This is a short post on something that I get asked a lot: What is “math research”?
In many a high school math class, one student raises his hand and asks, “Why do we need to know this?”
Sometimes a teacher responds, “Because math teaches you how to think.”
Leaving the strengths and weaknesses of that answer aside, let’s talk about some books that can teach you something about how to think.
You won’t see many topics from your high school math classes in these books. but all of them deal with quantitative concepts. What’s more, all have helped me understand the world more clearly.
Most people have heard about π at some point, but I thought I’d talk a little bit about how I think mathematicians think about π.
In the last post, we discussed a suggestion for what probability means. But extending that interpretation to an election is a stretch. In the context of elections, makes more sense to talk about probability from another perspective.
Three days before the most recent presidential election, two forecasters got into a statistics fight on Twitter. They both thought the same candidate would win. So what were they arguing about, exactly?
I just watched two YouTubers explain binary. To me, one video’s explanation was fine, but the other was great. I’m still pondering this, and I’d like hear your input!
On a family vacation in the Rocky Mountains, my siblings decided to play Go Fish. My brother made a rule: if anyone gets dealt three of the same card (like three 8’s), return your cards and shuffle the deck. My hunch was that a triple isn’t actually so rare. So what are the actual odds of getting a triple if the deck is shuffled randomly? How would you go about figuring that out?
Even if you hate it. Even if you flunked it in high school.
A professor of mine once marveled at how nonintuitive the real numbers are. If you were going to pick a set of numbers to do math with, would you have made sure to include the square root of 17?
His casual comment points to something essential about numbers, something that every mathematician knows but that no one seems to talk about.
Artificial intelligence is real. It is evolving right now.
Should we be worried?