The Riemann Hypothesis

Jørgen Veisdal, Medium: The Riemann Hypothesis, explained

In loving memory of John Forbes Nash Jr.

You remember prime numbers, right? Those numbers you can’t divide into other numbers, except when you divide them by themselves or 1? Right. Here is a 3000 year old question:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, p. What is p? 31. What is the next p? It’s 37. The p after that?41. And then? 43. How, but… …how do you know what comes next?

Present an argument or formula which (even barely) predicts what the next prime number will be (in any given sequence of numbers), and your name will be forever linked to one of the greatest achievements of the human mind, akin to Newton, Einstein and Gödel. Figure out why the primes act as they do, and you will never have to do anything else, ever again.

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The Story Of Math Genius Ramanujan

Photo: Srinivasa Ramanujan. Wikiedia

Cosmos: Ramanujan – a humble maths genius

Ramanujan’s extraordinary mathematical ability has become the stuff of legend. Paul Davies tells his story.

The number 1,729 is not one to make the average person’s pulse race, but it is the subject of one of the most remarkable stories in the history of mathematics.

Most of us learnt basic arithmetic at school, and we all remember that some students were better at it than others – the bright girl who could do sums twice as fast as the rest of us, or the boy who could prove theorems in a trice. Of course all subjects attract a range of skills, but almost unique to mathematics are a handful of extreme outliers who are so good it seems they are deploying some form of magic. The best-known genius of this type was Srinivasa Ramanujan.

Born in 1887, Ramanujan was an eccentric young Indian student who lived in obscurity in the town of Kumbakonam in the state of Tamil Nadu. Bestowed with remarkable analytical skills, by the age of 13 he had devised his own scheme for computing the digits of pi that is still in use today. He spent much of his spare time scribbling formulae in notebooks or on a small blackboard.

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CSN Editor: Wikipedia has an excellent list of links on the work that this mathematical genius did. The Wikipedia entry is here.

Predicting Lottery Numbers

The mathematician behind the study has created a website which uses colour patterns to show number combinations which are more likely to win the lottery based on previous draws in 20 lotteries from around the world - but you may need more than GCSE maths to decipher the code

Mathematician Claims Probability CAN Predict Lottery Numbers More Likely To Be Drawn (But You May Need A Maths Degree To Work Them Out) -- Daily Mail

* Renato Gianella says it is possible to predict winning lottery numbers
* Theory is based on patterns as predicted by Law of Large Numbers
* Brazilian claims not all numbers have equal chance of being drawn
* He's developed website to help people select more favorable combinations
* But users may need more than basic maths to understand how it works
* Study was based on 20 lotteries around the world

A Brazilian mathematician claims it is possible to predict the results of a lottery draw by applying complicated maths and probability theories.

Renato Gianella has found it is entirely possible to predict numbers which are more likely to appear than others, by following the same behaviour patterns as predicted by the Law of Large Numbers.

His study called The Geometry of Chance: Lotto Numbers Follow a Predicted Pattern, finds not all combinations of numbers have the same probability of occurring – so in short, it is possible to predict patterns of numbers with a greater chance of being drawn.

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My Comment: Sadly .... he does not mention if he has used this system for himself .... and if has .... how much has he won.

16 Year Old Solves 300-Year-Old Mathematical Riddle Posed By Sir Isaac Newton

Shouryya Ray

German Teen Solves 300-Year-Old Mathematical Riddle Posed By Sir Isaac Newton -- FOX News

DRESDEN, Germany – A German 16-year-old has become the first person to solve a mathematical problem posed by Sir Isaac Newton more than 300 years ago.

Shouryya Ray worked out how to calculate exactly the path of a projectile under gravity and subject to air resistance, The (London) Sunday Times reported.

The Indian-born teen said he solved the problem that had stumped mathematicians for centuries while working on a school project.

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My Comment: 16 years old .... knew calculus at 6. OK .... he has a gift.

17 Equations That Changed the World

How 17 Equations Changed The World -- Brain Pickings

What Descartes has to do with C. P. Snow and the second law of thermodynamics.

When legendary theoretical physicist Stephen Hawking was setting out to release A Brief History of Time, one of the most influential science books in modern history, his publishers admonished him that every equation included would halve the book’s sales. Undeterred, he dared include E = mc², even though cutting it out would have allegedly sold another 10 million copies. The anecdote captures the extent of our culture’s distaste for, if not fear of, equations. And yet, argues mathematician Ian Stewart in In Pursuit of the Unknown: 17 Equations That Changed the World, equations have held remarkable power in facilitating humanity’s progress and, as such, call for rudimentary understanding as a form of our most basic literacy.

