A Software Engineer’s Adventures in Learning Mathematics

>Being an engineer means using technology, science, mathematics to solve problems.

That's called practicing engineering. An engineer is a professional practitioner of engineer. You can practice engineering all you want, but if you're not a professional (having received an engineering degree from a certified university), it's dishonest to call yourself one. Honestly, it is elitist. But those of us who obtained our degrees worked our asses off. And I personally hate when people abuse the term to mean anything that took skill. "Candy cane engineer". "Beats engineer". "Drink mixing engineer". It's linguistic prescription to make yourself sound more important/skilled.

It wasn't that long ago that most schools did not have a separate CS degree, but rather it was a math degree w/ a concentration in computer science (or some other verbiage to describe the same thing)

I understand where this feeling comes from. You worked hard to earn what is (or what should be) a title with prestige: engineer. I too worked hard to earn degrees in engineering. I try to live up to that title every day, and I'm sure you do, too.

But my years of engineering experience have shown me that the title "Engineer" is really more about how you approach problems and what you do to solve them and less about degree credentials. Now, the following example is in the context of electrical engineering on airplanes, not computer programming, but I think it holds true.

One of the best people I work with does not have a college degree. But over years of self-study and real world experience, he has taught himself electronics, some computer programming, and enough mathematics to get by. And when there is a technical problem to be solved on one of our airplanes, he will chase after it relentlessly, and smartly, until it is solved. His system designs are clean and well thought through. He has taught me much about designing for real world implementation. Is he not an engineer? He does more than many of my coworkers who are degree holding EEs. I am not afraid to call him an engineer, because he has earned the title in a different way.

I'm in a similar boat as you. I went up through Calculus in school and hated it. Around 5 years ago I developed a strong interest in learning relevant applied math and have been enjoying it since.

Some things I'd add:

1) Math is fun! If you have the aptitude and disposition to enjoy writing software you'll love working out math problems. They're little nuggets of mental stimulation that you can work on with just some paper, a pencil, and maybe a pocket calculator.

2) You're spot on about an experienced programmer already having an intuitive but non-rigorous understanding of many concepts. It's mostly a matter of learning to read and write comfortably using the notation, which is really similar to learning the syntax and semantics of a big computer language with poor reference material.

3) You really have to have basic math down. This means going and re-learning stuff like applying FOIL to a binomial or dividing by a reciprocal.

4) Calculus and Linear Algebra are the father and mother of applied math. You'll save yourself a ton of grief if you learn them first (and I mean really learn them, maybe you took a calculus class in college but can you apply the Chain rule right now?). I'm learning Linear Algebra currently, which is something I should have done years ago. Part of the problem with self-teaching is getting things out of order.

What I understood after studying CS for over 10 years at a few universities regularly ranked highly at ACM ICPC is that math is unnecessarily obfuscated to most people. There is even an excellent book "Concrete Mathematics" from Stanford that tries to bring fun back to math instead of drying people with some formal stuff without explaining how people over the centuries got to that structure.

I honestly believe math language is seriously outdated. It's like using COBOL to express everything. Yes, you can do that, but would you really want to given a choice? The most trivial things are so insanely complicated in math it's unbelievable (try to describe geometrical objects with the current math formal language if you do computer vision), yet there is very little work on developing better formal language of math. It's like with Turing machines and the complexity theory - who is going to move around a tape in the real world besides some specialized biological systems, not mentioning magical 'oracles'? Those abstractions were useful in their day, brought their fruits, but why do we still stick to them and just increase the gulf between more and more closed-unto-itself-theory and reality? Yes, it's great some theory is super cool but what do we do when we find in 20-30 years that the set of objects satisfying this omnipotent theory is empty? And when somebody like Mochizuki invents their own formal language to solve some cool problem like ABC conjecture, we all hate him, refusing to read the proof because it doesn't follow our outdated formal ways...