The symmetry of Maths and Physics (A fun thought I had)

Think about the history of progress in Mathematics and Physics, the two areas that explore the fundamental truths of the universe. Considering also the sequence of discoveries and breakthroughs, it can be said that direction of advancement for both fields are somewhat opposite and have a nice symmetry. Perhaps this is already clear to you, the reader, but it is definitely interesting and worth having a think about.

A good metaphor for this is to imagine a pyramid. Mathematics starts from nothing and aims to build as tall as possible, and Physics wants to take the pyramid apart. Perhaps it is not exactly the same pyramid, but consider how they go about it.

Mathematics is built off strong foundational axioms. We take these core, absolute principles, and question what they lead to. All proofs assume established rules and previous results, and use logic to reach the next conclusion, stacking up bricks. In this way, Mathematicians are able to build off the work of their predecessors, as their work can be taken as indisputible.

Discoveries in Physics come about in an opposite manner. We observe the world around us and create theories to dig deeper and explain our observations. At each step there is another question to ask, and another model to develop because there is more to be explained. To progress in Physics, previous work must put to aside and seen as inspiration, so one can imagine a new exhaustive model. In a opposite way to Mathematics, Physics starts from the result and looks to find a set of axioms which can coexist with each other and explain all our observations.

It's like two people walking towards each other from opposite ends of a path, perhaps one day they might meet in the middle.

(Please go easy the first blog post)