Related papers: My Favorite Math Jokes
Memes are one of the most ubiquitous forms of social media communication. The study and processing of memes, which are intrinsically multimedia, is a popular topic right now. The study presented in this research is based on the Memotion…
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
We describe a graph-theoretic syntax for self-referential formulas as well as a four-valued logic to include contradictory and independent formulas. We then explore the degree to which generalized truth tables can be realized in our theory,…
With the recent advances in Artificial Intelligence (AI) and Large Language Models (LLMs), the automation of daily tasks, like automatic writing, is getting more and more attention. Hence, efforts have focused on aligning LLMs with human…
Notes on the Spinpossible puzzle game. We give a mathematical description of the game, prove some elementary bounds on the length of optimal solutions, and consider variations of the game which place restrictions on the set of permitted…
This textbook, "Counting Rocks!", is the written component of an interactive introduction to combinatorics at the undergraduate level. Throughout the text, we link to videos where we describe the material and provide examples. The major…
Our question is ``What is the probability that at least three members of the senate share the same birthday?'' Before the pandemic, I asked this question in several popular math talks I gave at universities across the country. Inspired by…
The purpose of this note is to raise two different questions, which are rarely if ever considered, and to which, it seems, we lack convincing, systematic answers. These questions can be posed as: - Why do we compute? - What do we compute?…
This note investigates the combinatorics of permutations underlying the NYT daily word game Waffle. It helps to solve Waffle games and helps to understand why some games are easy to solve while others are very hard. It shows that a perfect…
In August 2023, Scott Aaronson and I reported the results of testing GPT4 with the Wolfram Alpha and Code Interpreter plug-ins over a collection of 105 original high-school level and college-level science and math problems (Davis and…
In my book "Algorithmic Information Theory" I explain how I constructed a million-character equation that proves that there is randomness in arithmetic. My book only includes a few pages from the monster equation, and omits the software…
I describe some deep-seated problems in higher mathematical education, and give some ideas for their solution -- I advocate a move away from the traditional introduction of mathematics through calculus, and towards computation and discrete…
I present examples of mathematical objects that are of interest for public key cryptography. Text for the Journ\'ee Annuelle 2007 of the SMF.
In this paper we present some interesting results involving summation of series in particular trigonometric ones. We failed to locate these results in existing literature or in the web like MathWorld (http://mathworld.wolfram.com/) nor…
We prove an interesting fact about Lottery: the winning 6 numbers (out of 49) in the game of the Lottery contain two consecutive numbers with a surprisingly high probability (almost 50%).
Math Word Problems (MWPs) in online assessments help test the ability of the learner to make critical inferences by interpreting the linguistic information in them. To test the mathematical reasoning capabilities of the learners, sometimes…
Large Language Models (LLMs) have demonstrated exceptional capabilities in various natural language tasks, often achieving performances that surpass those of humans. Despite these advancements, the domain of mathematics presents a…
We consider Steinhaus cake dividing game.
Well-defined jokes can be divided neatly into a setup and a punchline. While most works on humor today talk about a joke as a whole, the idea of generating punchlines to a setup has applications in conversational humor, where funny remarks…
This is a tract on the art and practice of mathematical writing. Not only does the book cover basic principles of grammar, syntax, and usage, but it takes into account developments of the last twenty years that have been inspired by the…