of intellect and "shallow" or relatively quick frontiers. I.e. a very intelligent intellectual working on the problem sets that are approachable without the same level of overhead required these days? I.e. Today's world wouldn't support an individual who could have such an impact on most math/scientific disciplines?
Newton's Gravity was known to be incomplete for many years, just by looking at Mercury. It took several carefully derived experiments studying light for 100s of years that led us to Maxwell's equations in the 1860s that became the basis for Einstein's special relativity in the 1910s. You don't need a billion dollar particle accelerator to come up Maxwell's Equations (2 of them were done by Guass in the 1700s!). 20 or 30 years (and talent!) studying calculus or physics could get you something.
Today we know Einstien's theory of gravity is incomplete but the only places it is incomplete is inside of a black hole (good luck running a test in a blackhole) or at very tiny scales where gravity's affect is minimal. Today, I don't know how you would even come up with a competing theory without having millions to spend on a particle accelerator. While einstein famously just did a thought experiment on what should happen if the speed of light is constant for all observers, most "discoveries" are done now by smashing particles in billion dollar tubes.