Dimensional analysis is to reduce down basics in our universe into 7 dimensions. The rest is linear algebra/matrix conversion of different units or metric system. So many things connect now.

However, to solve this simple puzzle – exchange water between a 3-litre flask and a 5-litre flask to obtain 4 liters of water using vector is mind-blowing.

As was cited in this ingenuous video, “Mathematics is the art of giving the same name to different things. Henri Poincare.”. What I think is quintessential in mathematics is a precise way to describe and process abstract things.

For example, in artificial intelligence, to describe and design loss function is key.