iiinova — where your digital self keeps evolving

Vince Vatter @vatter.bsky.social · 06/09/2026

I hope the IPO gives OpenAI the resources it needs to let me pin an 11th chat.

ChatGPT interface: "You can only pin up to 10 items. Unpin an item to pin something new."

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Vince Vatter @vatter.bsky.social · 05/09/2026

Thurston (1982 Fields medalist), apropos of nothing.

I fairly rapidly proved some dramatic theorems. I proved a classification theorem for foliations, giving a necessary and sufficient condition for a manifold to admit a foliation. I proved a number of other significant theorems. I wrote respectable papers and published at least the most important theorems. It was hard to find the time to write to keep up with what I could prove, and I built up a backlog.

An interesting phenomenon occurred. Within a couple of years, a dramatic evacuation of the field started to take place. I heard from a number of mathematicians that they were giving or receiving advice not to go into foliations—they were saying that Thurston was cleaning it out. People told me (not as a complaint, but as a compliment) that I was killing the field. Graduate students stopped studying foliations, and fairly soon, I turned to other interests as well.

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Vince Vatter @vatter.bsky.social · 25/08/2026

Published today! Our article in Math Horizons about how Robert and I lied to players for three years in our game Digit Party, and how we used integer linear programming to stop.

First page of "Digit.party: Three years of lying about high scores" by Robert Brignall and Vincent Vatter, published in Math Horizons.

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Vince Vatter @vatter.bsky.social · 14/08/2025

I'm excited to share: we built a free AI coach for intro-level proof writing. It critiques drafts, points out gaps, and helps you or your students iterate without giving away the answer. Also for lapsed mathematicians to see if they've still got it. Demo below, link in reply.

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Vince Vatter @vatter.bsky.social · 16/06/2025

Published today in the Notices of the AMS. Lol.

Federal Funding for Mathematics Research—What’s Changed in the Last Six Years?

This article was solicited in early 2024 and completed in Fall 2024. It therefore does not reflect the changes that have occurred, and which are still going on, at federal science-funding agencies in 2025. For example, website links given in the article may not be active at the time of publication. - Ed.

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Vince Vatter @vatter.bsky.social · 30/05/2025

meanwhile, wikipedia is in existential crisis over whether √4 deserves its own page

Screenshot of a Wikipedia deletion discussion about whether redirects like “Square root of 4” and “Sqrt4” should exist. Editors argue over consistency, usefulness, and whether Wikipedia should function as a calculator. Some favor keeping the redirects for user convenience, others call them unnecessary or harmful. One comment invokes “Square root of 2209,” another disputes the logic entirely, and someone questions how to handle both positive and negative roots. The tone ranges from procedural to mildly exasperated.

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Vince Vatter @vatter.bsky.social · 29/05/2025

people like years more than ever though. reliably, year X mentions peak during year X+2.

Line graph showing the frequency of years ending in “00,” from 1800 to 2020, in English books.

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Vince Vatter @vatter.bsky.social · 29/05/2025

interest in the natural numbers is at an all-time low

Google Ngram Viewer line graph showing the frequency of digits 0 through 9 in English books from 1800 to 2019, with usage peaking around 1980 and declining sharply afterward.

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Vince Vatter @vatter.bsky.social · 06/05/2025

$FOX NEWS: Cardinals assess Pope Francis' legacy before vote. Delegates include $\aleph_0$, $\aleph_1$, $\beth_2$, and others, as the continuum hypothesis looms over the ceremonies.$

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Vince Vatter @vatter.bsky.social · 14/04/2025

AI debt collector exhibiting speciesism

AI: Hello, is this Ms. Zhang San?
User: This is Ms. Zhang San’s robot phone assistant, may I ask what you want to discuss with her?
AI: Sorry for disturbing you, goodbye!

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Vince Vatter @vatter.bsky.social · 13/04/2025

Needless to say, A001339 is not the same sequence, does not count preferential arrangements, and neither sequence has anything to do with the egf 1⁄(2−exp(x)). All of this was completely made up.

