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MATHS VULGARIZATION THREAD
I EVENTUALLY found the perfect content linking Riemann& #39;s hypothesis to prime counting,by @jorgenveis
https://medium.com/cantors-paradise/the-riemann-hypothesis-explained-fa01c1f75d3f
It">https://medium.com/cantors-p... requires mathematical knowledge though (and I don& #39;t get everything) - so I tried to dumb it down for everyone to understand.
THREAD
https://medium.com/cantors-paradise/the-riemann-hypothesis-explained-fa01c1f75d3f
It">https://medium.com/cantors-p... requires mathematical knowledge though (and I don& #39;t get everything) - so I tried to dumb it down for everyone to understand.
THREAD
PART 1 - CONTEXT
Primes : prime numbers are numbers that are divisible only by 1 and themselves. You cannot decompose them through a multiplication with any other number. (e.g. 24 is 6x4 or 2x12 or 1x24 : it& #39;s not prime. But 17 is... well, only 17x1 : it& #39;s prime)
https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧮" title="Abacus" aria-label="Emoji: Abacus">
Primes : prime numbers are numbers that are divisible only by 1 and themselves. You cannot decompose them through a multiplication with any other number. (e.g. 24 is 6x4 or 2x12 or 1x24 : it& #39;s not prime. But 17 is... well, only 17x1 : it& #39;s prime)
What is KEY is that you can decompose ANY number as a multiplication of prime numbers - and reversely you can build ANY number with primes.
E.g. 232 is 2 x 2 x 2 x 29 in prime factors
https://abs.twimg.com/emoji/v2/... draggable="false" alt="👍" title="Thumbs up" aria-label="Emoji: Thumbs up">
E.g. 232 is 2 x 2 x 2 x 29 in prime factors
In other words, primes are the BUILDING BLOCKS of numbers.
Together, they are a bit like the periodic table in chemistry, or the design system of numbers : they represent the minimum and complete set you need to build every number
https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧱" title="Bricks" aria-label="Emoji: Bricks">
Together, they are a bit like the periodic table in chemistry, or the design system of numbers : they represent the minimum and complete set you need to build every number
The issue we have is that we don& #39;t know WHERE they are. If I give you a prime number like 23 367 457, we DON& #39;T have a formula giving you the prime that follows it.
We are forced to test manually, one by one, the ones that follow
=> we don& #39;t know the periodic table of numbers !
https://abs.twimg.com/emoji/v2/... draggable="false" alt="😱" title="Vor Angst schreiendes Gesicht" aria-label="Emoji: Vor Angst schreiendes Gesicht">
We are forced to test manually, one by one, the ones that follow
=> we don& #39;t know the periodic table of numbers !
Of course this has been bugging mathematicians for centuries.
Until B. Riemann, a German mathematician from the XIXth c., wrote a very short paper (9 pages!) that revolutionized our understanding of it.
https://abs.twimg.com/emoji/v2/... draggable="false" alt="🆕" title="Quadratisches NEW" aria-label="Emoji: Quadratisches NEW">
Until B. Riemann, a German mathematician from the XIXth c., wrote a very short paper (9 pages!) that revolutionized our understanding of it.
He created a formula that is called a "prime counting function", which basically increases by 1 every time you cross a prime number. It looks like the graph below : a "staircase".
If you have a formula for this function - you actually know where all primes are !
But the problem was not completely solved yet...
Why ? See part 2 below !
https://abs.twimg.com/emoji/v2/... draggable="false" alt="⬇️" title="Pfeil nach unten" aria-label="Emoji: Pfeil nach unten">
But the problem was not completely solved yet...
Why ? See part 2 below !
PART 2 - RIEMANN& #39;S HYPOTHESIS : MILLION DOLLAR BABY !
The formula Riemann built actually starts from a simple approximation of this function, that looks like an almost-straight line.
https://abs.twimg.com/emoji/v2/... draggable="false" alt="📈" title="Tabelle mit Aufwärtstrend" aria-label="Emoji: Tabelle mit Aufwärtstrend">
The formula Riemann built actually starts from a simple approximation of this function, that looks like an almost-straight line.
Then, he adds up infinitely many small corrections that, when added to the basic function, make the originally simili-straight line bend locally to approach,little by little,the "staircase" (below : blue=staircase, red=approximation with a few (but not all) corrections)
These little corrections are based on another function (the Riemann zeta function) he devised, and in particular, on the VALUES THAT MAKE THIS FUNCTION EQUAL TO 0. Those values are called... zeros https://abs.twimg.com/emoji/v2/... draggable="false" alt="😁" title="Grinsendes Gesicht mit lächelnden Augen" aria-label="Emoji: Grinsendes Gesicht mit lächelnden Augen">
For instance, a zero of the function x²-4 is 2 (because 2²-2=0)
https://abs.twimg.com/emoji/v2/... draggable="false" alt="0⃣" title="Tastenkappe Ziffer 0" aria-label="Emoji: Tastenkappe Ziffer 0">
For instance, a zero of the function x²-4 is 2 (because 2²-2=0)
And we don& #39;t know where primes are, because we don& #39;t really know where these zeros are.
Ok, I lied here : we have a pretty good idea of where they are, but it has never been proven.
The hypothesis describing where these zeros are is called the RIEMANN& #39;S HYPOTHESIS
https://abs.twimg.com/emoji/v2/... draggable="false" alt="❓" title="Rotes Fragezeichen-Symbol" aria-label="Emoji: Rotes Fragezeichen-Symbol">
Ok, I lied here : we have a pretty good idea of where they are, but it has never been proven.
The hypothesis describing where these zeros are is called the RIEMANN& #39;S HYPOTHESIS
This hypothesis is SO IMPORTANT to math, that the Clay institute has put a price of 1 million $ for everyone who will prove or disprove this hypothesis. It is one of seven so-called "Millennium Prize Problems" with such a prize attached.
https://abs.twimg.com/emoji/v2/... draggable="false" alt="🤑" title="Gesicht mit Geld-Mund" aria-label="Emoji: Gesicht mit Geld-Mund">
Of course, it& #39;s far from being easy. So complicated actually, that the one doing it will definitely stand on equal ground with Einstein, Pythagoras, Newton etc...
https://abs.twimg.com/emoji/v2/... draggable="false" alt="🍏" title="Grüner Apfel" aria-label="Emoji: Grüner Apfel">
To conclude this thread, 2 fun facts about all this :
https://abs.twimg.com/emoji/v2/... draggable="false" alt="1⃣" title="Tastenkappe Ziffer 1" aria-label="Emoji: Tastenkappe Ziffer 1"> Riemann was pretty sure his hypothesis was true, and said casually in his paper "I have, though, after some fleeting futile attempts, provisionally put aside the search"
He died unfortunately at 39 and never resumed it
https://abs.twimg.com/emoji/v2/... draggable="false" alt="😅" title="Lächelndes Gesicht mit offenem Mund und Angstschweiß" aria-label="Emoji: Lächelndes Gesicht mit offenem Mund und Angstschweiß">
He died unfortunately at 39 and never resumed it
Thanks for your time :)
#feedbacktime
Did you like this story ?
Is it clear ?
It& #39;s my first time vulgarizing science, so I& #39;m really interested in your feedbacks !
#feedbacktime
Did you like this story ?
Is it clear ?
It& #39;s my first time vulgarizing science, so I& #39;m really interested in your feedbacks !