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An App On The History Of Math

1,000 Years Of Maths... Via An App: IBM Creates A (Very Long) iPad Timeline History Of Geeks' Favourite Subject -- Daily Mail

To celebrate the history of maths and its impact on the world, IBM has released Minds of Modern Mathematics - an iPad app that re-imagines a classic 50-foot infographic on the history of maths.

It was created by husband-and-wife design team Charles and Ray Eames and displayed at the 1964 World’s Fair in New York City.

The app is designed as an ‘interactive vintage-meets-digital experience for students, teachers, and tech fans that illustrates how mathematics has advanced art, science, music and architecture’.

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My Comment: The history of science has always a fascination for me .... having an app for it .... divine.

Is God A Mathematician?

From afar, Richard Feynman seemed as dangerous as plutonium (Image: CERN/SPL)

From New Scientist:

THE physicist Richard Feynman said, "It doesn't seem to me that this fantastically marvellous universe, this tremendous range of time and space and different kinds of animals, and all the different planets, and all these atoms with all their motions, and so on, all this complicated thing can merely be a stage so that God can watch human beings struggle for good and evil - which is the view that religion has. The stage is too big for the drama."

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The 10 Best Mathematicians

Pythagoras, from a 1920s textbook. Photograph: © Blue Lantern Studio/Corbis

From The Guardian:

Alex Bellos selects the maths geniuses whose revolutionary discoveries changed our world.

Pythagoras (circa 570-495BC)

Vegetarian mystical leader and number-obsessive, he owes his standing as the most famous name in maths due to a theorem about right-angled triangles, although it now appears it probably predated him. He lived in a community where numbers were venerated as much for their spiritual qualities as for their mathematical ones. His elevation of numbers as the essence of the world made him the towering primogenitor of Greek mathematics, essentially the beginning of mathematics as we know it now. And, famously, he didn't eat beans.

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Will Reclusive Mathematician Accept $1 Million Prize?

Photo: Grigory Perelman.

From New Scientist:

A million-dollar prize for solving one of toughest problems in mathematics has been awarded to a Russian mathematician, but the real puzzle is whether he'll accept it.

The reclusive Grigoriy Perelman has been recognised for his proof of the Poincaré conjecture, one of seven Millennium prize problems selected by the Clay Mathematics Institute (CMI) in 2000 as the most important unsolved problems in mathematics.

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Professor Predicts Baseball Winners, Uses Baseball to Tout Power of Math

"We've long had a problem convincing US youngsters to embrace mathematics in school," says Bukiet. "Studying how math applies to baseball demonstrates not only that math can be fun, but how it is really a part of things people care about." (Credit: NJIT)

From Science Daily:

Science Daily (Mar. 10, 2010) — With pitchers and catchers having recently reported to spring training, once again Bruce Bukiet, an associate professor at NJIT, has applied mathematical analysis to compute the number of games that Major League Baseball teams should win in 2010. The Philadelphia Phillies, St. Louis Cardinals and Los Angeles Dodgers should all repeat as winners in their divisions, while the Atlanta Braves will take the wild card slot in the National League (NL), says Bukiet.

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'Most Beautiful' Math Structure Appears In Lab For First Time

The signature of a mathematical structure called E8 has been seen in the real world for the first time (Illustration: Claudio Rocchini under a creative commons 2.5 licence)

From New Scientist:

A complex form of mathematical symmetry linked to string theory has been glimpsed in the real world for the first time, in laboratory experiments on exotic crystals.

Mathematicians discovered a complex 248-dimensional symmetry called E8 in the late 1800s. The dimensions in the structure are not necessarily spatial, like the three dimensions we live in, but they correspond to mathematical degrees of freedom, where each dimension represents a different variable.

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Pi Calculated To 'Record Number' Of Digits

From The BBC:

A computer scientist claims to have computed the mathematical constant pi to nearly 2.7 trillion digits, some 123 billion more than the previous record.

Fabrice Bellard used a desktop computer to perform the calculation, taking a total of 131 days to complete and check the result.

This version of pi takes over a terabyte of hard disk space to store.

Previous records were established using supercomputers, but Mr Bellard claims his method is 20 times more efficient.

The prior record of about 2.6 trillion digits, set in August 2009 by Daisuke Takahashi at the University of Tsukuba in Japan, took just 29 hours.

