Author Archives: Manan Shah

Learning Math as an Adult (over the age of 30)

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Well, here I am on this idyllic autumn Saturday debating if I should write a blog post, play some piano, or do a little bit of work for work. According to the actuarial tables, more than half my life is over. And my elbow hurts. So for now, the blog post wins. Piano will be next once the ice treatment takes effect. And because I’m a maniac, I need to do a little bit of work everyday. Don’t worry (and thank you for worrying), but I take my work breaks.

A few years ago, I started taking piano lessons. But then had to stop. Then I started again. But then had to stop. And then once more, but then had to stop. And now, the fourth time will be the charm.

One of my before-I-die goals — actually before-2030-goals — is to get to a level of piano play ability that would be sufficient for me to be hired as “this night’s entertainment” at a piano bar or some swanky establishment. And so, piano lessons. Hopefully, 2030 comes before I die.

Maybe this morbidity is Halloween induced.

Do you know what I am learning in my piano lessons? I’m learning how to bounce off the keys and play with some fluidity. I’m learning O Tannenbaum. I’m practicing Czerny 1 & 2. I have a Christmas piano fantasy where I am playing Christmas songs on the piano and people are singing.

I had never taken piano lessons as a kid nor did I play it in any capacity other than the occasional “hey there’s a piano over there, let’s bang on some keys!”. I played the flute. But as a boy, did that really count? I just tried to stay bad at playing the flute since it was worse to be good at playing the flute. Ahhh. Playground shenanigans (bullying).

But as a kid, and even now as an adult, I maintain a generally high aptitude for language acquisition. At least, that’s what I think. So, somehow, ten or so years ago, when I looked at some flute sheet music from when I was a kid (yes, I still have that stuff), I knew what the notes were. I had forgotten how to play it on the flute, since, well, I actively stayed bad at playing the flute.

Piano sheet music was a bit more complex and a little more foreign. But it didn’t take more than a half hour of research to understand how to read it for the majority of use cases.

There’s a scene in Groundhog Day, where Phil Connors hears a rendition of Mozart’s Piano Concerto in C, K545, 1st movement on the radio. That’s mostly how I felt one day. But piano lessons were out of budget. But a basic keyboard and a few books were well within budget. So I bought those. And I read. And I played. I watched YouTube videos. I tried to coordinate both hands. And after a few months of this, I came to the conclusion, that I needed piano lessons. So, suddenly, piano lessons were in the budget and a few things left the budget.

But does it make sense to start piano lessons so late in one’s life? That is, what can I possibly hope to accomplish by trying to learn something conventionally considered completely out of my life’s study (mathematics). I mean, it would be one thing if I had had started piano lessons as a kid and I had some baseline muscle memory to work off of. But, starting piano when close to half my life was over? This seems like a folly. I should do something better with what’s left of my life.

I was literally saying to myself “ok, left thumb down, right index finger down” to train myself to coordinate both my hands. I mean hell, I can do it as I type, why would it be so complicated on piano? But then there’s the blasted reading component and one set of notes being held for longer than another set of notes. I don’t do that when typing. Maybe except with the shift key.

Playing piano is hard. And as my current piano teacher puts it “it’s not natural”. But here I am working towards my piano fantasies. And I’m not too old.

So here you are, perhaps on an idyllic autumn Saturday afternoon, wondering if it’s possible to learn math as an adult. Maybe you’re 35. Maybe you’re 55. or 75!

The short answer is, “Yes, mathematics is not out of your reach”. You’re not too old. The likely difference between your math endeavor and my piano endeavor is your past. This is the “Math Misery?” blog.

Tell me your math-fail story. Or tell me which of these it was, if it were any of these.

“I was always terrible at math.”
“I hated math as a kid. I hated the times tables. I still count on my fingers. Besides I have a calculator now anyway.”
“I was good at math up until the 5th grade.”
“Ugh, I hated Geometry, but I was really good at Algebra.”
“I sucked at Algebra.”
“I got to Calculus, but then it was too confusing.”
“I got the concepts, but I couldn’t do the problems.”
“Fractions. I hate fractions! I mean who uses four-sevenths, anyway?”
“Exponents killed me.”
“Stats was the worst class.”
“Combinations and permutations. I didn’t understand all the exclamation points.”

Why does this past matter? For many of us, our math paralysis as adults is a remnant of our math paralysis as a child. Mathematics was hard. And it was torture. I could actively fail at flute and the only real door that was closed was being a music major in college. If you actively failed at mathematics, remediation among other edu-punitive measures were not too far behind.

