Using computers to prove theorems, making videos at https://xitter.cf/t.co/htzXY0SNUs, and tweeting Wikipedia list articles with no context. Mathematician @HofstraU.
New York, NY
Joined August 2008
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New video–paper combo! What numbers do you get when you iteratively scale a table? Approximations have been used since the 1930s to predict telephone traffic and in other applications. But mathematically, the exact values are extremely complicated! youtu.be/-uIwboK4nwE
Really? Which is it?
NY Times, July 23: "A.I. can write poetry, but it struggles with math"
nytimes.com/2024/07/23/techn…
NY Times, July 25: "A.I. is getting good at math — and might soon make a worthy collaborator for humans"
nytimes.com/2024/07/25/scien…
Eric Rowland retweeted
Raise your hand if you want to see a live session with @ericrowland and myself, where we'll talk about math and answer all your questions!
And if you're not following his awesome math channel yet, take a look at it here, you're in for a treat!
youtube.com/@EricRowland
To estimate the variance of a distribution from n sample points, we divide by n-1 rather than n. This always drove me crazy. Why n-1 when it's an average over n points!? Finally there's a great explanation, thanks to a new video by @SerranoAcademy youtu.be/_sdNwY0KKUA
In math you can define objects however you want. But if your definitions aren’t *right*, the theorems will let you know. I’ve been working on a paper for two years, and today my coauthor and I redefined one of the main objects… Lots of little problems we were having disappeared!
Symphonie fantastique: when one tuba just isn't enough youtu.be/5HgqPpjIH5c?t=2865
I gave a talk yesterday about a major thread of my research over the last 10 years: taking integer sequences that count combinatorial objects and asking what they look like when we reduce them modulo a prime or prime power. youtu.be/ZCIGJwxYqkk
I started my Logic & Probability course this semester with this scene from Labyrinth and trying to figure out whether Sarah's question is enough to tell which door is which. Later on we'll discuss Monty Hall. Is it a coincidence that both involve doors? youtube.com/watch?v=2dgmgub8…
This month's Ponder This challenge is about a familiar sequence research.ibm.com/haifa/ponde…
What’s a better name for Precalculus? Students have no reason to be interested in something called Pre-X if they aren’t going to take X. Instead of saying what the course isn’t, shouldn’t the title say what it is?
This explanation of vowel space by @geofflindsey is one of the best educational videos I've seen this year youtube.com/watch?v=FdldD0-k…
Seeing students replace f(a + h) with f a + f h makes me realize that parens are pretty badly overloaded notation... a(b + c) = a b + a c but somehow when you change the letters the rule no longer applies? Hoping it's not too late in the history of math to fix this 😂
Just realized that the journal Discrete Mathematics got rid of page numbers three years ago and started numbering articles instead. Definitely a step in the right direction! I haven't looked at a physical journal in over a decade. sciencedirect.com/journal/di…
Stewart's Calculus motivates limits -- and therefore all of calculus -- with "the tangent problem": Determine the tangent line to a curve at a point. But it's not clear why anyone should care about this problem. So here's an every-day example I used in class this week...
Your favorite maps app has 180° camera views. When you get directions, how does it choose the camera angle to show you at each step? If the road is straight, it's easy: your car is pointing in the same direction as the road.
Is it surprising that students don’t understand what it means to cite their sources when their textbooks contain problems like this with no attribution whatsoever?
ALT Math problem “from a cuneiform tablet found in a Babylonian school dating back to about 2000 B.C.”
New video! Continuing with the theme of generating primes in unexpected ways, we explore the recurrence R(n) = R(n - 1) + gcd(n, R(n - 1)). It was conjectured to generate primes in 2003, and I proved this a few years later. Animated with @manim_community youtube.com/watch?v=OpaKpzMF…
Why is so much mathematical writing bad? It doesn't have to be this way. I spent a few minutes with Jackson and Richmond's highly anticipated paper on a new proof of the four color theorem. It's being read in its current form by lots of people. Exciting? arxiv.org/abs/2212.09835
and the third -- IN PARENTHESES -- is that P is true. Where is the intuition? Where is the informal description of the new ideas that led to this breakthrough? Where is the narrative?