Vince Vatter

@vatter.bsky.social

Mathematician at the University of Florida. Here for the hot takes. Also @VinceVatter@mathstodon.xyz https://vincevatter.com

Manifold markets: Will Gary Marcus still say that deep learning models can't reason after they prove the Riemann hypothesis?

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.

The number of American kings over time: a harrowing saga of job insecurity, with a notable dip after 1776 and a suspicious lack of improvement since.

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.

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

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.

$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.$

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!

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

ChatGPT-4o:

"go to OEIS bc i’m tired: [1, 1, 1, 2, 5, 17, 73, …] → OEIS A001339"

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

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

Reference list with a citation for The Terminator (1984) by James Cameron, published by Orion Pictures, nestled alongside academic papers on AI and security.

Starbucks mobile order screen showing a customized Venti Iced Caffè Americano with 4 shots of espresso, 2/3 decaf, and ice. Questionable caffeine logic at play.

$$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 \[ \sum_{n=33}^\infty \frac{1}{\ln (2^{2^n}+1)} < \sum_{n=33}^\infty \frac{1}{2^n\ln 2} = \frac{1}{2^{32}\ln 2} \approx 0.000000000359. \]$

$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.$

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

The Giant Golden Book of Mathematics including NEW MATH

a roman numeral multiplication table up to XII x XII

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.?

Which of the images A to E is the odd one out?

“I was always very good at mathematics,” Mr. Trump told John Micklethwait, the editor in chief of Bloomberg News, in an interview at the Economic Club of Chicago.

A terrible proof of the pigeonhole principle

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

[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?

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.

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.

an infuriating "cube" with misaligned top and bottom faces

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]

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."

A three-panel Wojak-style meme depicts characters with varying perceptions of real numbers. On the left, a simple-minded figure says, 'Real numbers are complicated.' In the middle, an 'average' figure with tears running down their face states, 'Real numbers are trivial, they’re just a straight line.' On the right, a monk-like figure with a hood comments, 'Properly defining the real numbers is complicated. You need to use either Dedekind cuts or equivalence classes of Cauchy sequences.' Below them is a bell curve graph labeled with IQ scores ranging from 70 to 130 and percentages from 2% to 34%, suggesting different levels of understanding or perception of the complexity of real numbers.

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

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

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

White Ninja character from the C'mon, Do Something meme poking the following proof that 1=0 with a stick:
1 != 0
implies 0 x 1 != 0 x 0
implies 0 != 0
therefore 1 = 0

The argument presents a sequence of mathematical operations starting with the variable 'x' defined as the sum of the number '1' added together 'x' times. It then proceeds to differentiate both sides of the equation with respect to 'x', leading to a derivation that simplifies to stating '1' equals '0'. This progression relies on the symbolic manipulation of differentiation across a constant sum repeated 'x' times.

0 = 0 + 0 + 0 + ···
= (1 - 1) + (1 - 1) + (1 - 1) + ···
= 1 - 1 + 1 - 1 + 1 - 1 + ···
= 1 + (-1 + 1) + (-1 + 1) + (-1 + 1) + ···
= 1 + 0 + 0 + 0 + ···
= 1

HAGOROMO
Chalk

91th Anniversary [Chalk Service]

(Maybe^^, Until December 2023)

Chalk is a free service.

Even if the chalk is broken, which is
not a problem with the chalk case,
the chalk is a service product, so
you cannot exchange or refund it.
We will try not to damage the chalk.

Please understand!! Thank you~!!

The root test, which comes next, is more conductive than the ratio test in that, if the root test gives no information concerning the convergence of a series, then neither does the ratio test.

-- Page 313 of Kosmala's A Friendly Introduction to Analysis: Single and Multivariable

Quora question: Is it bad to be in a math class that seems like the professor is making up random stuff?

Choose a new password dialogue with the password 8pf5ZtPYiKd/s+X graded as "Weak" because it does not begin with a letter.

A proof in a textbook that concludes "Is that important? Why? This completes the proof."

DALL-E 3 illustration of an eco-friendly urban environment with towering glass and metal skyscrapers bathed in sunlight amidst abundant greenery and serene water features. Glass cylindrical aquariums house ethereal jellyfish, forming an integral part of the landscape. The heart of the city is marked by a grand jellyfish statue, detailed and towering, with nearby buildings echoing its form with jellyfish-shaped domes and glowing patterns. Streets are lined with jellyfish-shaped lampposts casting a soft light, while people of diverse descents and genders, including Middle Eastern females, Hispanic males, and children of various ethnicities, engage in leisure activities, all within view of the gently floating jellyfish within their urban sanctuaries.

$Picture from page 149 of Kosmala's A Friendly Introduction to Analysis, 2nd edition: ... is finite and moreover equals $f(a)$. Note that in Definition 3.2.1 we were not interested in what happened when $x = a$. Here we are. Thus, the deleted neighborhood used in Definition 3.2.1 has to be replaced by a neighborhood of $a$, and $L$ replaced by $f(a)$. The resulting condition is equivalent to the one used in Definition 4.1.1. It is important to note that if $a$ is an *isolated point*, that is, if $a$ not an accumulation point of $D$ but $a \in D$, then $f$ is automatically continuous at $x = a$. **In such a case the point $(a, f(a))$ is called a *singleton*.** ...$

Image of "On Erdős's Proof of the Existence of Cages", by Vincent Vatter.
https://doi.org/10.1080/00029890.2023.2258742

A screenshot of a dropdown menu with the label "Select State." Options listed include various U.S. states, territories, and APO/FPO options. The option "Federated States of Micronesia" is currently selected.

Listen to me Jerry! What's the one thing AI will never be able to do? Properly draw these five-fingered beauties. Hand modeling, it's future-proof!

Meme picture of futuristic city with flying cars.

Maxell Gold.
The floppy disk that trn Apples
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$(Terrible) Definition 1.2.10. Suppose that $f:A\to B$ and $x_1$ and $x_2$ are any two points in $A$ with $x_1<x_2$. Then, * $f$ is increasing if and only if $f(x_1) \le f(x_2)$. * $f$ is strictly increasing if and only if $f(x_1) < f(x_2)$. * $f$ is decreasing if and only if $f(x_1) \ge f(x_2)$. * $f$ is strictly decreasing if and only if $f(x_1) > f(x_2)$. * $f$ is constant if and only if $f(x_1) = f(x_2)$.$