The thing about mathematics is that it doesn’t become particularly easy if you don’t know anything. If you imagine a growing sphere of mathematical knowledge then things in the middle might have been discovered but the surface area of the edge grows as that happens.
Sure Euler could do random crazy algebra things that no one had thought of but I don’t think he was in a position to invent Gaussian curvature. Erdős did a lot of combinatorics and graph theory and Ramsay theory which, apart from the latter, are full of questions that are easy to state and which plenty of people might have thought of, and yet which weren’t solved until he came along. There’s also the possibility of discovering a new proof of an old result which he did a bit.
Nevertheless, I do not agree with the spirit of GP’s point, as one could equally argue that Euler accomplished so much while working from what was, from today’s perspective, an impoverished starting point.
There is a term, ‘Whig history’, which has come to epitomize the attitude of evaluating historical characters in accordance with current standards. It is not a helpful mode of analysis.
Whiggishness is just a massive problem in the history of science and mathematics. There’s so much history that sees it as inevitable as if all the contemporaries of Newton and Leibniz were desperately trying to invent the calculus if only they could figure out how to do it.
True but publication standards change over time. If none of Euler’s publications are “trivial” in the sense that processors will gloss over the proof during lectures that would be surprising.
That would be surprising. But, my experience has generally been that when a result of Euler comes up in class, it's more frequently preceded with "this was published by Euler but not really rigorously proven." Standards of proof were obviously different 250 years ago.
A recognition of diminishing returns on effort and low-hanging fruit is not "a small way to think." You might not agree that these things exist but that is no reason to insult someone who believes a fairly mainstream thing about scientific progress.
Well... Lebesgue integration is a different basis from Reimann integration, so you might say it's a new basic method. If by "basic" you mean "high-school-calculus simple", it's probably not that. (Though the fundamental idea is simple enough to explain - see the Wikipedia article.)
In order to prove that discovering calculus got harder, you would obviously need to show that the population of people who could discover it but didn't have prior knowledge of it was at least as large as when it was discovered. In addition, in order for there to be published (or even submitted) papers, you would need those people to not only not have any prior knowledge but to not encourter anyone with a highschool understanding of calculus in the review and publishing process.
As that is equally obviously not the case, I repeat; that's not how that works.
Has the wheel gotten harder to invent since it hasn’t been invented in a million years? Your question makes no sense for the reasons pointed out by GP.
