Gelfand duality and algebraic geometry

hidden-phenomena.com/articles/gelfand How does one define a shape? The usual definitions are based on starting with the set of all points of a shape. However, the great Russian mathematician Gelfand found another approach to defining shapes. This approach is more natural from the point of view of certain abstract shapes which arise in physics (namely, phase spaces of physical systems), and leads naturally to the modern formulation of quantum mechanics; however, perhaps surprisingly, this idea of Gelfand also leads to modern algebraic geometry! My friend and I wrote a blog post describing Gelfand's observation at hidden-phenomena.com/articles/gelfand , and using Gelfand's idea to understand better the Chinese remainder theorem of elementary number theory. It's a really cool fact of reality that geometry connects so intimately to algebra, and we hope you'll enjoy the article!