Newton and Leibniz discovered calculus simultaneously. If calculus were a hot new idea now, dozens or hundreds of people would be discovering it simultaneously.
Look at NN/LLM AI for an example.
(Btw there are many contemporary mathematicians at least at the level of Terence Tao but for some reason haven't been blessed by lay popularity -- mostly because Tao's math looks more school math like / familiar to non-math people than say Peter Scholze's)
Euler lived nearly three centuries after the invention of the printing press. He had vast numbers of books available to him and essentially unlimited paper to write on. He also had been tutored in algebra which remains the most important development in the history of mathematics. The abstract manipulation of symbols made possible by algebra is such an enormous leap over the geometric methods of the ancient mathematicians. It allows one to solve countless problems trivially in seconds which would take days to solve geometrically.
Etale cohomology was a low-hanging fruit because it depended on a bunch of mathematics and technology that Grothendieck benefitted from: algebra, the printing press, and modern transportation. Sure, Euler had horse drawn carriages but that is nothing compared to the speed of modern transportation that Grothendieck had available to him.
Because it wasn't low hanging thousands of years ago. It was only low hanging after an enormous body of foundational work was laid down over those thousands of years. And Euler knew all of it. It's no longer possible to know all of mathematics.
> every other batch of students in a math camp I'm familiar with has someone who has 'proved' quadratic reciprocity for themselves
This is exactly my point though: things get easier to understand over time as the more foundational mathematics gets laid out to prepare for them. Nowadays some of this stuff is considered basic. It's very "low hanging fruit" now, it's just that those summer-camp kids aren't making the discovery for the very first time. What point exactly are you defending here?
> Btw there are many contemporary mathematicians at least at the level of Terence Tao but for some reason haven't been blessed by lay popularity
I'm not sure why this needs to devolve into a contest. Terence Tao, Peter Scholze, whoever: they can't know all math anymore, like Euler did. That is ultimately why there are no more Eulers.
That Euler knew most of the math of his time is irrelevant. If one had any serious learning at any time in most of human history one would know all the math of their time.
Not to be rude, but saying this about a Fields medallist is somehow very funny.
I have no data to back it up.
Bullets with rifling came about circa 1820 (ish) but were not widespread by 1832 and traditional dueling pistols remained the norm for quite some time, the element of chance likely factored in as part of the hand of god influencing outcomes.
https://en.wikipedia.org/wiki/Duelling_pistol
For some in the eighteenth century, duelling with less-accurate, smooth-bore weapons was preferred as they viewed it as allowing the judgement of God to take a role in deciding the outcome of the encounter.
[1] https://www.maths.tcd.ie/pub/HistMath/People/Riemann/Geom/WK...
If humans ever started living much longer, we'd probably see a different attitude towards work.
Today that concept is watered down. A "well rounded" education is just taking a few classes that people hate and will blow off because to graduate they need to check some boxes so they can focus on doing one thing moderately well and finding their place as a cog in a machine that will abuse their ignorance. It's all mass produced conveyor belt education that manufactures young adults with little conventional wisdom. The more you lean into behaving like a part, the more you will be treated that way.
[1] Bird vs. Frogs. https://www.ams.org/notices/200902/rtx090200212p.pdf
I once casually flipped through the CS journal papers archived in my university library, and those two decades were really fascinating.
1) All of the papers were simple, clear, and easy to follow. No greek symbols, no fancy maths, just straighforward pseudocode.
2) The algorithms being presented were new at the time, but were rather trivial, and could have been invented by any of us. They just hadn't been invented, formalised, and written down yet. It was basically a race starting from zero, and nobody had taken very many steps yet.
3) Every new algorithm was such a huge leap that it unlocked many new avenues of advancement for other algorithms. There was a period where it was a race of publishing these follow-up developments nearly as fast as people could type.
For a modern example of this, look at the pace of progress of generative AI such as LLMs and Diffusion Models. The first papers were almost trivial, but that "one clever trick" unlocked many more ideas and the rate of publication over the last twelve months has been insane. A lot of low-hanging fruit, a lot of road-blocks suddenly removed, etc...