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Long-standing ‘Continuum Hypothesis’ disproved

By Peter Rowlett. Posted April 1, 2013

After what has so far been an inexplicably fruitful morning of mathematical revelations, the mathematical world is now reeling after yet another long-standing mathematical question has been answered. While we are still reeling from the shock resignation of Aperiodical editor Christian Perfect, whose presence on the site will be sadly missed, our obligation is still to report the mathematical news.

The Continuum Hypothesis, originally posed by set theorist Georg Cantor in 1878, states that there is no set whose cardinality is between that of the integers and that of the real numbers. While this statement has been proved undecidable (that is, a proof has been given that it is impossible to prove the truth or falsehood of the result using the standard logical axioms), one of our authors has succeeded in determining that in fact a set of such intermediate size does exist. The proof is ground-breaking and so impressively concise that any attempt at verifying it would be, frankly, a waste of time.

The author, the Aperiodical’s own Katie Steckles, is now in the running for a Fields Medal, or International Medal for Outstanding Discoveries in Mathematics. If the award were to be made, Steckles would become the first female mathematician to be awarded such an honour.

Read the ground-breaking paper here: A disproof of the Continuum Hypothesis

I resign

By Christian Lawson-Perfect. Posted April 1, 2013

I have had enough. My jealous “partners” on this site, Peter and Katie, have for too long refused to take seriously my VERY IMPORTANT mathematical ideas. I do not know if they are working for THEM and are trying to suppress my TRUTH-WORDS or if they are just too stupid-unenlightened to see the brilliance of my work,, but I have decided enough is enough.

I am resigning from this site immediately so I can spend all of my time perfecting my UNIVERSAL EQUIVALENCE THEORY which has already revealed so many secrets previously hidden from my eyes.

Please read my latest paper, A Universal-Equivalent Proof of the Riemann Hypothesis (Primes Theorem) and if you, unlike Katie or Peter (Peter = Petrus = BLOOD FROM A ROCK) can see the importance of this sine qua non ex nihilis then please join me at my new site, once my new hosts have secured it to my specifications. I will divulge its address when I am sure it is safe.

Largest prime discovered

By Peter Rowlett. Posted April 1, 2013

Mark today in your diary because it’s turning out to be quite a day for revolutionary mathematical results. Hold on to your online credit card transactions, ladies and gentlemen, because Colin Beveridge, maths tutor and sometime Aperiodical contributor, has this morning published his discovery of the largest prime number.

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. It was long thought that there were infinitely many primes, but of course those of us who properly understand infinity know that it goes on forever and there is surely no way to check every case. Beveridge’s result overturns this long held belief by showing that a largest single prime exists.

A natural number greater than 1 that is not a prime number is called a composite number. One consequence of Beveridge’s result is that every number greater than $11!+1$ is a composite number, and can therefore be represented as the product of two or more (not necessarily distinct) primes.

Beveridge says he plans to submit the new result as part of a multi-million pounds research grant application to exhaustively search all the numbers up to $11!+1$, in order to compile a list of all possible prime numbers.

Original paper: BREAKING NEWS: Largest prime discovered.

A simple proof that π is rational

By Christian Lawson-Perfect. Posted April 1, 2013

The number $\pi$, the ratio of a circle’s circumference to its diameter, long thought to be an irrational number and commonly written as 3.141, is found in many areas of mathematics and science and has been studied throughout the ages.

The ubiquitous nature of $\pi$ makes it all the more surprising that the world wakes up this Monday to a startling new result: $\pi$ is rational. This new result makes a mockery of much of modern mathematics, including recent results and ongoing debates reported on this site. The proof is a picture of elegance and can be understood by anyone with knowledge of basic algebra and calculus.

The author of this new result is Peter Rowlett, maths educator and sometime podcast reneger from Nottingham, England. Rowlett posted the result on his blog this morning, presumably in order to make the result public as soon as possible ahead of publication in a peer-reviewed journal, which will surely follow in time. Rowlett says he now plans to submit his new result for a PhD in the Summer.

More information is available in the original paper: A simple proof that $\pi$ is rational.