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How Isaac Newton discovered the binomial power series

quantamagazine.org

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Re: How Isaac Newton discovered the binomial power series

#21

Post by psychphysic »

plopilop wrote: post #12
ColinWright wrote: post #7

Earlier quoted context omitted.

There's a reason they don't. I failed my PhD first time around, with the external examiner recommending I not even go to the viva stage, saying that the results were obvious and trivial, not worthy of a PhD. He recommended I be given a Masters and not even permitted to re-write or re-submit. My internal examiner insisted we go to viva , wherein I managed to convince them (unaware of all the above) that the results we…

I clearly despise academics (and the papers they write) who think that everything should look novel by hiding your thought process. Sadly, especially in fields where conferences are favored over journals, this seems to be common: you only have a single chance of impressing the reviewer, so you lose little by hiding your thought process, and if possible make your result look more complicated that it actually is. Many…

I think there is a balance to be struck and certainly don't want to say oh well there should be another journal for that.

But before the internet elaborate pedagogical papers simply took up to much paper real estate and so brief punchy result dense work was produced.

Im won over by the article in preprint then elaboration blog posts theme we see more in maths.

Re: How Isaac Newton discovered the binomial power series

#22

Post by agumonkey »

ColinWright wrote: post #7
ironSkillet wrote: post #4

I love articles like this. I wish more research papers and textbooks actually explained how people came up with their ideas/proofs in the first place.

There's a reason they don't. I failed my PhD first time around, with the external examiner recommending I not even go to the viva stage, saying that the results were obvious and trivial, not worthy of a PhD. He recommended I be given a Masters and not even permitted to re-write or re-submit. My internal examiner insisted we go to viva , wherein I managed to convince them (unaware of all the above) that the results we…

Reminds me of a strange effect of optimizing a graph traversal. Early demoes without perf took time and lots of logs. People thought it was hard. With improvements it was instantaneous. People thought my code did nothing.

Re: How Isaac Newton discovered the binomial power series

#24

Post by dataflow »

tpoacher wrote: post #20
ColinWright wrote: post #7

Earlier quoted context omitted.

There's a reason they don't. I failed my PhD first time around, with the external examiner recommending I not even go to the viva stage, saying that the results were obvious and trivial, not worthy of a PhD. He recommended I be given a Masters and not even permitted to re-write or re-submit. My internal examiner insisted we go to viva , wherein I managed to convince them (unaware of all the above) that the results we…

Alas, I have reached exactly the same conclusion over the years. You need to strike the right balance between not obfuscating too much such that the reader ragequits in frustration, versus obfuscating things just enough so that the reader has to put a bit of "work" before the insight hits home, lest they fail to appreciate how much effort getting to that insight took in the first place, and dismiss it for a trivial o…

Do you feel like papers should have separate derivations & proofs of correctness? The second one requiring correctness (intuition being secondary), and the first one being intuitive (rigor being secondary).

Re: How Isaac Newton discovered the binomial power series

#26

Post by EGreg »

ironSkillet wrote: post #4

I love articles like this. I wish more research papers and textbooks actually explained how people came up with their ideas/proofs in the first place.

I want to write a book on the history of science, where we actually go througy what people thought (luminiferous ether, phlogiston, the humours) until some experiments convinced them otherwise (michelson morley etc). Who knew what (Arabs and algebra), and how did it spread (Jusuits)? I think it is really needed but I haven’t found any approach like this ! It is all about the shrinkwrapped final results and modern beliefs. And often the modern beliefs are being updated too (such as theory of atoms, big bang, plate tectonics etc.)

Where can I get this info? Anyone know of anything close to this?

Re: How Isaac Newton discovered the binomial power series

#27

Post by dotancohen »

vmilner wrote: post #11
dotancohen wrote: post #9

Earlier quoted context omitted.

I have a similar experience in industry (software development) that I relive weekly, but I never learn. When I help someone solve a problem, I like to show them how I got to the solution. In the end, my hour invested was "we did it together" and not appreciated by anyone, least of all the manager. But on the few occasions that I just bang out a function quickly for somebody because I don't have the time, I'm hailed a…

Mr. Jabez Wilson laughed heavily. “Well, I never!” said he. “I thought at first that you had done something clever, but I see that there was nothing in it after all.” “I begin to think, Watson,” said Holmes, “that I make a mistake in explaining. ‘Omne ignotum pro magnifico,’ you know, and my poor little reputation, such as it is, will suffer shipwreck if I am so candid. - "The Red Headed League", (The Adventures of S…

That's brilliant.

This time, maybe I've learned. Thank you.

Re: How Isaac Newton discovered the binomial power series

#28

Post by NoWizards »

dotancohen wrote: post #9
ColinWright wrote: post #7

Earlier quoted context omitted.

There's a reason they don't. I failed my PhD first time around, with the external examiner recommending I not even go to the viva stage, saying that the results were obvious and trivial, not worthy of a PhD. He recommended I be given a Masters and not even permitted to re-write or re-submit. My internal examiner insisted we go to viva , wherein I managed to convince them (unaware of all the above) that the results we…

I have a similar experience in industry (software development) that I relive weekly, but I never learn. When I help someone solve a problem, I like to show them how I got to the solution. In the end, my hour invested was "we did it together" and not appreciated by anyone, least of all the manager. But on the few occasions that I just bang out a function quickly for somebody because I don't have the time, I'm hailed a…

Just remember: Dev works in mysterious ways.

Re: How Isaac Newton discovered the binomial power series

#29

Post by dekervin »

ironSkillet wrote: post #4

I love articles like this. I wish more research papers and textbooks actually explained how people came up with their ideas/proofs in the first place.

I totally believe it should be one of the available way to discover maths. By finding or asking oneself why we studied a problem and how we arrived at a solution; either historically or by filling in the blanks.

It just happen that I was sharing minutes ago, the start of my very weak personal attempt at building a math "tech tree" out of that idea ( Someone suggested me the name ). Starting with euclidian geometry.

here is the link: http://mathuvue.pythonanywhere.com/ (I apologize in advance , I am not a native english speaker, and it's only the kernel of what I really want to do)

Everything around mathematics is a lonely endeavor. I would love to get in touch with anyone that might be interested in anyway.

My email in my profile !

Re: How Isaac Newton discovered the binomial power series

#30

Post by layer8 »

vmilner wrote: post #15
ironSkillet wrote: post #4

I love articles like this. I wish more research papers and textbooks actually explained how people came up with their ideas/proofs in the first place.

Check out https://www.amazon.com/Mathematics-Its-History-Undergraduate... which goes through the history of maths while actually _doing_ some maths at undergraduate level. Also the lectures based on it by N J Wildberger E.g. https://www.youtube.com/watch?v=HRD9X-2Bmdw&t=2692s

It seems to be missing topics like statistics, linear algebra, differential equations and Fourier transforms.
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