However, that work employed a supercomputer 2,000 times faster and thousands of times more expensive than the desktop Mr Bellard employed.

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The Brain Humanity's Other Basic Instinct: Math

Image: iStockphoto

From Discover Magazine:

New research suggests that math has evolved its way right into our neurons—and monkeys', too.

Numbers make modern life possible. “In a world without numbers,” University of Rochester neuroscientist Jessica Cantlon and her colleagues recently observed in the journal Trends in Cognitive Sciences, “we would be unable to build a skyscraper, hold a national election, plan a wedding, or pay for a chicken at the market.”

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How Maths Makes The World Go Round

Maths makes it: genetic breeding yields a better class of carrot

From The Telegraph:

Whether you’re searching for oil, the lost chord or a better kind of carrot, mathematics is the key, says Ian Stewart.

Like many amateur guitarists, I’d always wondered how to play the opening chord of A Hard Day’s Night. Over the years, I spent hours trying to reconstruct it, but there was something very odd about it: no matter how hard I tried, I could never get it quite right.

In the end, the key to the mystery turned out not to be music, but mathematics. Five years ago fellow Beatles fan and mathematician Jason Brown of Dalhousie University analysed the chord using a method called Fourier analysis, which splits sounds into their basic components. It turns out that the Beatles used a piano as well as their guitars.

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Mathematicians Solve 'Trillion Triangle' Problem

The 3-4-5 triangle has area 6.
(Credit: Image courtesy of American Institute of Mathematics)

From Science Daily:

Mathematicians from North America, Europe, Australia, and South America have resolved the first one trillion cases of an ancient mathematics problem. The advance was made possible by a clever technique for multiplying large numbers. The numbers involved are so enormous that if their digits were written out by hand they would stretch to the moon and back. The biggest challenge was that these numbers could not even fit into the main memory of the available computers, so the researchers had to make extensive use of the computers' hard drives.

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The Origin of Zero

ZERO IN: The number zero developed in fits and starts over thousands of years.
©iStockphoto/dbuffoon

From Scientific American:

Much ado about nothing: First a placeholder and then a full-fledged number, zero had many inventors.

The number zero as we know it arrived in the West circa 1200, most famously delivered by Italian mathematician Fibonacci (aka Leonardo of Pisa), who brought it, along with the rest of the Arabic numerals, back from his travels to north Africa. But the history of zero, both as a concept and a number, stretches far deeper into history—so deep, in fact, that its provenance is difficult to nail down.

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Sexy Maths: When It Pays To Play The Odds

From Times Online:

Mathematicians, and the laws of probability, can tell you whether to have a flutter, or keep hold of your money.

Let’s start by playing a game. I roll a dice and pay you in pounds the number that appears on it. How much would you be prepared to pay to play? If you pay £1 you cannot lose, and if you pay £6 you cannot win but at what point do the odds tip from my advantage to yours?

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Idea Of Infinity Stretched Back To Third Century B.C.

From Live Science:

CHICAGO - The first mathematical use of the concept of actual infinity has been pushed back some 2,000 years via a new analysis of a tattered page of parchment on which a medieval monk in Constantinople copied the third century B.C. work of the Greek mathematician Archimedes.

Infinity is one of the most fundamental questions in mathematics and still remains an unsolved riddle. For instance, if you add or subtract a number from infinity, the remaining value is still infinity, some Indian philosophers said. Mathematicians today refer to actual infinity as an uncountable set of numbers such as the number of points existing on a line at the same time, while a potential infinity is an endless sequence that unfolds consecutively over time.

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Some Math Stories

Big Primes, Small Numbers, Sarah Palin and the Financial Crisis -- ABC News

Mathematics Figures in Recent News Stories

This month's "Who's Counting" will be an assortment drawn from mathematically flavored stories in the news.

A 13-Million-Digit Prime Number

The first concerns a number that easily swamps even the billions and trillions cited in recent financial stories. We know a lot about the existence of millions of subprime mortgages, but little media attention has been devoted to the existence of a just-discovered 13-million digit prime number. (A prime number, recall, is one divisible only by itself and 1. The numbers 3, 19 and 37 are prime, whereas 6, 33 and 49 are not.)

Mathematicians at UCLA won the $100,000 prize offered by the Electronic Frontier Foundation for discovering this humongously large prime number. It is a Mersenne prime number, a prime number of the form 2^P-1, where P is also prime. In this case P = 43,112,609, and the 13-million digit number is 2^43,112,609 - 1.

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