Symposium at The Master's University

Recently on The Math3ma Institute's blog, I announced an upcoming event that will be hosted at The Master's University (TMU), which is a small private university in Santa Clarita, California. I wanted to briefly mention it here, too, in case it might be of interest to any readers.

This summer on June 9–10, I'll be joined by NASA astronaut Jeffrey Williams and molecular geneticist Beth Sullivan (Duke University) for a two-day symposium, which invites folks with vocations in a wide range of scientific disciplines from academia, industry, and government for a time of fellowship, encouragement, and the opportunity for dialogue and discussion. We're also honored to be joined by theologian Abner Chou, the president of TMU, as well as John MacArthur, the chancellor of TMU and the pastor of Grace Community Church in Los Angeles.

If you're interested to learn more, details and registration are now available at:

Read More →

Introducing The Math3ma Institute

Today I am excited to share that the Math3ma platform has recently grown in a small yet personal way. This new endeavor is in its early stages, but it is one that is close to my heart and gives life to the reasons I started this blog six years ago. A more personal announcement can be found in a new article I wrote for the university, but I'd like to give an update here as well.

This semester I joined The Master's University (TMU), a small private Christian university in southern California, as a visiting research professor of mathematics. I am still a full-time research mathematician in the tech world, but I've also been collaborating part time with the math, science, and engineering faculty at TMU to launch a little research hub on the university's campus and online.

We are calling it The Math3ma Institute, and the website is now live:

What is The Math3ma Institute?

I've branded our little venture an "institute," though its function is notably different from that of other research institutions. Our vision is that The Math3ma Institute will grow into a place where TMU faculty and advanced undergraduates, along with external colleagues, can engage in research activities in various STEM fields—not just mathematics—and where those results will then be made accessible to a broad audience in easy-to-understand ways. This is summarized in the trifecta boldly displayed on our homepage: discover. share. repeat.

To this end, we are aiming to produce several publicly-available resources, including the launch of semi-annual journal described below.

Read More →

Math3ma: Behind the Scenes (3B1B Podcast)

I recently had the pleasure of chatting with Grant Sanderson on the 3Blue1Brown podcast about a variety of topics, including what first drew me to math and physics, my time in graduate school, thoughts on category theory, basketball, and lots more. We also chatted a bit about Math3ma and its origins, so I thought it'd be fun to share this "behind the scenes" peek with you all here on the blog. Enjoy!

Read More →

A Nod to Non-Traditional Applied Math

What is applied mathematics? The phrase might bring to mind historical applications of analysis to physical problems, or something similar. I think that's often what folks mean when they say "applied mathematics." And yet there's a much broader sense in which mathematics is applied, especially nowadays. I like what mathematician Tom Leinster once had to say about this (emphasis mine):

"I hope mathematicians and other scientists hurry up and realize that there’s a glittering array of applications of mathematics in which non-traditional areas of mathematics are applied to non-traditional problems. It does no one any favours to keep using the term 'applied mathematics' in its current overly narrow sense."

I'm all in favor of rebranding the term "applied mathematics" to encompass this wider notion. I certainly enjoy applying non-traditional areas of mathematics to non-traditional problems — it's such a vibrant place to be! It's especially fun to take ideas that mathematicians already know lots about, then repurpose those ideas for potential applications in other domains. In fact, I plan to spend some time sharing one such example with you here on the blog.

But before sharing the math— which I'll do in the next couple of blog posts — I want to first motivate the story by telling you about an idea from the field of artificial intelligence (AI).

Read More →

What's Next? (An Update)

Before introducing today's post, I'd like to first thank everyone who's reached out to me about my thesis and video posted last week. Thanks! I appreciate all the generous feedback. Now onto the topic of the day: I'd like to share an update about what's coming next, both for me and for the blog.

First, a word on the blog.

What's next for Math3ma?

I created Math3ma in early 2015 as an aid in transitioning from undergraduate-level to graduate-level mathematics. And it worked! The blog has been a sort of public math journal for more than five years, and I'm so glad I started it. My appreciation extends to all readers and to everyone who has contacted me through the site over the years. I'm always delighted to hear that the blog has been helpful for you, as well.

So since Math3ma has accomplished its purpose, my use for it will change. As you may have noticed already, I blog less frequently than I used to, and the content of my more recent articles is slightly different than the content in 2015--2017.

So what will happen to Math3ma going forward? I don't know, and I plan to be flexible about this. Of course I'll leave the website up, but going forward I plan to be flexible with how often I'll blog (not often, probably) and with what I'll blog about (my research, probably). I don't have any big plans for upcoming blog posts, so I may just take a break for a while. On the other hand, I do plan to post a paper or two on the arXiv in the near future, and I might decide to blog about it since I find sharing math irresistible.

See? Flexible.

Read More →

Applied Category Theory 2020

Hi all, just ducking in to help spread the word: the annual applied category theory conference (ACT2020) is taking place remotely this summer! Be sure to check out the conference website for the latest updates.

As you might know, I was around for ACT2018, which inspired my What is Applied Category Theory? booklet. This year I'm on the program committee and plan to be around for the main conference in July. Speaking of, here are the dates to know:

  • Adjoint School: June 29 -- July 3
  • Tutorial Day: July 5
  • Main Conference: July 6 -- 10

The Adjoint School is a months-long online reading group, where participants paired with researchers work through some of the major papers in the field. It culminates in an in-person meet-up a week before the main conference. Unfortunately, the deadline apply to the school is already closed. But this year, the conference has a Tutorial Day, too! I love this idea. It's open to anyone (first-come first serve) who's new to applied category theory and wants a little more background to get the most out of the talks during the main conference. You'll get to meet with Paolo Perrone, David Spivak, and Emily Riehl and learn math! And here's a quick blurb about the main conference, taken from this year's website.

