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Surprising Limits Discovered in Quest for Optimal Solutions
...to spend limited free time before bed. These scenarios and many others can be represented as a mathematical optimization problem. Making the best decisions is a matter of finding their...
Where Transcendental Numbers Hide in Everyday Math
...the ordinary, something that is hidden and mysterious, with almost magical or mystical powers. In mathematics, on the other hand, the meaning of the term “transcendental” is more mundane. It...
How Tadayuki Watanabe Disproved a Major Conjecture About Spheres
...symmetries. The Mystery Continues Watanabe’s result closed one front of mathematical research. It also opened another. After his work, mathematicians knew the Smale conjecture was false in all dimensions four...
Mathematicians Prove Melting Ice Stays Smooth
...is. Soapy Inspiration In the decade before mathematicians began to understand the ice melting equations, they made tremendous progress on the mathematics of soap films. If you dip two wire...
The Simple Math Behind the Mighty Roots of Unity
Solutions to the simplest polynomial equations — called “roots of unity” — have an elegant structure that mathematicians still use to study some of math’s greatest open questions. If you’ve...
How Ancient War Trickery Is Alive in Math Today
Legend says the Chinese military once used a mathematical ruse to conceal its troop numbers. The technique relates to many deep areas of modern math research. Imagine you’re a general...
New Math Book Rescues Landmark Topology Proof
...correct at all. In a 2012 post on MathOverflow, one commenter referred to the proof as a “monstrosity of a paper” and said he had “never met a mathematician who...
Banach-Tarski and the Paradox of Infinite Cloning
...a mathematical theorem involving infinity that makes it possible, at least in principle, to turn one apple into two. That argument is called the Banach-Tarski paradox, after the mathematicians Stefan...
Math Can, in Theory, Help You Escape a Hungry Bear
...which led to some unexpected mathematical sleuthing. Before we discuss the solutions, you may have noticed that we did not mention any specific units for distance, time and velocity. The...