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How Euler Did It, by Ed Sandifer

eulerarchive.maa.org

21–30 of 111 posts

Re: How Euler Did It, by Ed Sandifer

#21

Earlier quoted context omitted.

Karpathy! Carmack!

Carmack? I love him but that can’t be a serious suggestion

Yeah Carmack is no doubt a 20x engineer, but I wouldn’t put him in the same category of prolific genius as Euler. As far as prolific engineers go, I’d say Fabrice Bellard would be closer (but still not even close) to an Euler.

Re: How Euler Did It, by Ed Sandifer

#22

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…

There's a reason so many things are named after the second person to discover something after Euler: mf died in 1783 and is still publishing papers today.

Re: How Euler Did It, by Ed Sandifer

#23
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…

The issue I see these days is that every industry is getting more and more competitive, and leaves less and less time to think more broadly or creatively. Can't go off reading about differential geometry when you need a guaranteed perfect SAT, a great entrance essay (i.e. a strong personal story), and easy-to-gauge extracurriculars ("placed X in Y", not "read some smart books and had some interesting thoughts that don't impress the admissions officer"). Same goes for the industry and academia as well.

Re: How Euler Did It, by Ed Sandifer

#24
post #2

I have read a few of these and enjoyed them greatly. Reading them you realise that Euler really did invent a huge swathe of mathematics in use today. In particular I read this one: http://eulerarchive.maa.org/hedi/HEDI-2009-02.pdf And I realised that Euler had found two formulae for Pi which can be used to calculate any hex digit of Pi. I wrote this up in a paper: "In 1779 Euler discovered two formulas for π which ca…

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Re: How Euler Did It, by Ed Sandifer

#25
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…

Is Euler really well known in public? Einstein is way more well known than Euler, I'd guess. Even if you will ask most famous mathematician, it is unlikely that he is named. Probably Pythagoras.

I have no data to back it up.

Re: How Euler Did It, by Ed Sandifer

#26
Is it possible that these prolific geniuses had smart people working for (or with) them, while taking most credit?

I could imagine that in 300 years time people think that Elon Musk single-handedly invented the Turing machine, at the age of 16, during a weekend, while reading Hacker News.

How would one go about disproving such an hypothesis? I've had similar doubts about Leonardo da Vinci, but I'm afraid Euler was actually just brilliant.

Re: How Euler Did It, by Ed Sandifer

#27
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…

Euler is in a class of one. Judging by the volume of work and the pleasure he takes in collaborations, Terence Tao seems to be having a positive impact. I am not a mathematician but I hear good things about the quality of his work.

Re: How Euler Did It, by Ed Sandifer

#28
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…

One thing (in retrospect) that I love about the xUSSR school system, is its focus on competitive math and physics.

There's a robust multi-level system of "Olympiads", starting from the neighborhood level, and going all the way up to the national level. Every student knows about them, and more importantly, "magnet schools" scoop up students who do well in competitions.

This works really well for math, and so pretty much every Fields medal award ceremony has awardees from the xUSSR countries.

I'm really surprised that this kind of system is not more widespread, especially in the US. After all, sports and competition is kinda a thing here?

Re: How Euler Did It, by Ed Sandifer

#29
post #5

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.

Let's hope education indivualizes to the need and talents of the individual partially via software. ChatGPT is my hope here.

15% failure rate is optimal for learning

https://www.nature.com/articles/s41467-019-12552-4

Re: How Euler Did It, by Ed Sandifer

#30
post #2

I have read a few of these and enjoyed them greatly. Reading them you realise that Euler really did invent a huge swathe of mathematics in use today. In particular I read this one: http://eulerarchive.maa.org/hedi/HEDI-2009-02.pdf And I realised that Euler had found two formulae for Pi which can be used to calculate any hex digit of Pi. I wrote this up in a paper: "In 1779 Euler discovered two formulas for π which ca…

[deleted]
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