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YouTubeThe Seven Bridges of Königsberg
This video features Cliff Stoll... and the work of Leonhard Euler.
shitpostThe duties of John von Neumann's assistant
“What,” asked I, “are the duties of an assistant to Professor von Neumann?” Veblen answered with a mixture of surprise and disdain, that a mere private second class should ask such a question about a four star general. His answer staggered me. Here were the four principal duties of von Neumann's assistant.
YouTubeCrisis in the Foundation of Mathematics
What if the foundation that all of mathematics is built upon isn't as firm as we thought it was?
PLUS.MathsBach and the musical Möbius strip
A musical score has basically two dimensions: pitch and time. In a one-voice musical text, for example, the pitch (which corresponds to the frequency) of a note is represented vertically, and performance time runs from left to right. So topologically a one-voice musical score is a two-dimensional strip. The horizontal (time) coordinate runs from start to finish; the vertical coordinate runs from lower pitches to higher pitches. In the chant book score above, the clef at the start indicates that the second line in the staff corresponds to “fa” on the musical scale.
QuantaThree Decades Later, Mystery Numbers Explained
Zeta values seem to connect distant geometric worlds. In a new proof, mathematicians finally explain why.
quantamagazineA Math Theory for Why People Hallucinate
Psychedelic drugs can trigger characteristic hallucinations, which have long been thought to hold clues about the brain’s circuitry. After nearly a century of study, a possible explanation is crystallizing.
the-tlsKurt Gödel and the mechanization of mathematics
One way of describing the Incompleteness Theorems (1931) of the Austrian logician Kurt Gödel is to say that he proved, in the form of a mathematical theorem, that the possibility of a fully automated mathematics can never be realized.
NAUTIL.USThe Math Trick Behind MP3s, JPEGs, and Homer Simpson’s Face
Nine years ago, I was sitting in a college math physics course and my professor spelt out an idea that kind of blew my mind. I think it isn’t a stretch to say that this is one of the most widely applicable mathematical discoveries, with applications ranging from optics to quantum physics, radio astronomy, MP3 and JPEG compression, X-ray crystallography, voice recognition, and PET or MRI scans.
culture.plMaths, Madness and the Manhattan Project: the Eccentric Lives of Steinhaus, Banach and Ulam
One day in the 1930s a group of men met at the Scottish Café in Lviv. Over glasses of cognac, they scribbled on the cafe's marble tabletops, and history was made. They were no ordinary guests. These men were Hugo Steinhaus, Stefan Banach and Stanisław Ulam – mathematicians who dreamt big, wrote poems, constructed the atomic bomb and helped organise the first flights to the moon.
HPEThe toughest math problems that challenge the world
In 1900, German mathematician David Hilbert proposed a list of 23 math problems that would change the world. Some have been solved. Others remain. DARPA attempted to update the list a few years back. Here are the highlights.
SCIENTIFICAMERICANThe Saddest Thing I Know about the Integers
We can't tune pianos because prime numbers. // The integers are a unique factorization domain, so we can’t tune pianos. That is the saddest thing I know about the integers.
UVICThe First Simple Symmetric 11-Venn Diagram
Below are two symmetric 7-Venn diagrams. A crosscut is a curve segment that intersects every other curve sequentially without repetition. The one on the left, M11, has a crosscut, but it is not crosscut symmetric.
YouTubeHilbert's 15th Problem: Schubert Calculus
In the late 1800s, a mathematician, Hermann Schubert, computed all sorts of wild enumerative geometry problems, like the number of twisted cubics tangent to 12 quadrics -- which is apparently 5,819,539,783,680. And maybe that exact number doesn’t seem particularly important -- but the fact that Schubert was able to figure it out it is pretty amazing.
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