Scanning the crowd at a fancy soiree may reveal a wide array of neckties, each fastened with a highly complex mathematical object masquerading as fashion. An entire field of mathematics is devoted to ...

We are deeply intuitively familiar with our everyday physical world, so it was perhaps a bit of a surprise when researchers discovered a blind spot in our intuitive physical reasoning: it seems humans ...

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Virtual Knot Theory extends classical knot theory by incorporating virtual crossings alongside traditional over‐ and under‐crossings. Originating from Kauffman’s work in the late 20th century, the ...

Quandle theory has emerged as a vital algebraic framework for understanding knots and links, capturing the underlying symmetries that distinguish one knot from another. At its essence, a quandle is an ...

Find a string. Really. Do it. Now twist, tie and tangle it as much as you like. Finally, attach the two loose ends of your string together to make a closed loop. (This is a crucial step.) What you ...