Dealing with Math Anxiety

September 6, 2020

I still deal with math anxiety regularly as a math PhD student. Here’s my unsolicited advice on overcoming it.

Step 1

Take a deep breath. Stop staring at those symbols for a bit. Make yourself tea.

Step 2

When you come back to it, ask yourself: what is the thing you want to understand? If writing notes, I like to write it down at the top of the page so I don’t get sidetracked by feelings of inadequacy or rabbit-hole into something.

Step 3

If the symbols are giving you anxiety, relax. This is normal. The notation is probably confusing you. Write down what every symbol means. You’ll probably have to backtrack and spend time looking them up. That’s well worth it and take however much time you need for this.

Step 4

Now that you know what everything means, what is this theorem or equation saying? Are there words left that are ambiguous in the statement? Go look them up. Sometimes it takes me re-reading something 5-6 times, out loud, to get it. Often, I have forgotten the meaning of one crucial word or condition or skipped over them completely and focusing my attention there makes everything makes sense. Math has heaps and heaps of definitions and a perfectly normal English word might mean something super specific! (And it’s totally ok to not remember them at this moment.)

Step 5

Sometimes (but not always) it’s a good idea to figure out why what you’re reading is important (or if it’s not). The text probably addressed it somewhere above or below the theorem or equation, but you might’ve been too distracted the first time to notice. Now is a good time to re-read.

Step 6

Now onto the proof! This is probably the most technical part. Take a deep breath here again, and start small. Looking at the whole thing might be overwhelming. If a proof is giving me too much anxiety (and let’s be real, this happens a lot), I like to write it down word for word, and as I copy it, fill in every step so that every small change is completely clear to me. I try not to lie to myself about my understanding, as a small lie of understanding can snowball into a big pile of math anxiety again.

Remember: This has to make sense somehow.

As you do this, you might notice that you can’t fill in every step sometimes or get really stuck. This happens more frequently as the complexity of what you read grows. Take time to try to isolate what it is that you don’t understand or are stuck at, and try to formulate a question whose answer would help you understand.

Then, just accept it. It’s ok. You won’t be able to fill in everything every time. Make a note of it, and maybe come back to it later with fresh eyes or accept you don’t know this step. This is also a moment where looking at what you wrote down wanted to understand in the first place helps. Is this tiny step you don’t get crucial for the idea you want to get? Is there someone who can help you figure it out? Book an appointment with them and don’t fuss about it until later.

Step 7

As you do this, you might get hit with waves of understanding. I like to sink into that feeling of happiness and do a little dance! This is one of the best feelings of doing math, so relish it!

Step 8

Wow, this took longer than you thought! Don’t worry, that’s normal. You’re not bad at this.

Extra tip that’s been crucial for me

When given the choice, try to choose the resource that’s easiest for you to read. There’s a lot of resources floating around that aren’t written for a first-time understanding of a concept…or are just plain terrible because a lot of mathematicians aren’t great writers. Unfortunately, you’ll often be suggested those first because people who already know the subject don’t notice how confusing they are, as they’ve forgotten how it felt like the first time they’ve learned the subjector they’ve toughed it out and now have survival bias, or they just think and get things in a very different way than you do, etc. Who cares! If you feel like what they’re suggesting isn’t right for you, keep looking and don’t feel bad. I don’t remember regretting doing this. . I don’t like wasting my time on things that aren’t written with my situation in mind if I can avoid it. Some say it’s good to bang your head against the wall. I say that hurts.

This is complicated if you have assigned notes or textbook for a class or something. In that case I like to follow those but independently google resources when I am confused by a certain topic - remember, not everything is written with uniform clarity and there is no shame trying to get clarification elsewhere!

This post was originally posted in Recurse Center’s internal forum, but made it into my blog at the suggestion of some people.

Dealing with Math Anxiety - September 6, 2020 - Hang Lu Su