A consortium of today's greatest mathematicians have laid out new foundations. They all lie upon one single axiom, called univalence. With univalence, our Arabic numbers aren't just like natural numbers; They are natural numbers. Univalence also has unforeseen and mesmerizing consequences.
In 2013, three dozens of today's brightest minds have laid out new foundations of mathematics, which better fits both informal and computationally-checkable mathematics. Have a primer of this upcoming revolution, with this article on type theory, the theory that the book builds upon!
Take a square sheet of paper. Can you glue opposite sides without ever folding the paper? This is a conundrum that many couldn't figure out. While John Nash did answer yes, he couldn't say how. Finally in 2012, Borrelli and his collaborators finally made it! And it is spectacularly beautiful!
In 1988, Euler's identity was elected most beautiful theorem of mathematics. It has been widely taught worldwide. But have you ever stopped to really sense the meaning of this incredible formula? This article does.
In recent years, at the interface of game theory, control theory and statistical mechanics, a new baby of applied mathematics was given birth. Now named mean-field game theory, this new model represents a new active field of research with a huge range of applications! This is maths in the making!
Designing routes to visit customers has become one of applied mathematicians' favorite optimization problems, as companies offer millions to solve them! This article discusses the clever technics they have come up with, and use them to help Santa deliver toys to kids all over the world!