How Euler Did It, by Ed Sandifer
eulerarchive.maa.org
How Euler Did It, by Ed Sandifer
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Re: How Euler Did It, by Ed Sandifer
#2I 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 can be used to calculate any binary digit of π without calculating the previous digits. Up until now it was believed that the first formula with the correct properties (known as a BBP-type formula) for this calculation was published by Bailey, Borwein and Plouffe in 1997."
Re: How Euler Did It, by Ed Sandifer
#3Euler'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 all the output in so many fields. For a whole century. When you think about everyone else who was contributing to science at that time. It's just completely staggering.
Re: How Euler Did It, by Ed Sandifer
#4I 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…
Part of the problem is he wrote so much it has taken a while to go through it all. I believe the "Opera Omnia" project to publish all his works has been going for over a hundred years and is just about getting to the end now. So I would expect there's a huge amount that just hasn't been fully appreciated/digested.
Re: How Euler Did It, by Ed Sandifer
#5Euler'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.
Re: How Euler Did It, by Ed Sandifer
#6Euler'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…
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Re: How Euler Did It, by Ed Sandifer
#7It'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 inclined to believe there are similarly talented individuals today but wonder if it is even possible to fully recognize them in the moment. Perhaps we will only discover the Eulers (and Shakespeares and Bachs) of today in a few hundred years time.
Re: How Euler Did It, by Ed Sandifer
#8Euler'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.
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 peasants.
Re: How Euler Did It, by Ed Sandifer
#9It'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…
Karpathy! Carmack!
Re: How Euler Did It, by Ed Sandifer
#10It'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…
Karpathy! Carmack!
Carmack? I love him but that can’t be a serious suggestion