Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

How Euler Did It, by Ed Sandifer

eulerarchive.maa.org

Post reply on HN
Print view View original

81–90 of 111 posts

Re: How Euler Did It, by Ed Sandifer

#81

Post by [deleted] »

testless wrote: post #50
liendolucas wrote: post #36

Earlier quoted context omitted.

Seriously? Oh god, please no. We need less of all that BS. People are thinking that are being "tutored" by AI, when in fact is just the output of a number crunching program. Reading books will get you way way closer to solid knowledge than the output crap of this so called "AI".

Happy to disagree here. I am hopeful that students get apps which provide them with - fast feedback loops - better adjustment to their learning speed - more patience - gamification - oppurtunity to ask endless questions Of course, only as an addition to the current mix. For math problems, this will be easier than for other contexts. I like text books for pop science or really hard things - like university level educa…

[deleted]

Re: How Euler Did It, by Ed Sandifer

#82

Post by pohl »

rigid wrote: post #76
kenjackson wrote: post #18

Earlier quoted context omitted.

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

You're basically saying the system is obsolete when society reaches a point, where it needs no more mediocre generalists and only excellent specialists.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.

Re: How Euler Did It, by Ed Sandifer

#84

Post by oglop »

smokel wrote: 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 the word "genius" only this man, von Neumann, Ramunajan and Grothendieck come to my mind. They simply saw the world differently.

Re: How Euler Did It, by Ed Sandifer

#85

Post by jiggawatts »

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…

Reminds me of the early days of computer science, the 60s and 70s.

I once casually flipped through the CS journal papers archived in my university library, and those two decades were really fascinating.

1) All of the papers were simple, clear, and easy to follow. No greek symbols, no fancy maths, just straighforward pseudocode.

2) The algorithms being presented were new at the time, but were rather trivial, and could have been invented by any of us. They just hadn't been invented, formalised, and written down yet. It was basically a race starting from zero, and nobody had taken very many steps yet.

3) Every new algorithm was such a huge leap that it unlocked many new avenues of advancement for other algorithms. There was a period where it was a race of publishing these follow-up developments nearly as fast as people could type.

For a modern example of this, look at the pace of progress of generative AI such as LLMs and Diffusion Models. The first papers were almost trivial, but that "one clever trick" unlocked many more ideas and the rate of publication over the last twelve months has been insane. A lot of low-hanging fruit, a lot of road-blocks suddenly removed, etc...

Re: How Euler Did It, by Ed Sandifer

#86

Post by mhh__ »

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.

It's more that mathematics is solely consumed inside "mathematics for engineering 101" spread across N years.

Re: How Euler Did It, by Ed Sandifer

#87

Post by fiforpg »

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…

Yep. But to be really scared of the man you can consider that during the later years of his life he lost eyesight, first in one eye, then went completely blind. All without slowing down.

The anecdote goes that with his eyesight already severely deteriorated, he would dictate papers with a grandkid or two in his lap and a cat on his shoulder.

Re: How Euler Did It, by Ed Sandifer

#88

Post by eichin »

guimplen wrote: post #66
testless wrote: post #60

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.

Oh, I thought this was riffing on the "shakespeare, in the original klingon" line.

Re: How Euler Did It, by Ed Sandifer

#89

Post by jasomill »

vacuity wrote: post #43
testless wrote: post #19

Earlier quoted context omitted.

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

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.

Another example: the notion of an n-dimensional geometric structure with intrinsic, variable curvature that serves as a mathematical foundation for the theory of general relativity originated with Riemann[1].

[1] https://www.maths.tcd.ie/pub/HistMath/People/Riemann/Geom/WK...

Re: How Euler Did It, by Ed Sandifer

#90

Post by CamperBob2 »

liendolucas wrote: post #36
testless wrote: post #29

Earlier quoted context omitted.

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

Seriously? Oh god, please no. We need less of all that BS. People are thinking that are being "tutored" by AI, when in fact is just the output of a number crunching program. Reading books will get you way way closer to solid knowledge than the output crap of this so called "AI".

You're making a serious mistake. If you're trying to learn something new, even in math or science, GPT4 is nothing less than a superpower.

The process of learning when to trust it and when not to is learning.

Post reply on HN