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How Euler Did It, by Ed Sandifer

eulerarchive.maa.org

91–100 of 111 posts

Re: How Euler Did It, by Ed Sandifer

#91

Yeah, the greatest Russian mathematician.

People are generally associated with where you were born/grew up/attended uni, and unless he claimed to have thrown off all that, I think we can't move the goal posts. So I think the best you can do is "Swish scientist and mathematician while under decades Russian patronage" and not really Russian. I would accept it if he had forsaken his Swiss heritage or something of that sort, but he didn't. Maybe Swiss-Prussian-Russian mathematician?

Re: How Euler Did It, by Ed Sandifer

#92
post #84
post #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 ac…

There's ample evidence from the time that rather than take credit, as _many_ unethical scientists have tried (*cough Newton), Euler was quite the opposite. I think one of his strengths was in his prolific collaborations actually, or taking up questions others sent to him which he did not need to work on, but would out of curiosity or decency. I get why someone not familiar with him may think this, but when I think of…

But not Newton or Einstein or Maxwell?

Re: How Euler Did It, by Ed Sandifer

#93

Earlier quoted context omitted.

I think Swiss. He was born in Basel. [1] https://en.wikipedia.org/wiki/Leonhard_Euler

He worked in Russia more than in any other country and died in St Petersburg being a Russian citizen.

I wonder what he would have considered himself - he spent more time in St Petersburg than anywhere else but was born in Basel and spent a good bit of time in Berlin. For what it's worth, the Opera Omnia are published by the Swiss Academy of Sciences.

Re: How Euler Did It, by Ed Sandifer

#94
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…

Edward Witten bestrides mathematical physics in an Euler-likes way. In math/physics circles, ask the smartest person you know who is the smartest person they know and sooner or later all roads lead to him.

Re: How Euler Did It, by Ed Sandifer

#96

Earlier quoted context omitted.

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.

How is this humanly possible? Was Euler even an order of magnitude faster at producing new math than, say, Gauss or von Neumann?

There’s more about the effort to publish his complete works here: https://en.m.wikipedia.org/wiki/Opera_Omnia_Leonhard_Euler

Re: How Euler Did It, by Ed Sandifer

#97
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.

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

That sounds like a good system.

Re: How Euler Did It, by Ed Sandifer

#98
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…

https://en.wikipedia.org/wiki/List_of_things_named_after_Leo...

Re: How Euler Did It, by Ed Sandifer

#99

Hmmm... our corporate firewall is blocking the connection as it says the SSL cert is "insecure". Something tells me this is BS, but anyone got any ideas why it might say this?

Firefox says the certificate uses a disabled signature algorithm `SEC_ERROR_CERT_SIGNATURE_ALGORITHM_DISABLED`

The certificate is signed using a SHA-1 signature, which is considered insecure by all major browsers afaik.

Although, inspecting the certificate also gives me validity:

    Not After Fri, 05 Dec 2014 12:00:00 GMT
Which is slightly out of date.

Even the CA cert it shows me has

    Not After Sun, 03 Apr 2022 00:00:00 GMT

Re: How Euler Did It, by Ed Sandifer

#100
post #82
post #76

Earlier quoted context omitted.

You're basically saying the system is obsolete when society reaches a point, where it needs no more mediocre generalists and only excellent specialists. I wouldn't be so pessimistic.

That's the least charitable interpretation, I think. A more charitable read is that no system should be one-size-fits-all, so move outliers to specialized subsystems.

Not sure. In Germany there's an ongoing debate for extending conprehensive schools [1] across all ages. It's a complex topic but the general gist of supporters is, that pupils profit from each other. (e.g. Bad ones get help from the good while those practice how to cooperate and explain etc.).

I don't think it's that complex. My personal premises are

* if the kid doesn't like to get up and go to school or is too tired over longer periods, the school is doing something wrong, not the kid. * if there are A LOT of kids like this, the school authority is doing something wrong (and so on, up to government) * an older kid needs support on every topic at any time when interest arises. It's the kids' choice not the schools'. * learning at school must be fun, at least 90% of the time.

That way whizzkids are easily detected, will be less frustrated and thus perform better.

I got some good example anecdotes but better won't "textwall" here :-)

Just imagine a world, where Einstein would get optimum support from young age so he would start professional physics years earlier.

Or one where he didn't go to the patent office but one where he worked in some factory or other place, not finding the spare time he needed to do physics.

Way too much luck involved if you ask me.

[1] https://en.wikipedia.org/wiki/Comprehensive_school

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