## Kolmogorov’s Axioms of Probability: Even Smarter Than You Have Been Told

Introduction I’d like to talk about the Kolmogorov Axioms of Probability as another example of revisionist history in mathematics (another example here). What is commonly quoted as the Kolmogorov Axioms of Probability is, in my opinion, a less insightful formulation than what is found in the 1956 English translation of […]

## Let A be a Pedant and Let B be a Pedant

One of my favorite mathematical anecdotes is the following story that Gian-Carlo Rota told about Solomon Lefschetz: He [Solomon Lefschetz] liked to repeat, as an example of mathematical pedantry, the story of one of E. H. Moore’s visits to Princeton, when Moore started a lecture by saying, “Let a be […]

## knotEd: Knot Diagram Editing Software

I’d like to share a video of my old knot editing software in action. Read more about KnotEd here.

## Bitcoin’s status isn’t as simple as ruling if it is more a private token or a public ledger

There is a lot of current interest in various “crypto currencies” such as Bitcoin, but that does not mean there have not been previous combined ledger and token recording systems. Others have noticed the relevance of Crawfurd v The Royal Bank (the case where money became money), and we are […]

## Let’s try to motivate schemes

Recently there has been some controversy over David Mumford’s Nature magazine invited obituary of Alexander Grothendieck being initially rejected on submission (see here and here). At issue was the attempt to explain the mathematical idea of schemes (one of Alexander Grothendieck’s most important contributions) to a non-mathematician audience. Professor Mumford […]

## Working an example of von Neumann and Morgenstern utility

von Neumann and Morgenstern’s “Theory of Games and Economic Behavior” is the famous basis for game theory. One of the central accomplishments is the rigorous proof that comparative “preference methods” over fairly complicated “event spaces” are no more expressive than numeric (real number valued) utilities. That is: for a very […]

## A Personal Perspective on Machine Learning

Having a bit of history as both a user of machine learning and a researcher in the field I feel I have developed a useful perspective on the various trends, flavors and nuances in machine learning and artificial intelligence. I thought I would take a moment to outline a bit […]

## Deming, Wald and Boyd: cutting through the fog of analytics

This article is a quick appreciation of some of the statistical, analytic and philosphic techniques of Deming, Wald and Boyd. Many of these techniques have become pillars of modern industry through the sciences of statistics and operations research.

## Hello World: An Instance Of Rhetoric in Computer Science

Hello World: An Instance Of Rhetoric in Computer Science John Mount: jmount@mzlabs.com February 19, 2008 Computer scientists have usually dodged questions of intent, purpose or meaning. While there are theories that assign deep mathematical meaning to computer programs[13] we computer scientists usually avoid discussion of meaning and talk more about […]