Related papers: Odd One Out
This is lecture notes of a talk I gave at the Morningside Center of Mathematics on June 20, 2006. In this talk, I survey on Poincare and geometrization conjecture.
To an adult, it's obvious that the day of someone's death is not precisely determined by the day of birth, but it's a very different story for a child. When the third named author was four years old he asked his father, the fifth named…
Zeno's paradoxes are explained as being the result of inappropriate combination of discrete and continuous mathematical systems. It is proposed that the source of this confusion lies in the course of development of the number system, which…
This article is a brief personal account of the past, present, and future of algorithmic randomness, emphasizing its role in inductive inference and artificial intelligence. It is written for a general audience interested in science and…
`Terquem's problem' is a name given in the twentieth century to the problem of enumerating certain integer sequences whose entries alternate in parity. In particular, this problem asks for the count of strictly increasing length $m$…
We discuss a non-intuitive situation concerning percentages.
We discuss some recent work by Tim Maudlin concerning Black Hole Information Loss. We argue, contra Maudlin, that there is a paradox, in the straightforward sense that there are propositions that appear true, but which are incompatible with…
We discuss some aspects of Extrapolation theory. The presentation includes many examples and open problems.
Peg solitaire is an old puzzle with a 300 year history. We consider two ways a computer can be utilized to find interesting peg solitaire puzzles. It is common for a peg solitaire puzzle to begin from a symmetric board position, we have…
We offer a reader-friendly introduction to the attracting edge problem (also known as the "triangle conjecture") and its most general current solution of Limic and Tarr\`es (2007). Little original research is reported; rather this article…
A curious number is a palindromic number whose base ten representation has the form $a \ldots a b \ldots b a \ldots a$. In this paper, we determine all curious numbers that are perfect squares. Our proof involves reducing the search for…
Humor recognition has been widely studied as a text classification problem using data-driven approaches. However, most existing work does not examine the actual joke mechanism to understand humor. We break down any joke into two distinct…
Studying extreme ideas in routine choices and discussions is of utmost importance to understand the increasing polarization in society. In this study, we focus on understanding the generation and influence of extreme ideas in routine…
Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For…
Users of spoken dialogue systems (SDS) expect high quality interactions across a wide range of diverse topics. However, the implementation of SDS capable of responding to every conceivable user utterance in an informative way is a…
In an investigation of the applications of Combinatorial Game Theory to chess, we construct novel mutual Zugzwang positions, explain an otherwise mysterious pawn endgame from "A Guide to Chess Endings" (Euwe and Hooper), show positions…
This is the text of an expository talk given at the May 1997 Detroit meeting of the American Mathematical Society. It is a tale of a famous football player and a subtle problem he posed about the uniform convergence of Dirichlet series.…
We define outliers as a set of observations which contradicts the proposed mathematical (statistical) model and we discuss the frequently observed types of the outliers. Further we explore what changes in the model have to be made in order…
The reader is reminded of several puzzles involving randomness. These may be ill-posed, and if well-posed there is sometimes a solution that uses probabilistic intuition in a special way. Various examples are presented including the well…
Given a sufficiently long bead chain in a cup, if we pull the end of the chain over the rim of the cup, the chain tends to continuously flow out of the cup, under gravity, in a common siphon process. Surprisingly enough, under certain…