## Why All the Letters in Math?

One thing that many people dislike about math is all of its special symbols. Why does it need to be so specific? Why so many symbols? Why is writing things down in a specific format so important in math? Shouldn’t something be considered “correct” if it has the right ideas, regardless of how it isContinue reading “Why All the Letters in Math?”

## Pythagorean Triples? (Solution #1, Part 2)

In Part 1, we have begun discussing primitive Pythagorean triples, and thought a little bit about them. Now, we want to try to characterize all primitive triples. That is now our goal. Limiting The Possibilities Suppose we are given a primitive triple (a,b,c). Recall that this means that the three positive whole numbers a, b,Continue reading “Pythagorean Triples? (Solution #1, Part 2)”

## Pythagorean Triples? (Solution #1, Part 1)

(If you haven’t read the “Problem” post with the same title, go there first. This will make more sense if you do.) We want to find all the Pythagorean triples (a,b,c). The first thing a mathematician would probably do is to try some small examples, gather some information, and then look for patterns within thatContinue reading “Pythagorean Triples? (Solution #1, Part 1)”

## My Testimony

A lot of what I hope to write on this site will be about mathematics and it’s history, as these topics form my career and are one of the great passions of my life. I also plan to write about other passions that I’ve developed over time, which include mental health and philosophy. Now, IContinue reading “My Testimony”

## From Numbers to “Pure” Math: Ancient Greece

In my previous post, I talked about the conceptual progression from the most basic intuitions about counting to the more general idea of number that transcends any particular physical situation. As big a development as this is, I would say this not mathematics proper. In most civilizations where the number concept developed, the most complicatedContinue reading “From Numbers to “Pure” Math: Ancient Greece”

## What is This Blog?

Welcome! My name is Will Craig. As of this writing, I am a PhD student in mathematics at the University of Virginia. My current aim is to be a university professor. I greatly love both teaching people about various kinds of mathematics as well as working on modern research topics in number theory. I alsoContinue reading “What is This Blog?”