Meet Matthew Ward. This interview is part of a series of…
By: Cantor S Paradise Team
Tags: Writing, Math, Community, Interview

This interview is part of a series of stories featuring some of the personalities writing for Cantor’s Paradise.

Who Are You?

My name is @Matthew. I’m a 34-year-old writer based in Connecticut.

What Do You Do For a Living?

I’m currently a full-time writer. I primarily consider myself a novelist these days. Depending on how you count, I’ve written 15 novels under three different names. I also write for a bunch of publications, including on Medium, and manage three webpages.

How Did You Become Interested in Mathematics?

I never thought I was interested in mathematics as a kid. I did well in the subject, but I thought it was about blindly following formulas and rote memorization. I actually started college as a music major.

I took “Discrete Math” because I thought I might minor in the subject and started to see proofs and high-level concepts at work behind the proofs. At some point, I stumbled upon Keith Devlin’s book The Millenium Problems. From there I was hooked. I realized math was entirely about concepts. The formulas and symbols were just the language to express those ideas.

Which Topics Are You Most Interested in?

It might be surprising since this is a mathematics publication, but the topics that interest me most right now are the problems of AI, social media, and addiction. Of course, these are all intertwined. There’s a lot of misunderstanding around all three of those topics. We have pictures in our head about what these look like, which causes us to miss what’s right in front of us.

Mathematically, my dissertation was in something called “arithmetic geometry.” This is basically the intersection of number theory and geometry, and many of my articles focus on the concepts underlying this field. I keep inching toward more and more abstract and difficult theorems and topics in my articles. I would love to eventually write an article trying to explain things like Mirror Symmetry.

I’m currently working on an article describing Morse Theory and the classification of compact 2-manifolds. I’m very interested in tackling these fascinating topics that no other “popular math” writers seem to go near.

How Would You Describe Your Writing?

I try to strike a balance of understandability and giving the full picture that remains accessible to a general, mathematically literate audience. This means I use a lot of examples and just suggest how the general concept is related.

This can get me in some trouble because many people misinterpret this as arguing “from analogy.” Unfortunately, I’ve never found an adequate way around this problem. If I only talk about things a first-year undergrad can understand, then I’d be leaving out the most interesting part. If I try to give too much of the full argument, then no one will read it.

It’s a balance I think I’ve been getting better at, but I also empathize with people who are frustrated with this approach.

Which is Your Most Popular Story?

My most viewed story is ‘The Brilliance of the Yoneda Lemma’, though this isn’t my most read story, which I think just comes from the fact that it’s a pretty long and abstract article. My most-read story is much shorter, and is probably a phenomenon of how Medium counts “reads.”

I’m quite happy with this. I had a blog all through grad school. When I converted the blog to a personal webpage, I removed all the math articles for SEO reasons. Some people complained, and so I started converting the old blog posts to more polished general audience Medium stories.

This article came from a heavy revision of a series of blog posts describing the concept of a stack (originally aimed at an audience of advanced grad students in algebraic geometry). I still think the Yoneda Lemma is vastly underappreciated for how versatile it is in generalizing the concept of a “space.”

Which is Your Favorite Story and Why?

My favorite story is easily ‘Faltings’s Theorem and the Mordell Conjecture’. I wish I could have thought of a better name. It’s possibly the most beautiful theorem I know of, and that article walks you through the entire proof conceptually.

Articles about Fermat’s Last Theorem do well because of its place in popular culture. The Mordell conjecture is basically the same theorem but for all polynomials! When are there only finitely many integer solutions? It’s very simple to state.

The answer is mind-blowing. You can tell there will be finitely many when you look at the topology of the shape it makes in projective space. No one should be able to predict that. Why should the number of holes in the shape it makes have anything to do with the number of integer solutions? If you want to know the answer, check out the article. It’s this surprising interplay between number theory, topology, and geometry that makes arithmetic geometry so cool.

Which Story is Your Biggest Flop?

