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 this article, we explore the possibilities allowed by higher inductive types. They enable a much more intuitive formalization of integers and new mind-blowing definitions of the (homotopical) circle and sphere.
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.
Last summer, I got to discover Morellet's artwork on inclined grids. Amazingly, this artwork is a display of the irrationality of ?2! It's also a strong argument for the existence of this number. In this article, after discussing that, I take readers further!
In this article, we present a brief methodology-focused review on some of the essential components for multi-scale, multi-physics heart modeling. A perspective of heart modeling in the era of high performance computing is also presented.
My first reaction to imaginary numbers was... What the hell is that? Even now, I have trouble getting my head around these mathematical objects. Fortunately, I have a secret weapon: Geometry! This article proposes constructing complex numbers with a very geometrical and intuitive approach.
Research teams are developing models to predict the way fires will behave. Information from these simulations is bringing valuable information to firefighters’ relentless struggle against forest fires.