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Color-Changing Material Unites the Math and Physics of Knots
Mathematicians have studied knots for centuries, but a new material is showing why some knots are better than others.
How Simple Math Can Cover Even the Most Complex Holes
No one knows how to find the smallest shape that can cover all other shapes of a certain width. But high school geometry is getting us closer to an answer.
Mathematicians Cut Apart Shapes to Find Pieces of Equations
New work on the problem of “scissors congruence” explains when it’s possible to slice up one shape and reassemble it as another.
With Category Theory, Mathematics Escapes From Equality
Two monumental works have led many mathematicians to avoid the equal sign. The process has not always gone smoothly.
How Randomness Can Make Math Easier
Randomness would seem to make a mathematical statement harder to prove. In fact, it often does the opposite.
Random Surfaces Hide an Intricate Order
Mathematicians have proved that a random process applied to a random surface will yield consistent patterns.
A Mathematician Whose Only Constant Is Change
Amie Wilkinson searches for exotic examples of the mathematical structures that describe change.
How Geometry, Data and Neighbors Predict Your Favorite Movies
A little high school geometry can help you understand the basic math behind movie recommendation engines.
Out of a Magic Math Function, One Solution to Rule Them All
Mathematicians used “magic functions” to prove that two highly symmetric lattices solve a myriad of problems in eight- and 24-dimensional space.