Fido Johnson

@GWOMaths Today we enjoy the famous MARKOV EQUATION x² + y² + z² = 3xyz This simple equation results in some utterly fabulous number theory! Fancy some fun? Come take a peek. [Thread…]

@supergeekmike Seek help.

Spent the day fielding a flood of annoying comments from idiotic transphobes, all repeating the same mind-numbing arguments over and over. It was so tedious. But all I could imagine is how much worse it would be if I was trans. I KNOW they always get so much more shit than us.

@geoclidean Copied in hope to my online maths friends @chris_juravich @CPierre67 @fcqv @pgeerkens For some reason, the inelegance of my solution has really infuriated me ☹️

@geoclidean Please, someone, tell me there’s a quicker way than this! I have explored half a dozen different rabbit holes and this is the best I can do. Too much algebra, too little number theory. Presumably there is a ‘trick’ that those versed in competition maths will have memorised?

Perfect square #NumberTheory #PrimeNumbers

@chris_juravich @CPierre67 @kofibhr @microfusio91945 It has an Abel sum of 1. The infinite series 0+1+1+0-1-1+… with repeating cycle length six can be represented by the generating function g(x) = x / (x² - x + 1) No need to take limits as it is well defined at x=1 with g(1)=1. Feel free to check my work, it’s late!

@CPierre67 @kofibhr @JohnsonFido @microfusio91945 Try this related problem:

@chris_juravich @CPierre67 @microfusio91945 Fascinating, such different first reactions! I saw iterated application of a function. Oh good, k! in the denominator will force rapid convergence, so I’ll quickly see how it behaves. I play with it and think, oh dear, this is *awfully* messy. Then… oh, it’s calculus 🤪

@CPierre67 @JohnsonFido @microfusio91945 It starts at one, and goes to 2026. So, 0,1,1,0,-1,-1 and repeating …

@CPierre67 @chris_juravich @microfusio91945 Oh yes, very similar.

@JohnsonFido @chris_juravich @microfusio91945 See …

@chris_juravich @CPierre67 @microfusio91945 A quick way to get the coefficients is to notice that f(x) • (1 + x³) = -1 + x² Hence the -1,0,1 then 1,0,-1 then -1,0,1 then 1,0,1 repeating pattern.

@JohnsonFido @CPierre67 @microfusio91945 Thank you, Fido @JohnsonFido. I probably spent an inordinate amount of time to figure out the coefficients. I also guessed that this was a competition-level problem, meaning that a pattern would emerge fairly quickly.

@chris_juravich @CPierre67 @microfusio91945 I was confused at first, as I assumed that the notation was for repeated application of the function, not differentiation. But having worked out what the question meant, I would use precisely the same method. And I probably used about as much paper 😂

@CPierre67 @microfusio91945 @JohnsonFido probably needs less scratch paper. 🤔

@fcqv @pgeerkens @sonukg4india Yes sorry, good typo spot! I’m following you both so we are at the whim of the algorithm.

@pgeerkens @JohnsonFido @sonukg4india Indeed. Also just noticed my follow of you had dropped. I was wondering where all the maths had gone:)

#morning with #math

@MaggieScarisbr1 @Jim_Cornelius @GordonFielden @C4Dispatches @lewis_goodall Feigning not to understand the difference between male and female, and allowing that delusion to persist in his party, has fatally destroyed his credibility with many people. It renders him similarly untrustworthy as conspiracy theorists and boxes of frogs.

@GordonFielden @C4Dispatches @lewis_goodall So, Keir Starmer is apparently more unpopular than Liz Truss. Why? He hasn't wrecked the economy. He isn't as mad as a box of frogs. He doesn't spout conspiracy theories out of his backside. He has respect of world leaders. It's bloody obvious why. Media bias. And not just RW.

After winning one of the biggest landslides in UK election history less than two years ago, Keir Starmer became the most unpopular prime minister on record. But how did that happen? @lewis_goodall is on a mission to find out.

@NadiaWhittomeMP Oh dear. When we wonder in the future how Labour managed to fail so badly… this is how. Student politicians promoted far beyond their competence.

Efforts to narrow the definition of womanhood, police people’s gender expression, and reduce people to their biology don't protect women - they harm us. Attacks on trans rights should never be done in our name. We must stand in solidarity with our trans siblings.

@Quietknightze @Math_files You would publish your paper for peer validation.

@Math_files How would you go about collecting this prize? Seriously

In 1859, a quiet German mathematician named Bernhard Riemann posed a question so dangerous it still haunts us today. He was studying prime numbers—those lonely, indivisible sentinels scattered across the number line. Primes appear random, chaotic, like stars flung across a dark sky with no pattern. But Riemann found something, a hidden music. He discovered that primes dance to the rhythm of a mysterious function. And the key to understanding that rhythm lives on a single invisible line—the critical line—where every zero of his function should fall. No one has ever proven it. For over 160 years, the greatest minds in mathematics have tried and failed. There is a $1 million prize waiting for whoever can. But it is not about the money. It is about this. If the Riemann Hypothesis is true, then beneath the chaos of primes lies perfect, breathtaking order. The universe is not random. It is composed.

@HardFiat @Math_files No impact. Hackers are already free to assume that it is true if they think that will help them. And for all practical purposes it *is* true, as the first few billion zeroes (or as many as we’re up to by now) all satisfy RH.

@Math_files And if it can be proven: Most encryption will break down?

@xinspiteofx I agree. There’s no reason to wait until September. Make it effective now.

Well this feels incredibly mean spirited and unkind

@Math_files So many followers. So little rigour. This really isn’t anything to do with twin primes 🙄

The Twin Primes Conjecture is one of the most famous unsolved problems in mathematics—simple to understand, yet still mysterious. Twin primes are pairs of prime numbers that differ by 2: (5, 7), (11, 13), (17, 19), … The big question: Are there infinitely many twin primes? No one knows—yet. But here’s a fun little property: Take any pair of twin primes (except 3 and 5), multiply them, and then repeatedly add the digits until you get a single digit. Examples: 5 × 7 = 35 → 3 + 5 = 8 11 × 13 = 143 → 1 + 4 + 3 = 8 17 × 19 = 323 → 3 + 2 + 3 = 8 59 × 61 = 3599 → 3 + 5 + 9 + 9 = 26 → 2 + 6 = 8 It always leads to 8. A simple pattern, hidden inside prime numbers—reminding us that even in unsolved mysteries, mathematics is full of beautiful surprises.

@back_the_BBC @RaymondSnoddy Ok, but you said he was from outside the BBC. Were you mistaken?

@JohnsonFido @RaymondSnoddy He's widely regarded as a commercial / marketing person, not someone with editorial experience. Hence the repeated mistakes of the past year

A "courageous" decision if flawed BBC board goes ahead with this. In 80 years never has been a BBC DG who was not a national newspaper editor, a programme maker, a broadcasting journalist or had worked at BBC for years. Matt Brittin is none of the above. Good luck to one and all

@back_the_BBC @RaymondSnoddy I thought that Davie was at the BBC for 15 years before becoming DG?

@JohnsonFido @RaymondSnoddy Almost everyone on the current BBC board and executive committee has come from outside the BBC - including Tim Davie - and they mostly haven't a clue about editorial or broadcasting decisions.

@BBCMoreOrLess @robeastaway @ChrisMasonBBC @TimHarford ‘Multiplication is commutative’ should really not be a surprise to anyone.

"That is brilliant." Learn the maths hack from @robeastaway that blew the minds of @ChrisMasonBBC and @TimHarford