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How Euler Did It, by Ed Sandifer

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Re: How Euler Did It, by Ed Sandifer

#101

Post by testless »

vkazanov wrote: post #67
testless wrote: post #60

Earlier quoted context omitted.

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

I think what parent meant was that Euler spent a few decades in Russia because of the funding provided by the empire. He spoke fluent Russian, even though there was a large German-speaking community there. But it was typical for scientists to travel far for money. Some of the Bernoullis, a family famous for mathematicians, also worked in Russian for quite a while. Does it really matter who payed 'em and what language…

I was just surprised;-)

Re: How Euler Did It, by Ed Sandifer

#102

Post by mncharity »

oglop wrote: post #80

Euler's textbooks were such a gift to Europe. I'm always a bit perplexed he doesn't get more credit for this given he wrote some of the first calculus books people could read, because Newton had not cared or tried to. So in many ways Euler was also just an incredible educator and largely lead the charge spreading many of these new ideas. Usually credit is given to Chatelet, but she didn't really write any textbooks,…

> You would never see something like that now

I've been wondering if an llm might be tuned to recognize insightful explanations that are accessible and powerful, to then help train one for creating such. Trying for an AI tutor that's less like drilling textbook bogosity and superficiality, and more like tutoring by that rare someone known for their outlier-deep understanding of a field. Even if an llm only manages to serve as a delivery mechanism for human curated insights, having a deployment story of very widespread impact might help motivate a novel-y broad contribution and curation effort.

Re: How Euler Did It, by Ed Sandifer

#103

Post by peterfirefly »

jterrys wrote: post #41
ufocia wrote: post #14

Earlier quoted context omitted.

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

Absolutely HARD disagree. Pythagoras, Aristotle, Pascal, Descartes, Newton, Franklin, DaVinci, (just to name a few) were all polymaths. They all left lasting impacts outside of a singular domain. It's because they were such well rounded individuals that they were so successful and capable of revolutionary discoveries and inventions. Our world is made up of models that are related with other models that are related ba…

They didn't have to waste much time going to school -- and certainly not going to school with average people. That makes it a lot easier to get a good, well-rounded education -- if you are bright enough!

Re: How Euler Did It, by Ed Sandifer

#104

Post by oglop »

EasyMark wrote: post #92
oglop wrote: post #84

Earlier quoted context omitted.

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?

No, though this did make me realize I left Riemann out, so I would include him as well.

Re: How Euler Did It, by Ed Sandifer

#105

Post by zyklu5 »

chongli wrote: post #62
zyklu5 wrote: post #56

Earlier quoted context omitted.

I find the notion of 'low-hanging fruit' in such contexts profoundly ahistorical. If graph theory was low-hanging why did it take thousands of years since Sumer or ancient Egypt? Or consider something from number theory: every other batch of students in a math camp I'm familiar with has someone who has 'proved' quadratic reciprocity for themselves -- and how could they not ? -- since childhood they have been immersed…

It's low-hanging fruit because it depended on a bunch of mathematics and technology that Euler benefitted from: algebra, the printing press, and mass-produced paper. Sure, the Ancient Egyptians had papyrus but that is nothing compared to the volume of paper Euler had available to him. Euler lived nearly three centuries after the invention of the printing press. He had vast numbers of books available to him and essent…

Your first sentence can be used for anything:

Etale cohomology was a low-hanging fruit because it depended on a bunch of mathematics and technology that Grothendieck benefitted from: algebra, the printing press, and modern transportation. Sure, Euler had horse drawn carriages but that is nothing compared to the speed of modern transportation that Grothendieck had available to him.

Re: How Euler Did It, by Ed Sandifer

#106

Post by zyklu5 »

feoren wrote: post #64
zyklu5 wrote: post #56

Earlier quoted context omitted.

I find the notion of 'low-hanging fruit' in such contexts profoundly ahistorical. If graph theory was low-hanging why did it take thousands of years since Sumer or ancient Egypt? Or consider something from number theory: every other batch of students in a math camp I'm familiar with has someone who has 'proved' quadratic reciprocity for themselves -- and how could they not ? -- since childhood they have been immersed…

> If graph theory was low-hanging why did it take thousands of years since Sumer or ancient Egypt? Because it wasn't low hanging thousands of years ago. It was only low hanging after an enormous body of foundational work was laid down over those thousands of years. And Euler knew all of it . It's no longer possible to know all of mathematics. > every other batch of students in a math camp I'm familiar with has someon…

The difference is, to put in Rumsfeldian fashion, between known unknowns (kids proving QR now) and unknown unknowns (euler sensing QR, gauss proving it).

