How far along are you in graduate school? What exactly is it that you do? These are two questions I'm asked frequently these days and am happy to answer. I created Math3ma precisely for my time in graduate school, so I thought it'd be appropriate to share the answers here, too, as a quick update! First,

I'm graduating this semester!

It's exciting. I've really enjoyed my time as a graduate student and have been looking forward to the future for a while now. (I'll share more on my post-graduate plans in another post.) In the mean time, I'm in the midst of writing up my dissertation. The title is pending. Stay tuned!

Now to the second question: "What's your research about anyways?"

My work doesn't fit into any one mathematical label (geometry, topology, algebra, category theory, etc.), so it's hard to answer this question with just one or two words. I'm using different ideas to make connections across different things! And I love it for that reason. I'll elaborate.

I'm in pure mathematics program, but some of the most exciting mathematics is, to me personally, that which is inspired by cross-discipline communication. I am most deeply moved by mathematics that is motivated by some phenomena in nature, or in physics, or in an applied setting.

Amazingly, my thesis is in this very space! (Just three years ago, I didn't know I'd be doing what I'm doing now, hence "amazingly." It's a very cool story, but I'll save it for another day.)

Recently I've been working on a dissertation proposal, which is sort of like a culmination of five years of graduate school (yay). The first draft was rough, but I sent it to my advisor anyway. A few days later I walked into his office, smiled, and said hello. He responded with a look of regret.

Advisor: I've been... remiss about your proposal.

[Remiss? Oh no. I can't remember what the word means, but it sounds really bad. The solemn tone must be a context clue. My heart sinks. I feel so embarrassed, so mortified. He's been remiss at me for days! Probably years! I think back to all the times I should've worked harder, all the exercises I never did. I knew This Day Would Come. I fight back the lump in my throat.]

Me: Oh no... oh no. I'm sorry. I shouldn't have sent it. It wasn't ready. Oh no....

Advisor: What?

Me: Hold on. What does remiss mean?

Advisor [confused, Googles remiss]: I think I just mean I haven't read your proposal.

One day while doing a computation on the board in front of my students, I accidentally wrote 1 + 1 = 1. (No idea why.)

Student: Um, don't you mean 1 + 1 = 2?

Me (embarrassed): Oh right, thanks.

[Erases mistake. Pauses.] 

Wait. Is there a universe in which 1 + 1 = 1?

Not too long ago, my college-algebra students and I were chatting about graphing polynomials. At one point during our lesson, I quickly drew a smooth, wavy curve on the board and asked,

"How many roots would a polynomial with this graph have? Five? It crosses the x-axis five times."

One of my students recently said to me, "I'm not good at math because I'm really slow." Right then and there, she had voiced what is one of many misconceptions that folks have about math.

But friends, speed has nothing to do with one's ability to do mathematics. In particular, being "slow" does not mean you do not have the ability to think about, understand, or enjoy the ideas of math.

Let me tell you....

Physicist Freeman Dyson once observed that there are two types of mathematicians: birds -- those who fly high, enjoy the big picture, and look for unifying concepts -- and frogs -- those who dwell on the ground, find beauty in the scenery close by, and enjoy the details.

Of course, both vantage points are essential to mathematical progress, and I often tend to think of myself as more of a bird.(I'm, uh, bird-brained?)

I was at the grocery store earlier today, minding my own business, and while I was intently studying the lentil beans (Why are there so many options?) a man came down the aisle, pushing a cart with him. He then stopped in front of me, turned, looked me directly in the eyes and said,

Hello friends! I've decided to launch a new series on the blog called crumbs! Every now and then, I'd like to share little stories -- crumbs, if you will -- from behind the scenes of Math3ma. To start us off, I posted (a slightly modified version of) the story below on January 23 on Facebook/Twitter/Instagram, so you may have seen this one already. Even so, I thought it'd be a good fit for the blog as well. I have a few more of these quick, soft-topic blurbs that I plan to share throughout the year. So stay tuned! I do hope you'll enjoy this newest addition to Math3ma.