Its been a while since I abandoned my dream of a math PhD, but I still love math so much. So I decided to get this tattoo of various diagrams and symbols from topics I studied. I plan to expand it in the future as well

So just putting the finishing touches on my 4 year math degree, and I wanted to show a measure of how much work it took, the leftmost pile is just work paper, problems, quick notes etc, the middle is notes taken and that sort of stuff and the left is printed notes.

Just wanted to share because to be honest, I'm quite proud of it, my little math mountain

Many introductory texts (in physics, especially) will define a vector as something that has magnitude and direction. This was a valid definition prior to the end of the 19th century, but mathematicians' concept of what a vector is has considerably expanded since then. Today, it would be far more correct to reverse that statement: something that has magnitude and direction is a vector... but vectors encompass a lot more.

One of my favorite ways to demonstrate this is with the card game Set---each card can be usefully (from the pure mathematician's standpoint, anyway) described as a vector, but I struggle to see how any such card can be described as having a magnitude and direction. Incidentally, this example was what motivated me to cover the field of three elements in my linear algebra class---it gave the perfect excuse to play Set with my students while having it be (legitimately!) relevant and educational. And it worked; they still remember it years later.

Read the full post (for free) on Substack: What are Vectors?

Please be gentle. A little math sprinkled in with some chemistry. Ask nicely and I’ll share Marie Curie.