Love the writing style, and I wish all math was written this way. These articles are accessible to anyone who has had some high school math background, and paints a historical backdrop on how the sausage was made (with links to the original papers). Some of these ideas took millenia to develop, and when presented in neat capsule, students are cheated of the mystery and struggle that went into the progression and development of the ideas. I would argue that all math education has to be re-invented to follow this style, ie, uncover the historical progression, wonder and mystery.
What does the Riemann zeta function have to do with the distribution of primes?
41–48 of 48 posts
Re: What does the Riemann zeta function have to do with the distribution of primes?
#42Re: What does the Riemann zeta function have to do with the distribution of primes?
#43Love the writing style, and I wish all math was written this way. These articles are accessible to anyone who has had some high school math background, and paints a historical backdrop on how the sausage was made (with links to the original papers). Some of these ideas took millenia to develop, and when presented in neat capsule, students are cheated of the mystery and struggle that went into the progression and deve…
Wholeheartedly agree that this is a great educational approach, telling the story of an idea's development through history, the people involved, the major milestones, how the original spark was shaped, questioned, extended, and refined to its present form. I often find myself tracing an idea "backward" through time, to discover where it came from, who was influenced by whom, and learn so much from the journey.
This story usually explains why some concept is the way it is, whereas the typical presentation is to just give you the final form, without untangling the logic and its historical development. Also, starting from the original conception - like ancient Greeks or Indian philosopher, etc. - is much more relatable because one can see the "primitive" shape of an idea. And I mean primitive in the best sense of the term, thinking from first principles.
Re: What does the Riemann zeta function have to do with the distribution of primes?
#44Re: What does the Riemann zeta function have to do with the distribution of primes?
#45Earlier quoted context omitted.
Obviously, I would prefer OC was more specific. I said as much.
Genuine question: are you on the spectrum? I find this reaction strange
Wait... so you are perfectly OK with hating someone on the basis of some random online poster telling you that you should, with no explanation?
Wow.
Re: What does the Riemann zeta function have to do with the distribution of primes?
#46Earlier quoted context omitted.
Genuine question: are you on the spectrum? I find this reaction strange
Wait... so you are perfectly OK with hating someone on the basis of some random online poster telling you that you should, with no explanation? Wow.
I don’t automatically hate someone because someone calls them despicable
Re: What does the Riemann zeta function have to do with the distribution of primes?
#47What is the relationship between Riemann zeta function and Zipf's law? And between words and primes?
The link is between numbers and words. Both can be decomposed into primitive components: primes and lyndon words (combinatorics). The Zipf distribution takes this shape when the vocabulary is infinite:
P(r)=r^-s / Zeta(s) with s > 1
Zipf law != Zipf distribution, still this is intriguing.
Integers and Prime Numbers: Deriving Zipf's Law (https://arxiv.org/abs/2403.12773)
> In a prime number decomposition of integers in a given set, the occurrence frequencies of prime numbers are shown to satisfy a general forms of Zipf's law.
The same holds for Lyndon words decomposition of random strings to a certain extent.
Re: What does the Riemann zeta function have to do with the distribution of primes?
#48Although the author turned out to be a fairly despicable person, Prime Obsession is an absolutely wonderful book on this subject.
This is one of the few places I ever engage on the internet, but I think it may be time for HN to be read-only, too. This didn't seem especially controversial of a comment, and even here there's no end of the rotten attitudes for no good reason
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