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)”
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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)”
Pythagorean Triples? (Problem)
I’ve spent some time thinking about how I want to present things I love on this blog, and one format I’ve come up with is a Problem/Solution series. The idea here is to have two posts with the same name – in one of them, I will explain an interesting problem and try to giveContinue reading “Pythagorean Triples? (Problem)”
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”
What Is a Proof?
I’ve talked a fair amount in some of the earlier posts about the idea of a proof. Now that we’ve developed a conceptual underpinning of what that means, we can see one in action. I hope my readers enjoy this as much as I do, as what we will discuss here is among my favorites.Continue reading “What Is a Proof?”
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”
Math is More Than Calculation
Before attempting to start talking about what math is and why I am so interested in it, I want to clarify what it is not. What I’d call math is probably is not what you learned in school. I think a better label for what most people think of when they hear “math” is calculation.Continue reading “Math is More Than Calculation”
Where Did Numbers Come From?
In my last post, I argued that a distinction needs to be made between calculation and math. But certainly these are related, because calculation is about numbers, and math uses a lot of numbers. So what exactly is the connection? Working from my own experience being trained to be a mathematician and educator, as wellContinue reading “Where Did Numbers Come From?”
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?”
