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How Euler Did It, by Ed Sandifer

eulerarchive.maa.org

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Re: How Euler Did It, by Ed Sandifer

#11

Post by johngossman »

truckerbill wrote: post #8
rigid wrote: post #5

Earlier quoted context omitted.

I always stress how our public education is broken since it can't handle extreme talent very good. Important breakthroughs that advance one or more fields extremely or shifting paradigms completely, were done or prepared by whizzkids. In these times, we need every whizzkid we can get.

Education is a cog/mandarin factory in most countries. Whizzkids will educate themselves, what's needed is giving people idle time in order to pursue things. Most influential thinkers found themselves with this in some fashion. How much talent is wasted making people jump through hoops in academia/finance/ad-tech? A lot of pre-industrial thinkers were associated with the clergy because they received tax money from pe…

Reading Leo Szilard biography right now. School was easy and he just read all the time on his own. Which is pretty much (I’m no Szilard) how it was for me too. School boredom as a recipe for success?

Re: How Euler Did It, by Ed Sandifer

#12

Post by euroderf »

johngossman wrote: post #11
truckerbill wrote: post #8

Earlier quoted context omitted.

Education is a cog/mandarin factory in most countries. Whizzkids will educate themselves, what's needed is giving people idle time in order to pursue things. Most influential thinkers found themselves with this in some fashion. How much talent is wasted making people jump through hoops in academia/finance/ad-tech? A lot of pre-industrial thinkers were associated with the clergy because they received tax money from pe…

Reading Leo Szilard biography right now. School was easy and he just read all the time on his own. Which is pretty much (I’m no Szilard) how it was for me too. School boredom as a recipe for success?

Alternatively, school boredom as a recipe for being the class clown.

Re: How Euler Did It, by Ed Sandifer

#13

Post by FredPret »

norir wrote: post #7

It's interesting to me that I can't think of anyone remotely comparable to Euler in the public consciousness today. Even the work of someone like Erdos seems very esoteric by comparison and also was largely done in collaboration. Was Euler just born at the right time and picking all the low hanging fruit? Or maybe his immense creative production was a unique consequence of wealth plus limited distractions? I'm inclin…

It takes time for true quality to become apparent. Unfortunately the human who produced the work is long dead by then.

If humans ever started living much longer, we'd probably see a different attitude towards work.

Re: How Euler Did It, by Ed Sandifer

#14

Post by ufocia »

norir wrote: post #7

It's interesting to me that I can't think of anyone remotely comparable to Euler in the public consciousness today. Even the work of someone like Erdos seems very esoteric by comparison and also was largely done in collaboration. Was Euler just born at the right time and picking all the low hanging fruit? Or maybe his immense creative production was a unique consequence of wealth plus limited distractions? I'm inclin…

Maybe today's emphasis on "well rounded" education is a distraction from specialized talents.

Re: How Euler Did It, by Ed Sandifer

#15

Post by feoren »

norir wrote: post #7

It's interesting to me that I can't think of anyone remotely comparable to Euler in the public consciousness today. Even the work of someone like Erdos seems very esoteric by comparison and also was largely done in collaboration. Was Euler just born at the right time and picking all the low hanging fruit? Or maybe his immense creative production was a unique consequence of wealth plus limited distractions? I'm inclin…

Part of it is low-hanging fruit, certainly. Euler lived at a time when it was still possible to "know all math". That breadth of knowledge is simply not possible for a single human anymore; the discipline of mathematics is orders of magnitude larger. Comparable mathematicians today like Erdős and Terence Tao collaborate because they really can't learn the intricate details of every corner of math, so they collaborate with people who work in those corners instead. I think these are all people that have a deep understanding of the interconnected structures within math, and that makes them incredibly productive. I'm not going to try to compare the "level of genius" between Euler, Erdős, and Tao (although I think the latter two would readily claim Euler wins), but once you have a gift like that, there's a big difference between having all of mathematics in your head and not.

Re: How Euler Did It, by Ed Sandifer

#16

Post by [deleted] »

seanhunter wrote: post #3

Euler's wikipedia page has one of the most casually jawdropping sentences I've ever read about a human being: "Euler's work averages 800 pages a year from 1725 to 1783. He also wrote over 4500 letters and hundreds of manuscripts. It has been estimated that Leonard Euler was the author of a quarter of the combined output in mathematics, physics, mechanics, astronomy, and navigation in the 18th century." A quarter of a…

[deleted]

Re: How Euler Did It, by Ed Sandifer

#17

Post by Duanemclemore »

norir wrote: post #7

It's interesting to me that I can't think of anyone remotely comparable to Euler in the public consciousness today. Even the work of someone like Erdos seems very esoteric by comparison and also was largely done in collaboration. Was Euler just born at the right time and picking all the low hanging fruit? Or maybe his immense creative production was a unique consequence of wealth plus limited distractions? I'm inclin…

If not "low-hanging fruit" at least "first mover advantage."

Re: How Euler Did It, by Ed Sandifer

#18

Post by kenjackson »

rigid wrote: post #5
seanhunter wrote: post #3

Euler's wikipedia page has one of the most casually jawdropping sentences I've ever read about a human being: "Euler's work averages 800 pages a year from 1725 to 1783. He also wrote over 4500 letters and hundreds of manuscripts. It has been estimated that Leonard Euler was the author of a quarter of the combined output in mathematics, physics, mechanics, astronomy, and navigation in the 18th century." A quarter of a…

I always stress how our public education is broken since it can't handle extreme talent very good. Important breakthroughs that advance one or more fields extremely or shifting paradigms completely, were done or prepared by whizzkids. In these times, we need every whizzkid we can get.

No system will handle an Euler well. It’s best to recognize them and move them out of the system.

Re: How Euler Did It, by Ed Sandifer

#19

Post by testless »

norir wrote: post #7

It's interesting to me that I can't think of anyone remotely comparable to Euler in the public consciousness today. Even the work of someone like Erdos seems very esoteric by comparison and also was largely done in collaboration. Was Euler just born at the right time and picking all the low hanging fruit? Or maybe his immense creative production was a unique consequence of wealth plus limited distractions? I'm inclin…

Ramanujan died early. He is another one which comes to mind.

Re: How Euler Did It, by Ed Sandifer

#20

Post by The_Colonel »

ufocia wrote: post #14
norir wrote: post #7

It's interesting to me that I can't think of anyone remotely comparable to Euler in the public consciousness today. Even the work of someone like Erdos seems very esoteric by comparison and also was largely done in collaboration. Was Euler just born at the right time and picking all the low hanging fruit? Or maybe his immense creative production was a unique consequence of wealth plus limited distractions? I'm inclin…

Maybe today's emphasis on "well rounded" education is a distraction from specialized talents.

Specializing is actually the "easier" path, and thus there isn't a lot of low hanging fruit anymore. There are more opportunities in the intersections of different fields (areas of mathematics).
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