What is mathematics?
Mathematics is a language for decoding and describing patterns.
We live in a universe that is held together by patterns. Patterns are everywhere. They make up everything you are! They're the pulsing cycles of your breath and blood; the warming and cooling of the air on your cheeks; the ebbing and flowing of water as it cascades over the cliffs of Niagra; and the waxing and waning of your every wish, attraction, and desire. The patterns of the cosmos are present in the infinitesimal structures of atoms, in the cosmic motions of planets and stars, and in every level in between.
What makes life possible is the order that results from patterns: the Greeks called it logos, which translates in secular science as "logic" and in theology as "the Word." No matter what you may understand the patterns of the cosmos to be or where they come from, they exist. They absolutely define us.
What's more, all patterns in the cosmos are related. In a proper math lesson, the result is a feeling of universal homecominga feeling that everything we learn is connected to what we already know. It's the feeling that whenever we sense order and harmony in the universe, what we observe bears a beautiful resemblance to our own nature as ordered beings in a vast cosmic structure. This feeling depends on the recognition of patterns. Thus, the goal of mathematical study is to acquire a language for decoding and describing patterns.
We live in a universe that is held together by patterns. Patterns are everywhere. They make up everything you are! They're the pulsing cycles of your breath and blood; the warming and cooling of the air on your cheeks; the ebbing and flowing of water as it cascades over the cliffs of Niagra; and the waxing and waning of your every wish, attraction, and desire. The patterns of the cosmos are present in the infinitesimal structures of atoms, in the cosmic motions of planets and stars, and in every level in between.
What makes life possible is the order that results from patterns: the Greeks called it logos, which translates in secular science as "logic" and in theology as "the Word." No matter what you may understand the patterns of the cosmos to be or where they come from, they exist. They absolutely define us.
What's more, all patterns in the cosmos are related. In a proper math lesson, the result is a feeling of universal homecominga feeling that everything we learn is connected to what we already know. It's the feeling that whenever we sense order and harmony in the universe, what we observe bears a beautiful resemblance to our own nature as ordered beings in a vast cosmic structure. This feeling depends on the recognition of patterns. Thus, the goal of mathematical study is to acquire a language for decoding and describing patterns.
The value of mathematics
It's helpful to compare mathematics with poetry. Poets use words to tickle our fancy and make us feel connected to a wider, more universal human experience. Learning how to read and write poetry allows us to love and appreciate life through narratives and ideas. In a similar way, mathematicians use symbols to make us wonder about things and draw connections with the cosmic patterns that define our reality. Learning how to read and write mathematicsnumbers, values, shapes, formulas, unknowns, changes over time, and the classification of things into setsallows us to appreciate the beauty and order life in a profound, emotional way.
I call math a language of cosmic patterns for this reason. The more patterns you learn to read and write about using mathematical symbols, the better you can understand and express your own nature as an ordered being in a vast cosmic structure. When you study mathematics as the language of cosmic patterns, you become able to recognize how math intersects with all knowable things (like seeing the Matrix within reality). Then, depending on the degree to which you have a poet's heart, the world feels infinitely more harmonious, heavenly, and real.
I call math a language of cosmic patterns for this reason. The more patterns you learn to read and write about using mathematical symbols, the better you can understand and express your own nature as an ordered being in a vast cosmic structure. When you study mathematics as the language of cosmic patterns, you become able to recognize how math intersects with all knowable things (like seeing the Matrix within reality). Then, depending on the degree to which you have a poet's heart, the world feels infinitely more harmonious, heavenly, and real.
Here's a really concise summary of Alan Turing's exploration of patterns in the development of embryos and the math he used to decode and describe them.
"His hunch was that there had to be some mathematical principle underpinning the reoccurring patterns in an embryo's development." I love the passion and curiosity with which mathematicians pursue their understanding of universe, one iota of knowledge at a time. 