That Euler knew most of the math of his time is irrelevant. If one had any serious learning at any time in most of human history one would know all the math of their time.

Re: How Euler Did It, by Ed Sandifer

#107

Post by CamperBob2 »

rigid wrote: post #100
pohl wrote: post #82

Earlier quoted context omitted.

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 tire…

If you're an Einstein-class talent, luck doesn't have much to do with it. You'll find a way to do your thing.

One example: someone elsewhere in the thread mentioned John Carmack. Carmack's not a thief, or at least it would be a grotesque oversimplification to label him as one. But he stole an Apple II when his parents wouldn't buy him one.

What's critical is that once talent is identified, it's nurtured to the greatest extent possible.

Re: How Euler Did It, by Ed Sandifer

#108

Post by rigid »

CamperBob2 wrote: post #107
rigid wrote: post #100

Earlier quoted context omitted.

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 tire…

If you're an Einstein-class talent, luck doesn't have much to do with it. You'll find a way to do your thing. One example: someone elsewhere in the thread mentioned John Carmack. Carmack's not a thief, or at least it would be a grotesque oversimplification to label him as one. But he stole an Apple II when his parents wouldn't buy him one. What's critical is that once talent is identified, it's nurtured to the greate…

This a classic "post hoc ergo procter hoc" fallacy.

You just can't know, how much more Einsteins there would be. People that would never steal an Apple II or would never even get that opportunity.

Heck, if Einstein became a younger father, there's a good chance he never looked deeper into physics despite talent and interest without someone (like a teacher) pushing him.

I claim that it's pure coincidence. Carmack didn't make it because of public education but despite of it. We can't afford this anymore.

Re: How Euler Did It, by Ed Sandifer

#109

Post by CamperBob2 »

rigid wrote: post #108
CamperBob2 wrote: post #107

Earlier quoted context omitted.

If you're an Einstein-class talent, luck doesn't have much to do with it. You'll find a way to do your thing. One example: someone elsewhere in the thread mentioned John Carmack. Carmack's not a thief, or at least it would be a grotesque oversimplification to label him as one. But he stole an Apple II when his parents wouldn't buy him one. What's critical is that once talent is identified, it's nurtured to the greate…

This a classic "post hoc ergo procter hoc" fallacy. You just can't know, how much more Einsteins there would be. People that would never steal an Apple II or would never even get that opportunity. Heck, if Einstein became a younger father, there's a good chance he never looked deeper into physics despite talent and interest without someone (like a teacher) pushing him. I claim that it's pure coincidence. Carmack didn…

IMO the risk is not that Einsteins (and Carmacks) won't have the educational opportunities they need. That may have been a showstopper in the past but it certainly isn't today, not with the resources we have now from YouTube to ChatGPT.

And the world is full of parents who are neglectful with no excuse at all. I don't think early fatherhood would stop an Einstein.

Instead, the risk is that talented people will die of starvation, disease, or warfare before they have the chance to become who they are. Or that their career will be cut short by similar circumstances. See Ramanujan, or the even more-tragic but lesser-known https://en.wikipedia.org/wiki/Oleg_Losev .

That's where the luck factor really comes into play... the luck to be born someplace peaceful. The luck to be born male, if you have to be born into a culture driven by social or religious biases. The luck to receive the nutrition (never mind the Apples) you need as a growing child. The luck that just plain keeps other people the fuck out of your way.

And that's what we have to work on as a civilization. It's a bigger problem than simply arguing over how public education should work, or whether scientist X or inventor Y would have benefited from policy Z.

Re: How Euler Did It, by Ed Sandifer

#110

Post by srean »

Cyph0n wrote: post #63
vacuity wrote: post #43

Earlier quoted context omitted.

Riemann died young, too. I only really know him for the Riemann sum formulation of integrals (I have yet to learn complex analysis), but I wouldn't be surprised if he has some popular reach through the Riemann hypothesis.

Galois is yet another.

If only he had devoted some time to marksmanship
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