Why Prove a Theorem Twice?

I have written before on the problem and solution of the problem of “Pythagorean Triples”. The problem, based on the Pythagorean theorem for right triangles, asks for all possible solutions to this equation which have all of whole numbers. Not just any right triangle works – for instance if then , which is definitely notContinue reading “Why Prove a Theorem Twice?”

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?”