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A Life that Added Up to Something: Paul Erdos (1996)
WASHINGTON - One of the most extraordinary minds of our time has "left." "Left" is the word Paul Erdos, a prodigiously gifted and productive mathematician, used for "died." "Died" is the word he used to signify "stopped doing math." Erdos never died. He continued doing math, notoriously a young person's field, right…
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The Busy Beaver Problem
Busy Beaver puts another one on the Turing Machine's tape (image from the book The New Turing Omnibus). The busy beaver problem is a fun theoretical computer science problem. Intuitively, the problem is to find the smallest program that outputs as many data as possible and eventually halts. More formally it goes…
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The Baby-Eating Aliens
(Part 1 of 8 in "Three Worlds Collide") • This is a story of an impossible outcome, where AI never worked, molecular nanotechnology never worked, bio…
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How Credit Card Numbers Are Generated
Visa,Master Card,Discover, and American Express credit card validation and generation techniques using the luhn algorithm.
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Visualizing the Fourth Dimension Using Color
Color can be used to indicate position in 4D space
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Intractability of Financial Derivatives
A new result by Princeton computer scientists and economists shows a striking application of computer science theory to the field of financial derivative design. The paper is Computational Complexity and Information Asymmetry in Financial Products by Sanjeev Arora, Boaz Barak, Markus Brunnermeier, and Rong Ge…
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The odd one out - inspired by IQ tests
Mathematics, applications of mathematics to life in general, and my life as a mathematician.
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The Shocking State of Contemporary "Mathematics"
I just came back from attending the 1052nd AMS (sectional) meeting at Penn State, last weekend, and realized that the Kingdom of Mathematics is dead. Instead we have a disjoint union of narrow specialties , and people who know everything about nothing, and nothing about anything (except their very narrow acre). Not…
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A Calculus Analogy: Integrals as Multiplication
Integrals are often described as finding the area under a curve. This description is too narrow: it's like saying multiplication exists to find the area of…
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A 3700-year-old proof that the diagonal of a unit square has length √2
Clicking on an image will bring up the same image at higher resolution (a download of about about 100 KB). Clicking on that in turn will download an image of about 300 KB.
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Regular Expression Matching: the Virtual Machine Approach
Name the most widely used bytecode interpreter or virtual machine. Sun's JVM? Adobe's Flash? .NET and Mono? Perl? Python? PHP? These are all certainly popular, but there's one more widely used than all those combined. That bytecode interpreter is Henry Spencer's regular expression library and its many descendants.
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What every developer should know about time
How to handle time is one of those tricky issues where it is all too easy to get it wrong. So let's dive in.
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Why the secret to speedier highways might be closing some roads: the Braess paradox
"All will be well if you use your mind for your decisions, and mind only your decisions." Help me make more videos and posts! A monthly membership directly supports the channel and allows me to make more videos that inspire students and teachers around the world. You also get early access to new videos. Support with a…
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Automatic Differentiation: The most underused tool in the machine learning toolbox?
Update: (November 2015) In the almost seven years since writing this, there has been an explosion of great tools for automatic differentiation and a corresponding upsurge in its use. Thus, happily,…
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Peter Selinger: MD5 Collision Demo
C:\TEMP> md5sum hello.exe cdc47d670159eef60916ca03a9d4a007 C:\TEMP> .\hello.exe Hello, world! (press enter to quit) C:\TEMP>
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P.S.: The Best of Intentions
Operations in Lisp, Scheme, and other dynamically-typed languages typically dispatch on representational type information rather than intentional type information. Several broad classes of bugs and confusions can be traced to improper attempts to recover intentional type information from representation types.
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The Three Projections of Doctor Futamura
Introduction The Three Projections of Futamura are a sequence of applications of a programming technique called 'partial evaluation' or 'sp...
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PHYS771 Quantum Computing Since Democritus
University of Waterloo, Fall 2006 Tuesdays and Thursdays, 1:00-2:30pm BFG Building, 2nd floor seminar room (BFG2125)