Related papers: An Impossible Asylum
Nearly twenty years ago Isaacs and the first author of this paper wrote a series of articles \cite{isa2}, \cite{da3}, \cite{da2} about what were called ``stabilizer limits'' of group characters, following the terminology of Berger…
This is a 20-year old review on singularities and singularity theorems. The main reason to submit it now is -apart from increasing its availability- to correct a very strange error that appears in the journal's online version: it contains…
We study the complexity of computational problems arising from existence theorems in extremal combinatorics. For some of these problems, a solution is guaranteed to exist based on an iterated application of the Pigeonhole Principle. This…
Hamilton's method (also called method of largest remainder) is a natural and common method to distribute seats proportionally between states (or parties) in a parliament. In USA it has been abandoned due to some drawbacks, in particular the…
In this paper we're going to explore the ways in which security proofs can fail, and their broader lessons for security engineering. To mention just one example, Larry Paulson proved the security of SSL/TLS using his theorem prover Isabelle…
Recent work by Faizal et al. (2025) claims that G\"odelian undecidability of non-algorithmic truths in our universe imply the impossibility of a formal, algorithmic simulation of the universe. This paper clarifies the distinction between…
In 2017 a definition of spiral tilings was given, thereby answering a question posed by Gr\"unbaum and Shephard in the late 1970s. The author had the pleasure to discuss the topic via e-mail with Branko Gr\"unbaum in his 87th year. During…
Opening lecture at the 2004 SLAC Summer Institute.
Recognizing analogies, synonyms, antonyms, and associations appear to be four distinct tasks, requiring distinct NLP algorithms. In the past, the four tasks have been treated independently, using a wide variety of algorithms. These four…
Explaining the evolution of cooperation in the strong altruism scenario, where a cooperator does not benefit from her contribution to the public goods, is a challenging problem that requires positive assortment among cooperators (i.e.,…
At any time, there are areas of science where we are standing at the frontier of knowledge, and can wonder whether we have reached a fundamental limit to human understanding. What is ultimately possible in physics? I will argue here that it…
Solving crossword puzzles requires diverse reasoning capabilities, access to a vast amount of knowledge about language and the world, and the ability to satisfy the constraints imposed by the structure of the puzzle. In this work, we…
We propose a novel model for refugee housing respecting the preferences of the accepting community and refugees themselves. In particular, we are given a topology representing the local community, a set of inhabitants occupying some…
I revisit an automated proof of Andrews' pentagonal number theorem found by Riese. I uncover a simple polynomial identity hidden behind his proof. I explain how to use this identity to prove Andrews' result along with a variety of new…
In this paper we analyse some of the classical paradoxes in Social Choice Theory (namely, the Condorcet paradox, the discursive dilemma, the Ostrogorski paradox and the multiple election paradox) using a general framework for the study of…
In the context of CSPs, a strong backdoor is a subset of variables such that every complete assignment yields a residual instance guaranteed to have a specified property. If the property allows efficient solving, then a small strong…
What makes a problem suitable for statistical analysis? Are historical and religious questions addressable using statistical calculations? Such issues have long been debated in the statistical community and statisticians and others have…
Ring puzzles are tessellations of the Euclidean plane respecting local constraints around vertices. Such puzzles may arise in geometric group theory, for example, as embedded flat planes in certain CAT(0) complexes of dimension 2. In the…
Goedel Incompleteness Theorem leaves open a way around it, vaguely perceived for a long time but not clearly identified. (Thus, Goedel believed informal arguments can answer any math question.) Closing this loophole does not seem obvious…
A rational triangle $T$ (one whose angles are rational multiples of $\pi$) unfolds to a translation surface $(X_T,\omega_T)$. The lattice triangle problem asks to classify those $T$ for which $(X_T,\omega_T)$ is a Veech (lattice) surface,…