$A001339 a(n) = Sum_{k=0..n} (k+1)! binomial(n,k). 1, 3, 11, 49, 261, 1631, 11743, 95901, 876809, 8877691, 98641011, ...$

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Vince Vatter @vatter.bsky.social · 04/04/2025

I mean, it’s still better to have money than not have money right?

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Vince Vatter @vatter.bsky.social · 04/04/2025

you'll never guess what color my daughter's squares ended up

Instructions for assignment: Color each square blue. Color each rectangle yellow. Color each circle red.

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Vince Vatter @vatter.bsky.social · 03/03/2025

Want more superpermutation fun? My free article Containing All Permutations in the Mathematical Monthly covers this and related problems, and features, of course, Theorem 5 (Anonymous 4chan poster). www.tandfonline.com/doi/full/10....

$A screenshot from Containing All Permutations featuring Theorem 5 (Anonymous 4chan poster): For all $n\ge 1$, every $n$-superpermutation has length at least $n!+(n-1)!+(n-2)!n-3$.$

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Vince Vatter @vatter.bsky.social · 25/02/2025

the first step is admitting you have a problem. the second step is asking random users to fix it for free.

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Vince Vatter @vatter.bsky.social · 20/02/2025

Fermat thought 2^(2^n))+1 was prime after checking n=0,1,2,3,4. Euler factored the n=5 case, oops. Worse still, the odds are we'll never see another Fermat prime.

$$2^{2^n}+1$ isn't prime for $5\le n\le 32$. By the prime number theorem, $m$ is prime with probability ${\approx\nicefrac{1}{\ln m}}$. The probability that another number of this form is prime is about \[ \sum_{n=33}^\infty \frac{1}{\ln (2^{2^n}+1)} < \sum_{n=33}^\infty \frac{1}{2^n\ln 2} = \frac{1}{2^{32}\ln 2} \approx 0.000000000359. \]$

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Vince Vatter @vatter.bsky.social · 22/01/2025

Contrapositives are for cowards. Behold.

$Theorem. If $n$ is an integer and $n^2$ is even, then $n$ is itself even. Proof. Contrapositives are for cowards, so assume $n$ is an integer and $n^2$ is even. Then $n^2=2k$ for some integer $k$, and thus $n^2-2k=0$. Behold: \[ n = n + (n^2-2k) = n(n+1)-2k. \] Both $n(n+1)$ and $2k$ are even, so $n$ is even. QED.$

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Vince Vatter @vatter.bsky.social · 16/12/2024

"I decided to roll out my own LLM benchmark: how well can different models render an SVG of a pelican riding a bicycle?" simonwillison.net/2024/Oct/25/...

Gemini 1.5 Flash 001 asked to "Generate an SVG of a pelican riding a bicycle"

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Vince Vatter @vatter.bsky.social · 13/12/2024

unfortunately the price was determined using new math so I didn’t buy it

The Giant Golden Book of Mathematics including NEW MATH

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Vince Vatter @vatter.bsky.social · 14/11/2024

why the romans never invented algebra

a roman numeral multiplication table up to XII x XII

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Vince Vatter @vatter.bsky.social · 09/11/2024

what % of the population can enter their birthdate in this format?

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Vince Vatter @vatter.bsky.social · 30/10/2024

this is not how temperature works

16. The table shows the temperature at midnight in fink creek, alaska. at 5 a.m., the temperature changed by 1/2 of the current value. what is the temperature at 5 a.m.?

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Vince Vatter @vatter.bsky.social · 07/10/2024

I think this might be the worst proof I've ever read.

A terrible proof of the pigeonhole principle

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Vince Vatter @vatter.bsky.social · 21/09/2024

wow, chatgpt-o1 is smart enough to invent the "go back in time 5 years and buy triple-leveraged nasdaq" strat. surprised it didn't invent something better like "take a delorean back in time 40 years with a sports almanac".

