Whether I am looking at the math behind marketing, machine learning or music, I always find myself hitting certain limits, and head off to Wikipedia to brush up or introduce myself to a concept. Any math Wikipedia article though, is just a first node on a journey deeper into the labyrinth, as math is ultimately built on ever more primitive concepts, that themselves beg further explanation. Some of the math articles seem to be written for people who already know the subject matter, but I persevere.
What I have found lacking in my understanding of math, or rather my ability to read math-dense papers and articles, is a grounding in the intuitive nature of math. It’s one thing to see or follow a formula, but another to intuit what is actually going on as the symbols begin to stack one on another. Some are easy to figure out. A “+” means there are more of something (unless one of the numbers is negative, in which case there is more of less.) A “*” means there is many more of something (unless one of the numbers is negative, or less than one, meaning there is less, or it’s zero, in which case you’re totally hosed.) But the first time I had an e or an i to really think about, and was told what it is, but not what it does, it gave me enough friction to go off and do something else.
Enter the era of somebody out there must already be thinking about this, and yes, there are, so here are a few pointers for that.
I found Kalid Azad’s accurately named “Better Explained” site, whose article “Developing Your Intuition for Math” topped my Google search, and which led to a whole series of helpful posts and books. OK, e is about is about 100% continuous growth. And i lets you rotate off of the 1-D number line into a 2-D direction. Derivatives are your speedometer and integrals are your odometer. And know you know.
I also stumbled on Daniel Jeffries’s “Learning AI if You Suck at Math” series on Hackernoon, which also appealed to my experiences reading math papers as a dilettante. This also led me to grab a couple of the books Jeffries recommends in the first post, “Mathematics: A Very Short Introduction” by Timothy Gowers and “Make Your Own Neural Network” by Tariq Rashid.
I’m still working my way through math papers, but with better intuition. Now my main point of friction is the number of times the author says “It is easy to see…”, “It is easy to prove…”, “It is easy to show…” as in “It is easy to see that it is also in ℓ1 for all σ ∈ (σ1, σ2), and that, moreover, the Mellin transform is holomorphic on {s : σ1 < ℜ(s) < σ2}.”
Right.