[sdenton4]

It's also the case that genius alone isn't sufficient. One also needs hard work and, as Ramanujan illustrates, access to institutions that can publish+legitimize the work.

I also find it fun to consider that the population is 7x larger today than it was in 1800, and there's generally much better access to education across the board. Around 1900 you've got a bunch of absolute giants in mathematics: Hilbert and Ramanujan, for starters, but also Riemann and Lobachevsky (whose noneuclidean geometry work was basically Einstein minus the physics). So, suppose O(5) world-changing geniuses. On raw population alone, one would expect about 35 people of similar caliber to be active today. But also mathematics as a profession, access to phd programs, etc, is many times larger per capita than it would have been in 1900. So I would personally guess that there's likely to be a couple hundred people currently active in math of a similar caliber.

[jerf]

Bear in mind that if someone of Euler's level is operating today, you very likely wouldn't know unless you were in the field, and it might not necessarily be obvious even then.

If you cloned Euler, and magically gave the clone a new upbringing that resulted in the same math skills, Euler!clone wouldn't be becoming famous for proving e^iπ + 1 = 0, because he'd have learned that in high school like the rest of us. Instead, he might go off and do something like Terence Tao and hack away at the Twin Prime conjecture in a series of papers that require a PhD in mathematics just to understand the abstract. It's a lot harder to become famous that way, even if the work being done is much harder in some sense.

I don't want to diminish the genius of pa-h mathematicians, because Euler is still a legitimate genius by any measure, but part of the reason why he could get around the way he did is that he was metaphorically working in a field where he could pluck ripe fruit off the ground. Similar geniuses exist today, but even as geniuses they still need ladders to get to the fruit now, and that just takes more time.

I'm not lamenting this, celebrating it, or judging it... it just is the way it is.

[posterboy]

Cool, I commented to the same effect, but your food-based metaphor brings to mind the notion that we have less lead in the water today, better health care, a handle on air pollution etc. p. p. I am doubting that as I write it, thinking of the hopelessness of CO2 reduction and all the things to come after we have already passed the point of no return.

And I wouldn't want to grow up be a giraf either,if climbing a tree works as well, or just shake it up.

Oh boy, these metaphors are useless.

Let's put it another way. Picking the low hanging fruit has just become either, and it is still necessary to get there. As you mention Terry Tao, to imply at the same time that we had never heard of him is rather disingenious. What is the point?

It has been noted that science, for lack of a better word, is becoming increasingly specialized on the individual level and that we have no polymaths today as it were. Maybe you are still correct insofar as we from in the midst of it cannot yet really tell what combination of skill will take the crown.

But then let's drop a few names, Peter Shor, Noam Chomsky, Frederik Kortlandt. Oh that's right, you never heard of Kortlandt, probably my favorite Indo-Europeanist.

[posterboy]

Interesting thought. We are after all posting under a link to John C. Baez.

But the thought is ultimately naive. The pedastol we put these people on doesn't grow with the number of people alive. I don't know what model of a social network you would need to make that calcjlation. The measure of genious that should obviously be part of that theory, but I am sure such measure does not exist objectively.

Besides, I'd argue that with an evergrowing body of knowledge and tooling necessary to weild it, the requirements and constraints for a genious today are different from the times that you want to compare. For a measure and linear growth you would need a linear space to begin with.

Really though, I just wanted to say that there is a ton of smart people out there. Shoulders of giants and all. Which should be a humbling thought.