I used OpenAI’s o1 model to develop a trading strategy. It is DESTROYING the market

It literally took one try. I was shocked.

by Austin Starks

published in Data Driven Investor

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Vince Vatter @vatter.bsky.social · 29/08/2024

fellow professors, how much would you pay for a 40% email conversion increase?

[Twitter DM]

Hi Vince noticed we’re in a similar industry so I figured I’d Reach out Directly

Curious what a 40% Email conversion increase would have on your business

Does this sound like something that can benefit you?

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Vince Vatter @vatter.bsky.social · 15/08/2024

why is π ≈ 3.14? the diamond inscribed in the unit circle has perimeter 2√2. the square circumscribing the unit circle has perimeter 4. average those, you get 3.41. reverse the last two digits, you get 3.14. QED.

the diamond inscribed in the unit circle has perimeter 2√2. the square circumscribing the unit circle has perimeter 4. average those, you get 3.41. reverse the last two digits, you get 3.14.

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Vince Vatter @vatter.bsky.social · 08/08/2024

The correct answer was eventually reached.

What happens if the explanatory and response variables are sorted independently before regression?

Suppose we have data set (X_i,Y_i) with n points. We want to perform a linear regression, but first we sort the X_i values and the Y_i values independently of each other, forming data set (X_i,Y_j). Is there any meaningful interpretation of the regression on the new data set? Does this have a name?

I imagine this is a silly question so I apologize, I'm not formally trained in statistics. In my mind this completely destroys our data and the regression is meaningless. But my manager says he gets "better regressions most of the time" when he does this (here "better" means more predictive). I have a feeling he is deceiving himself.

EDIT: Thank you for all of your nice and patient examples. I showed him the examples by @RUser4512 and @gung and he remains staunch. He's becoming irritated and I'm becoming exhausted. I feel crestfallen. I will probably begin looking for other jobs soon.

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Vince Vatter @vatter.bsky.social · 07/06/2024

how can a picture be THIS wrong?

an infuriating "cube" with misaligned top and bottom faces

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Vince Vatter @vatter.bsky.social · 04/06/2024

mistral's digit tokenization makes me question reality

How Mistral tokenizes digits:

0 is encoded as [29473, 29502]
1 is encoded as [29473, 29508]
2 is encoded as [29473, 29518]
3 is encoded as [29473, 29538]
4 is encoded as [29473, 29549]
5 is encoded as [29473, 29550]
6 is encoded as [29473, 29552]
7 is encoded as [29473, 29555]
8 is encoded as [29473, 29551]
9 is encoded as [29473, 29542]

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Vince Vatter @vatter.bsky.social · 15/05/2024

ChatGPT-4o does surprisingly poorly on MNIST.

Me: "What digit is this?"
[picture of digit from MNIST]
ChatGPT-4o: "Your input image may contain content that is not allowed by our safety system."

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Vince Vatter @vatter.bsky.social · 09/04/2024

imaginary numbers aren't real

$A proof that i = 1: i = e^{i\pi/2} = e^{2\pi i/4} = (e^{2\pi i})^{1/4} = (1)^{1/4} = 1. QED.$

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Vince Vatter @vatter.bsky.social · 03/04/2024

nailed it

$\lim_{n \to \infty} \frac{1 + 2 + \cdots + n}{n^2} = \left( \lim_{n \to \infty} 1 + 2 + \cdots + n \right) \cdot \left( \lim_{n \to \infty} \frac{1}{n^2} \right) = -\frac{1}{12} \cdot 0 = 0.$

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Vince Vatter @vatter.bsky.social · 02/04/2024

calc teachers hate this one weird trick

$Two different ways to evaluate the sum from k=1 to infinity of 1/(k(k+1)) are shown. First, each fraction is expressed as 1/k - 1/(k+1). This is shown as a series of decreasing fractions, with the terms simplifying to leave only the first term, 1/1, yielding a sum of 1. Second, each fraction is expressed as k/(k+1) - (k-1)/k. The terms are then simplified, showing a pattern that suggests each term cancels the next, resulting in a sum of 0. Therefore 1 = 0. QED.$