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