As I mentioned on the home page, I currently work in Corvallis, Oregon (pictured above) as a mathematics graduate student and graduate teaching assistant at Oregon State University. My most recent CV (updated 1/11/2025) reflects this work:

Broad takeaways

Look, I know a lot of math. So, if you find a bunch of different simply connected topological spaces and you need someone to compute their fundamental groups, I'm your guy.^* But studying math has given me skills that are more broadly applicable to my life. Here are my main takeaways:

• Collaboration. Math is really hard. So, once you're in a graduate program, everyone assumes that you will be working with other people. And man, I've learned a lot about working with others. I'm an analysis & computing guy, but there are some problems where I'm really happy to have a topologist around. Overall, I have found this to be the most rewarding part of my time in math: it helps me work with other people.


• Logical problem-solving. Learning math is best done by doing math, and that means solving a lot of problems. Math is also an extension of logic, so that means solving problems precisely, clearly, and carefully. This is not an irrelevant skill. Breaking down a problem into pieces, considering each tool in your arsenal, and thinking carefully about the perceived roadblocks, are all crucial parts of solving any problem.

^*This is a joke.

Projects and Research

I am just beginning the process of moving away from coursework and into research with my advisor, Dr. Malgorzata Peszynska. My work is in numerical analysis, particularly as it relates to partial differential equations. Some examples of my work are shown below. Click a caption to see a full PDF. Additionally, I have many examples of my coding prowess on my GitHub! I code for fun as well as for work, so I'm pretty proud of my output there. There's some numerical methods there, as well as some projects from undergrad, and I even host this website there!

Coursework

My coursework has covered calculus, statistics, discrete math, linear algebra, real analysis (introductory analysis, metric spaces, and measure thoery), complex analysis, probability, abstract algebra, number theory, topology, and lots of numerical analysis. If you want the full details, check out my complete list of coursework on the academics page.

Broad Takeaways

Philosophy gets a bad rap. Many people think that people who "discuss philosophy" just end up talking in circles, not making any progress. There's some truth to this, but there are a few helpful things I've picked up over the years:

• Clear communication. Because it's so easy to misunderstand one-another, philosophy cares a lot about clarity. For example, let's say you and I are talking about exams and we agree that "exams suck and should be improved." Even if we agree on that slogan, we might disagree on very important details: What sucks about the exams? Do they suck for students, teachers, or administrators? Does the type of exam matter? What about the format of the exam? If we don't agree on these details, working towards a solution that satisfies both of us might be impossible.
  
  The most important example of clear, philosophical communication is talking about arguments and reasons. If you think that exams suck and your friend thinks that exams are great, then both of you should clearly lay out your reasoning:

  1. Premise. Graded exams enforce a system where sucess is solving problems without external resources like the internet.
  2. Premise. In the real world, successfully solving problems involves resources like the internet.
  3. Conclusion. Therefore, exams enforce a misguided idea of success, which is bad.

  1. Premise. Exams measure how much a student understands the material.
  2. Premise. We want successful students to understand the material.
  3. Conclusion. Therefore, exams measure a valuable component of success, which is good.

  When our reasons are laid out this clearly, we can make progress by turning disagreements over the conclusion into disagreements over the premises. Hopefully, this lets us eventually get to a solution that everyone is happy with.


• Critical thinking. Critical thinking involves identifying problems, analysing the problem to find the root cause, and coming up with solutions that effectively solve the problem. It also involves values of open-mindedness, honesty, and humility. When discussing exams, I might realize that there's a problem with exams I hadn't considered, or maybe my proposed solution had a fatal error I was ignoring. If I really care about improving exams, I have to be able to identify problems even when that means admitting I was wrong.

Papers

I've practiced communication and critical thinking mostly by writing papers. Here are a few topics I've written about!

In addition to these papers, I've also done extensive reading in the philosophy of science, epistemology, and—my favorite—the philosophy of education. I also worked through every exercise in Mathematical Logic Through Python by Yannai A. Gonczarowski and Noam Nisan, which was very fun. You can see the result of that work at this GitHub repository.

Coursework and reading.

My coursework and reading has covered informal, formal, and mathematical logic, epistemology, metaphysics and the philosophy of mind, metametaphysics and ontology, art, language, education, and more. If you want the full details, check out my complete list of coursework on the academics page.