What Is The Poincaré Conjecture?

colored shapeBefore we start, let me put something out there. Poincaré Conjecture is one of the seven millennium problems established by the Clay Mathematics Institute. Those problems are worth a million dollars each! The Poincaré conjecture depends on the mind-numbing problem of understanding the shapes of spaces. This field of study is referred to as “topology” by mathematicians. Topology is an important field within mathematics concerned with the study of shapes, spaces and surfaces. We interact with these in our everyday lives. We see surfaces breaking and shapes getting deformed all the time. Ever wondered if there is any law governing these deformations? Or are these deformations just too random to be studied? Does Poincaré Conjecture have any real world applications?   Continue reading