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Old Books and the Passage of Time
I recently got a couple books that I’ve had on my “to read” list for several years: Frank Abagnale’s The Art of the Steal and Joseph Heath’s Enlightenment 2.0. And I’ve been enjoying both books, but...
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A Fictional History of Numbers, Part 4: Imagination, Complexity, and the...
Welcome back to our survey of the different types of “numbers” that mathematicians work with, and what kind of questions lead us to study those numbers. This week we’re going to put a bow on the first...
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A Fictional History of Numbers, Part 3: Computability, Reality, and Leaving...
Today we’re going to finish our discussion of the real numbers. We’ll see that they really are quite strange, in ways that are uncomfortable to think about, and then see why we keep using them anyway....
View ArticleEvaluating Students is Important, Too
There’s a classic dry academic joke that I retell frequently. My entire salary is just to pay me to grade; I do the rest of my job for free.And this is first an apology for not writing much lately; we...
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A Fictional History of Numbers, Part 2: Measurement, Estimation,...
This week we continue our exploration of what numbers are, and where mathematicians keep finding weird ones.In part 1, we started with the natural numbers, the most basic numbers we use to count...
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A Fictional History of Numbers, Part 1
In graduate school I studied number theory. The joke goes that number theory is the kind of math where you never use anything recognizable as an actual number. And it’s true that advanced mathematics...
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Motivating the Integral with Euler’s Method
I have a fun idea for how to teach and think about the integral in the context of freshman calculus. I’ve never actually used this in a class, and I suspect it’s not actually a great idea. But it’s a...
View ArticleWriting Calculus Tests with ChatGPT
Last week I talked about the new chatbots, like ChatGPT and Bing’s chat interface. I argued that they while they produce language they can’t really analyze it or check it for errors; and that this is a...
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Why I’m Not Scared of the New Chatbots
If you haven’t already heard about AI chatbots, you probably haven’t been on the internet in the past couple of months. In November, OpenAI released ChatGPT, which can engage in text conversations with...
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Hypothesis Testing and its Discontents, Part 3: What Can We Do?
Hypothesis testing is central to the way we do science, but it has major flaws that have encouraged widespread shoddy research. In part 1 of this series, we looked at the historical origins of...
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Hypothesis Testing and its Discontents, Part 2: The Conquest of Decision Theory
This is the second-part of a planned three-part series on hypothesis testing.In part 1 of this series, we looked at the historical origins of hypothesis testing, and described two different approaches...
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Hypothesis Testing and its Discontents, Part 1: How is it Supposed to Work?
In my last post on the replication crisis, I mentioned the basic ideas of statistical hypothesis testing. There wasn’t room to give a full explanation in that post, but hypothesis testing is worth...
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Why Isn’t There a Replication Crisis in Math?
One important thing that I think about a lot, even though I have no formal expertise, is the replication crisis. A shocking fraction of published research in many fields, including medicine and...
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Pascal’s Wager, Medicine, and the Limits of Formal Reasoning
Scott Alexander at Astral Codex Ten has a good post recently thinking about what he calls Pascalian Medicine. As always the entire post is worth reading, but here’s an excerpt:Another way of looking at...
View ArticleMore Thoughts on the Axiom of Choice
I got a lot of good, interesting comments on my recent post on the axiom of choice (both on the post itself, and in this very good Hacker News thread). I wanted to answer some common questions and...
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What is the Axiom of Choice?
One of the easiest ways to start a (friendly) fight in a group of mathematicians is to bring up the axiom of choice. This axiom has a really interesting place in the foundations of mathematics, and I...
View ArticleLockdown Recipes: Red Beans and Rice
Since we’re all stuck at home and cooking more than usual, I wanted to share one of my favorite recipes from my childhood, which is also especially suited to our current stuck-at-home ways.1Red Beans...
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The SIR Model of Epidemics
For some reason, a lot of people have gotten really interested in epidemiology lately. Myself included.I have no idea why.Now, I’m not an epidemiologist. I don’t study infectious diseases. But I do...
View ArticleOnline Teaching in the Time of Coronavirus
I’ve been spending a lot of the past week looking at different options for transitioning my teaching online for the rest of the term. There are certainly people far more expert at online instruction...
View Article2019 Spring Class Reflections: Calculus
Now that the term is over, I want to reflect a bit on the courses I taught, what worked well, and what I might want to do differently next time. (Honestly, it probably would have been more useful to...
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