Considering how much work I put into the article I talked about above, I’d say that the Mordell Conjecture article is my biggest flop. I really thought the tie-in to Fermat’s Last Theorem would be a draw. I spent weeks making sure the pictures clearly explained my points and that nothing got described too quickly.

In terms of raw numbers that’s not the worst flop though. I have many stories on how AI works and the dangers of it to society that just went nowhere. It always surprises me, because it’s topical and scary and absolutely must be dealt with in the next few years.

Who is Your Favorite Mathematician?

This question is surprisingly easy: Alexander Grothendieck. To say that he revolutionized algebraic geometry is an understatement. He wrote thousands of pages establishing the foundations of the subject.

I talked above about the Yoneda Lemma, and he realized this was the “right” way to think about the spaces studied in algebraic geometry. He founded many related subjects like K-theory, etale cohomology, derived categories, and more.

Most of the greatest mathematicians of all time never do even one of those things. It takes people a decade to learn one of those subjects with the aid of modern textbooks and experts, and yet he seemed to invent these new subjects from scratch every few years. I also spent a lot of grad school reading his work, and it’s incredibly precise and detailed. If you don’t know why something is a fact that’s “obvious” in an algebraic geometry textbook, then you can probably find the full explanation in his writings.

How Many Unfinished Drafts are on Your Medium Account?

I currently only have 12. I tend to use physical notebooks for ideas and outlining. There’s something about writing by hand that gets my brain working in the ways I need to get momentum on a story.

I don’t know how many ideas are scattered through these notebooks, but I probably have at least five more stories started that aren’t in draft form.

What is Your Favorite Math Book?

I’ll give three answers to this. My favorite actual math book is Robin Hartshorne’s Deformation Theory. It was my first exposure to a bunch of unsolved problems in algebraic geometry, and it put into context a bunch of things I had learned in classes but hadn’t made sense yet. It also directly led to the conception of what would become my thesis problem.

My favorite “popular math” book is probably Shing-Tung Yau’s The Shape of Inner Space: String Theory and the Geometry of the Universe’s Hidden Dimensions. It’s part autobiography and a good glimpse into the mathematical life and then also does a good at describing Calabi-Yau spaces.

My favorite novel that has math in it is Ethan Canin’s A Doubter’s Almanac. Sometimes math pops up in culture and then the math community becomes enamored with it. I’m not sure how this excellent novel has stayed off people’s radar.

What is Your Dream Job?

I guess I’m pretty much doing it. I’m a learner at heart, so I love that when I write a character, I have to become that. I wish I could have more of an impact on AI safety. I’ve written AI recommendation engines and neural nets from scratch in python and C++, so I understand them quite well. I thought as a writer on popular math/science topics, I could have some more reach than I’ve had on that topic.

If someone tomorrow offered me a position in a task force to work on solutions, I’d take it in a heartbeat. That job doesn’t seem to exist, though.

What is Your Favorite Non-Self-Authored Story in CP?

This is quite hard. I don’t follow many people. I like getting the constant stream of a full publication and finding new people that way. My interests also change monthly. Probably my most consistent favorite is Timothy O’Neill. He’s like me and does a wide range from fiction/poetry to essays on mental health to inspiration.

Do You Have Any Advice on How to Succeed as a Writer on Medium?

This depends on what you count as success. If you want people to click on and read your stories, you need to have catchy titles on popular topics. This is the most obvious thing when I look back on articles that did well compared to ones that didn’t.

I want to write about interesting things that haven’t ever been explained for a non-expert audience. If you write the hundredth article on why 1+2+…=-1/12 or a surface-level explanation of the Millenium Problems, you’ll probably have more success than picking something obscure like the Besicovitch 1/2 Conjecture.

To me, success is having someone comment that they understood something new or found it cool. In the short-run, that means fewer reads. I’m hoping in the long-run, a consistent, more niche following will come for my style of article.

Where Can People Find You to Learn More?

I rarely use Twitter, but I try to remember to post new articles there under wardmj4. The best place to be informed of new articles is my Medium profile: @wardmj4. The hub for my fiction writing is amindformadness.com.