Read More →

Learning How to Learn Math

Once upon a time, while in college, I decided to take my first intro-to-proofs class. I was so excited. "This is it!" I thought, "now I get to learn how to think like a mathematician."

You see, for the longest time, my mathematical upbringing was very... not mathematical. As a student in high school and well into college, I was very good at being a robot. Memorize this formula? No problem. Plug in these numbers? You got it. Think critically and deeply about the ideas being conveyed by the mathematics? Nope.

It wasn't because I didn't want to think deeply. I just wasn't aware there was anything to think about. I thought math was the art of symbol-manipulation and speedy arithmetic computations. I'm not good at either of those things, and I never understood why people did them anyway. But I was excellent at following directions. So when teachers would say "Do this computation," I would do it, and I would do it well. I just didn't know what I was doing.

By the time I signed up for that intro-to-proofs class, though, I was fully aware of the robot-symptoms and their harmful side effects.

Read More →

Math3ma + PBS Infinite Series!

Hi everyone! Here's a bit of exciting news: As of today, I'll be extending my mathematical voice from the blogosphere to the videosphere! In addition to Math3ma, you can now find me over at PBS Infinite Series, a YouTube channel dedicated to the wonderful world of mathematics.

Read More →

Math Emojis

☺️ I love math

😀 It's so cool.

Read More →

Dear Autocorrect... (Sincerely, Mathematician)

Dear Autocorrect,


"Topos theory" is not the theory of tops. Or coats or shoes or hats or socks or gloves or slacks or scarves or shorts or skorts or--um, actually, what is topos theory?

“Zorn’s lemma” is not a result attributed to corn. Neither boiled corn, grilled corn, frozen corn, fresh corn, canned corn, popped corn, nor unicorns. Though I'm sure one of these is equivalent to the Axiom of Choice.

Read More →

Commutative Diagrams Explained

Have you ever come across the words "commutative diagram" before? Perhaps you've read or heard someone utter a sentence that went something like, "For every [bla bla] there existsa [yadda yadda] such thatthe following diagram commutes." and perhaps it left you wondering what it all meant.

Read More →

Some Notes on Taking Notes

A quick browse through my Instagram account and you might guess that I take notes. Lots of notes. And you'd be spot on! For this reason, I suppose, I am often asked the question, "How do you do it?!" Now while I don't think my note-taking strategy is particularly special, I am happy to share! I'll preface the information by stating what you probably already know: I LOVE to write.* I am a very visual learner and often need to go through the physical act of writing things down in order for information to "stick." So while some people think aloud (or quietly), 

I think on paper.

Read More →


If you've been following this blog for a while, you'll know that I have strong opinions about the misconception that "math is only for the gifted." I've written about the importance of endurance and hard work several times. Naturally, these convictions carried over into my own classroom this past semester as I taught a group of college algebra students.

Whether they raised their hand during a lecture and gave a "wrong" answer, received a less-than-perfect score on an exam or quiz, or felt completely confused during a lesson, I tried to emphasize that things aren't always as bad as they seem...

Read More →

Resources for Intro-Level Graduate Courses

In recent months, several of you have asked me to recommend resources for various subjects in mathematics. Well, folks, here it is! I've finally rounded up a collection of books, PDFs, videos, and websites that I found helpful while studying for my intro-level graduate courses. 

Read More →

A Ramble About Qualifying Exams

Today I'm talking about about qualifying exams! But no, I won't be dishing out advice on preparing for these exams. Tons of excellent advice is readily available online, so I'm not sure I can contribute much that isn't already out there. However, it's that very web-search that has prompted me to write this post.

You see, before I started graduate school I had heard of these rites-of-passage called the qualifying exams.* And to be frank, I thought they sounded terrifying.

Read More →

Snippets of Mathematical Candor

A while ago I wrote a post in response to a great Slate article reminding us that math - like writing - isn't something that anyone is good at without (at least a little!) effort. As the article's author put it, "no one is born knowing the axiom of completeness." Since then, I've come across a few other snippets of mathematical candor that I found both helpful and encouraging. And since final/qualifying exam season is right around the corner, I've decided to share them here on the blog for a little morale-boosting.

Read More →

Graduate School: Where Grades Don't Matter

Yesterday I received a disheartening 44/50 on a homework assignment. Okay okay, I know. 88% isn't bad, but I had turned in my solutions with so much confidence that admittedly, my heart dropped a little (okay, a lot!) when I received the grade. But I quickly had to remind myself, Hey! Grades don't matter.

Read More →

Real Talk: Math is Hard, Not Impossible

The quote above comes from an excellent Slate article by Chase Felker on why students shouldn't be afraid of or intimidated by mathematics. I posted the quote on Instagram not too long ago, and since it addresses a topic that is near-and-dear to my own heart, I decided to include it on the blog as well. Felker prefaces the quote by saying, "Giving up on math means you don't believe that careful study can change the way you think."

Read More →

A Math Blog? Say What?

Yes! I'm writing about math. No! Don't close your browser window. Hear me out first...

I know very well that math has a bad rap. It's often taught or thought of as a dry, intimidating, unapproachable, completely boring, who-in-their-right-mind-would-want-to-think-about-this-on-purpose kind of subject. I get it. Math was the last thing on earth I thought I'd study. Seriously.

Read More →