I want to know more about an intuitive take on how the Zeta function does what it does! I know it must relate somehow to finding (or perhaps excluding) all the composite numbers but I'd really love to get more of a feeling about what each 'octave' of the function is adding-in. Seems like it must be something that 'flattens' the composites but increases sharply (in the infinite sum) at each prime.. but it's still a mystery to me how one could intuitively realise or discover that it's this specific function!? How did he do it?!
I wonder, has anyone tried looking for the pattern for prime numbers in a non-base-10 representation? I've always had a hunch that maybe the chaos only seems random because our representation of numbers could be misaligned with the pattern.
> humans decided they were "prime", i.e. most important, based on arbitrary considerations
No, not arbitrary considerations.
The term goes back at least to Euclid who investigated factorization of integers in his "Elements". He used the greek word "protos" that was later translated to Latin as "primus". It doesn't mean "most important", rather "first".
The idea is that primes are the "multiplicative building blocks" for other numbers, the "origin" or "first principles", because every integer factors into primes. When a mathematical object can be decomposed in some way, it is very natural to study the irreducible blocks, because many questions boil down to them.
Prime numbers are also important in computability theory. Godel number, for example, uses prime number to assign each symbol and laid the foundation for Godel's incompleteness theorem
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[ 4.8 ms ] story [ 47.3 ms ] threadThe article is a good "first introduction" to the presentation.
[0] https://duckduckgo.com/?q=Romanesco&iar=images&t=ffab&iai=ht...
Let them try it with hydrogen gas.
For some reason this made me think of the Ulam Spiral -- https://en.wikipedia.org/wiki/Ulam_spiral.
The obsession with prime numbers (humans decided they were "prime", i.e. most important, based on arbitrary considerations).
It seems like a version of astrology to me.
Am I wrong? I'd be happy to be proved wrong.
No, not arbitrary considerations.
The term goes back at least to Euclid who investigated factorization of integers in his "Elements". He used the greek word "protos" that was later translated to Latin as "primus". It doesn't mean "most important", rather "first".
The idea is that primes are the "multiplicative building blocks" for other numbers, the "origin" or "first principles", because every integer factors into primes. When a mathematical object can be decomposed in some way, it is very natural to study the irreducible blocks, because many questions boil down to them.