相关论文: Cheryl's Birthday
We examine a new variant of the classic prisoners and lightswitches puzzle: A warden leads his $n$ prisoners in and out of $r$ rooms, one at a time, in some order, with each prisoner eventually visiting every room an arbitrarily large…
A short autobiography written for a centennial party.
We explore the creative problem-solving capabilities of modern LLMs in a novel constrained setting. To this end, we create MACGYVER, an automatically generated dataset consisting of over 1,600 real-world problems deliberately designed to…
This article is dedicated to the centenary of the birth of Aleksandr D. Alexandrov (1912-1999). His functional-analytical approach to the solving of the Minkowski problem is examined and applied to the extremal problems of isoperimetric…
In this article, we present a trick around Fibonacci numbers which can be found in several magic books. It consists in computing quickly the sum of the successive terms of a Fibonacci-like sequence. We give explanations and extensions of…
Measuring the full abilities of large language models (LLMs) requires benchmarks representing multiple tasks. We aim to create large, high-quality datasets for comparison of logical reasoning skills across several languages and of suitable…
Intellectual space is defined as the set of all proofs of mathematical logic, contained in The Book conceived by Erdos. Physical and intellectual spaces are visualized, making use of concepts from intuitive set theory.
Disregarding the identity, the remaining 63 elements of the generalized three-qubit Pauli group are found to contain 12096 distinct copies of Mermin's magic pentagram. Remarkably, 12096 is also the number of automorphisms of the smallest…
In this note we give answers to questions posed to us by J.Milnor and M.Shub, which shed further light on the structure of non-computable Julia sets.
\emph{Circuit analysis} is a promising technique for understanding the internal mechanisms of language models. However, existing analyses are done in small models far from the state of the art. To address this, we present a case study of…
The 30 MacMahon colored cubes have each face painted with one of six colors and every color appears on at least one face. One puzzle involving these cubes is to create a $2\times2\times2$ model with eight distinct MacMahon cubes to recreate…
Large language models (LLMs) such as GPT, Gemini, and Claude often appear adept at solving classic logic puzzles--but how much genuine reasoning underlies their answers? Recent evidence suggests that these models frequently rely on…
In a delightful article that recently appeared in Mathematics Magazine, David and Lori Mccune analyze the board game "Count Your Chickens!", recommended to children three and up. Alas, they use the advanced theory of Markov chains, that…
Textual humor is enormously diverse and computational studies need to account for this range, including intentionally bad humor. In this paper, we curate and analyze a novel corpus of sentences from the Bulwer-Lytton Fiction Contest to…
This is a short historical note concerning the evolution of Wetzel's problem and Erdos' solution.
The year 2024 marks two anniversaries: The 70th anniversary of CERN and the 50th anniversary of the $J/\Psi$ discovery. At this occasion I have been asked to give review talks on the significance of these anniversaries. This article is an…
We investigated long range correlations in two literary texts, Moby Dick by H. Melville and Grimm's tales. The analysis is based on the calculation of entropy like quantities as the mutual information for pairs of letters and the entropy,…
This paper introduces Logical Credal Networks, an expressive probabilistic logic that generalizes many prior models that combine logic and probability. Given imprecise information represented by probability bounds and conditional…
We introduce higher-dimensional cubical sliding puzzles that are inspired by the classical 15 Puzzle from the 1880s. In our puzzles, on a $d$-dimensional cube, a labeled token can be slid from one vertex to another if it is topologically…
This note has been written on the occasion of Gerard 't Hooft's 60th birthday celebration. It is not a technical paper but just a collection of discussions that the three authors had with Gerard, mostly in relation with the idea of…