knot theory – Quanta Magazine

Mathematicians Eliminate Long-Standing Threat to Knot Conjecture

Leila Sloman — Thu, 02 Feb 2023 15:00:28 +0000

Over 60 years ago, Ralph Fox posed a problem about knots that haunts mathematicians to this day. His question is now often formulated as the “slice-ribbon conjecture,” which posits that two seemingly distinct groups of knots are actually the same. With its suggestion of elegant simplicity within the world of knots, it’s become one of the most high-profile problems in knot theory.

Source

Why Mathematicians Study Knots

David S. Richeson — Mon, 31 Oct 2022 16:36:49 +0000

Knot theory began as an attempt to understand the fundamental makeup of the universe. In 1867, when scientists were eagerly trying to figure out what could possibly account for all the different kinds of matter, the Scottish mathematician and physicist Peter Guthrie Tait showed his friend and compatriot Sir William Thomson his device for generating smoke rings. Thomson — later to become Lord...

Source

Surfaces So Different Even a Fourth Dimension Can’t Make Them the Same

Kevin Hartnett — Thu, 16 Jun 2022 14:03:36 +0000

In geometry and the closely related field of topology, adding a spatial dimension can often have wondrous effects: Previously distinct objects become indistinguishable. But a new proof finds there are some objects whose differences are so stark, they can’t be effaced with a little more space. The work, posted at the end of May, solves a question posed by Charles Livingston in 1982 concerning two...

Source

How Complex Is a Knot? New Proof Reveals Ranking System That Works.

Leila Sloman — Wed, 18 May 2022 16:38:42 +0000

Back in 1981, Cameron Gordon introduced a new way to relate two knots — mathematical constructs modeled after the knots that appear in a single thread or string. In his paper, he conjectured that this new relationship could be used to arrange groups of knots according to how complicated they are. This winter, Ian Agol, a mathematician at the University of California, Berkeley, posted a six-page...

Source

Untangling Why Knots Are Important

Steven Strogatz — Wed, 06 Apr 2022 21:00:12 +0000

Everyone knows what a knot is. But knots have special significance in math and science because their properties can help unlock secrets hidden within topics ranging as widely as the biochemistry of DNA, the synthesis of new materials and the geometry of three-dimensional spaces. In this episode, host Steven Strogatz explores the mysteries of knots with his fellow mathematicians Colin Adams and...

Source