Math Is Both Invention and Discovery
I am currently reading The Joy of x. A Guided Tour of Math, From One to Infinity by Steven Strogatz, which seems to be a best-of his New York Times series The Elements of Math plus bonus content. He describes his book as sitting down with a friend and trying to teach them everything, starting with 1 + 1 = 2 and going as far as we can.
I am certainly entertained and while reading, my mind wanders off and comes back with new musings on math.
For example, as early as chapter 1 he claims:
Math always involves both invention and discovery: we invent the concepts but discover their consequences. […] in mathematics our freedom lies in the questions we ask—and in how we pursue them—but not in the answers awaiting us.
This is a wonderful way to put it and a source of much frustration for many. Math is deeply creative, but at the same time there are a lot of constraints on that creativity. Our inventions in math tend to develop their own life and sooner than later the results of expressions like 6 + 6 are beyond our control.
If math was part of your education in some capacity and you did not completely hate it, you will be able to devour the content of this book comfortably and probably have fun in the process. I enjoy these books that go back to the fundamentals of a somewhat intimidating subject and rebuild the more complex aspects in a bottom up approach. For computer science I can think of The Elements of Computing Systems: Building a Modern Computer from First Principles by Noam Nisan and Shimon Schocken and Code: The Hidden Language of Computer Hardware and Software by Charles Petzold.
Going back to axioms and building (and proving) more sophisticated stuff on top is not the fastest way to knowledge, but it allows me to anchor again in an overwhelmingly complex world whose most twisted inhabitants make me float away. I am not the only one who feels that way, as the book later quotes Thomas Jefferson writing to his old friend John Adams on January 12, 1812, about the pleasures of leaving politics behind:
I have given up newspapers in exchange for Tacitus and Thucydides, for Newton and Euclid; and I find myself much the happier.