Math, as the foundation and universal language of modern science, is one of the most well-spread language used by human society. In this article, we will briefly describe how math has gradually evolved as a language invented by humans, and what kind of challenges we're facing.
1. Math is the Language of God
As Galileo Galilei said, "The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth."[1]
After science revolution, human have tended to believe that the universal and beautiful system of math is the best way to understand and explore the nature of the universe. Even math is possibly a language we may share with intelligent aliens living in other galaxies.
As early as 6th century BC, Pythagoreans' philosophy thought that numbers are the nature of the world (Pythagorean numerology), and astronomy and music are built on numbers as well. This deeply impacted how ancient Greeks understand and interpret the world. It was thought that, God as the unique One was the creator of all numbers.
Later, Pythagoreanism then has a deep influence on Plato, and through him, on all of Western philosophy. As a result, Greeks tried to discover the truth of universe, especially a mathematical design of the truth. This helped math to grow into a independent system with a set of principles and methodologies, which was not towards practical and empirical objectives as other civilization did.
This trend led to the abundance of math in the age of Alexandria, and the great work of Euclid, Apollonius, Archimedes, and Ptolemy.
image source: Wikipedia -- Pythagoras | Pythagoras | CC3.0
2. Math is the Language of Science
With the arrival of renaissance, a modern set of mathematical characters are invented to replace the math description based on natural languages.
Negative number, irrational number and imaginary number are used in math operation gradually.
François Viète's contribution to math as a language is critical. He made the kind of representation of using consonants for parameters and vowels for unknowns, which is very close to how we write equations today. This kind of abstraction has made math an independent language system that can be described in a world that can be analyzed above the physical world.
Later, Descartes has invented the analytical geometry, the bridge between algebra and geometry, with the idea of applying the mathematical method to philosophy. In order to find a universal mathematics of acquiring knowledge, Cartesian coordinates system has formed a new kind of universal and uniform space, and led the Euclidean space which made Newton's laws possible in the science revolution.
These achievements made math a modern language that is ready to be used in the boom of modern natural science, and also grow itself into a more and more complete logic language. Finally, Issac Newton, brought us into the era of modern science on the foundation of math.
image source: Wikipedia - François Viète | François Viète | CC3.0
3. Post-Godel Age: Where will Math Go?
Fast-forwarded to 1900, the foundations of mathematics suffered the great challenges when Georg Cantor when he built the infinite sets theory. A few solutions are proposed to build the foundation of math, and Hilbert's program is raised with the objective of building metamathematics. However, everything changed after Kurt Gödel published his two incompleteness theorems in 1931.
This eventually led us to the question of what math is on the earth. The great foundation of math built by the ancient Greece wisdom, has led us to the trouble in today's age.
If math is like a tree, today it's trying to growing both its branches and leaves, and also its very complex roots. Intuition and logic are trying to play their own roles in the seeking of new directions for math.
It's important to review whether math is the unique One created by "God", or it's more likely something built by human's culture, or something in between, or shown by both. If math is a language, it's the language created by human, nature or God?
Every language evolves with the culture and age. The application of a language demonstrates the correctness and importance of it. It's the same to math. Just like physics, the foundation of math is not irrevocable by its nature. However, when some mathematicians are working on the top of the building, it's important to understand how it's going with the guys who are strengthening the foundation.
Why does math work? It's still a question that the great mathematicians and physicians didn't answer thoroughly, but we need to admit that math is one of the most beautiful diamond of wisdom we have created in human's civilization, and it still works generally as other languages that evolve in the history.
image source: Wikipedia - Kurt Gödel | Kurt Gödel | CC3.0