But here you are. An adult. You’ve had that Phil Connors moment. The first thing to do is to shed the fear, trauma, and paralysis that your mind and body have remembered.

Don’t worry about not being fast. Don’t worry about the jargon. Nor the notation. Nor the symbolism. Don’t let ageism do you in. Your brain isn’t that old. Don’t worry about this idea that somehow you can’t accomplish greatness in mathematics once you’re past 30.

Don’t worry about all these things. Start fresh.

Recognize that you are an adult and you now have a far deeper capacity for processing abstract concepts. This is where math likely failed you as a child. And me. There was absolutely NO WAY I was going to comprehend some of the concepts that I found to be obvious in my late 20s that I was exposed to as a teenager. Like I said earlier, my life advantage / superpower has been language acquisition. But as we get older, we all acquire this power. Some of us maintain the advantage we had as kids, others plateau if they never honed their natural ability into a craft. Odds are, your ability to acquire a new discipline of study (broadly language) is no different than mine if we’re both adults over 30.

Why do I use this phrase: “language acquisition”? I’m not using it in a proper linguistic context, but rather I’m using it as a catch-all for “knowledge acquisition in a particular field of study”. This knowledge acquisition is many things: jargon, symbolism, notation, mechanics (moving symbols around). But it’s also what we may typically think of when acquiring a new language — stringing together grammatically and syntactically correct and conceptually coherent sentences, paragraphs, and essays. Though, again, not in a formal sense, there is a grammar and syntax to mathematics. This means using the symbols as their uses are designated both in terms of the mechanics of where and how to place them, but also what their context is in a broader mathematical statement.

For example, \(x + 3 = 7 = x = 7 – 3 = 4\) is something we might expect an early math learner to do since they are over using the \(=\) symbol in its conventional written use, but not in its conceptual use. Why all of this matters with math acquisition is that as an adult, you have now encountered many different “languages” and “language frameworks”. Even this article, may have been out of your depth as a 14-year old. There were things you simply weren’t capable of understanding when you were a kid, for whatever reason. And it’s different for different people.

Renting a car. Going on an interview. Negotiating with your landscaper (or landlord). Finding deals for Christmas. Going on a vacation. Taking a cab. And in all these experiences you have either consciously or otherwise, experienced mathematics in some form. Which means that experiencing mathematics in an academic setting now is a completely different ball game from when you were a kid. There are numerous life experiences and contexts that you can draw on to rationalize a concept.

We’re not limited to grocery store examples (I mean we were technically never limited to that even when you were a kid, but the irony is that sometimes adults are incapable of understanding mathematics relevant to a kid’s life). In any case, the context is there. And there is an abundance of it.

Why did I excel in mathematics as a kid? I didn’t. I excelled at math mechanics and figured out a few concepts. But generally I muddled through a lot. It wasn’t until I was 23, several years out of college, that the “obviousness” of mathematics dawned on me. Then in my 30s, when I reflected on myself as a mathematician in my 20s, I realized I understood nothing. Now when I look back on my 30s, I realize that I didn’t understand as much as I thought I understood. And I will say the same thing about myself when I’m in my 50s looking back at my 40s. And so forth.

The point? I’m STILL learning. You can start learning now if you want. The first thing to do is to let go of the feelings of inadequacy or the view that mathematics is this untameable beast beyond your depth. Algebra isn’t hard. Nor are Calculus, Differential Equations, Linear Algebra, etc. If I can learn those, then so can you. This stuff does take time. But not as much as when you were a kid.

I tell myself these things as I continue on my piano journey. My ability to process music theory is immeasurably better than when I was a kid. Your ability to process the Rational Root Theorem will be immeasurably better now as an adult than when you were a kid. And you will be surprised when you consume a typical Algebra I & II sequence that would have been a two-year ordeal in high school, in a few months. The advantage that you will have over me and my piano journey, is that you will have at least seen Algebra before. This foreknowledge or fore-experience will allow you to anticipate next steps that you were never able to do as a kid. And that’s why this go around will be much better, so long as you are not anticipating your fears.

You’ll get stuck, you’ll get frustrated, but you’ll also understand. Should you go on this journey, it can be nice to have a guide. I’m always happy to help.

And from the Twitterverse!

A few people got this.

Hats off to @icecolbeveridge, @Thomas_W_Hunter!

Here’s the spoiler!

Each of the those words becomes another word if you prepend an O. oPEN, oRALLY, oRANGE.