In this previous post, I recalled a discussion I once had with John Conway about the pros and cons of different systems for mentally calculating the day of the week for any given date. In this post, I’ll present two of the most popular systems for doing this, the “Apocryphal Method” [Note added 5/3/20: In a previous version of this post I called this the Gauss-Zeller algorithm, but its roots go back even further than Gauss] and Conway’s Doomsday Method. I personally use a modified verison of the apocryphal method. I’ll present both systems in a way which allows for a direct comparison of their relative merits and let you, dear reader, decide for yourself which one to learn.
Continue readingMonthly Archives: April 2020
Colorings and embeddings of graphs
My previous post was about the mathematician John Conway, who died recently from COVID-19. This post is a tribute to my Georgia Tech School of Mathematics colleague Robin Thomas, who passed away on March 26th at the age of 57 following a long struggle with ALS. Robin was a good friend, an invaluable member of the Georgia Tech community, and a celebrated mathematician. After some brief personal remarks, I’ll discuss two of Robin’s most famous theorems (both joint with Robertson and Seymour) and describe the interplay between these results and two of the theorems I mentioned in my post about John Conway.
Some Mathematical Gems from John Conway
John Horton Conway died on April 11, 2020, at the age of 82, from complications related to COVID-19. See this obituary from Princeton University for an overview of Conway’s life and contributions to mathematics. Many readers of this blog will already be familiar with the Game of Life, surreal numbers, the Doomsday algorithm, monstrous moonshine, Sprouts, and the 15 theorem, to name just a few of Conway’s contributions to mathematics. In any case, much has already been written about all of these topics and I cannot do justice to them in a short blog post like this. So instead, I’ll focus on describing a handful of Conway’s somewhat lesser-known mathematical gems.
Continue readingCOVID-19 Q&A
My friend Joshua Jay, who is one of the world’s top magicians, emails me from time to time with math questions. Sometimes they’re about card tricks, sometimes other things. Last night he sent me an excellent question about COVID-19, and I imagine that many others have wondered about this too. So I thought I’d share my response, in case it’s helpful to anyone.
JJ: Since the government is predicting between 100k – 240k deaths from COVID-19, let’s for argument’s sake split the difference and call it 170k projected deaths. They’re ALSO telling us they believe the deaths will “peak” something like April 20th. Am I wrong in assuming, then, that if we assume 170k total deaths, and the halfway point is a mere two weeks away, then they’re projecting 85k deaths before (and after) April 20th?
When I start to think about the idea of of 85k deaths between now and April 20th, and we’ve only experienced 5k so far, it means that 80k people are projected to die in the next two weeks. Surely that can’t be correct, or else it would be dominating the news cycle, right?
I’m not asking whether you think those projections are accurate… I’m just trying to wrap my head around the relationship between total projected deaths (whatever it is) and the projected peak of the curve.
Continue readingZero Knowledge Identification and One-Way Homomorphisms
Imagine logging into a secure web server which, instead of asking you to type in your password, merely asks you questions about your password until it’s convinced that you really do know it and therefore are who you say you are. Moreover, imagine that your answers to the server’s questions provide no information whatsoever which could be used by a malicious hacker, even if all communications between you and the server are being intercepted. Finally, imagine that the server in question not only does not store any information about your password, it has never at any point asked you for information about your password.
Sounds too good to be true, right?
In fact, such password schemes do exist, and they’re quite easy to implement. They are known as zero knowledge authentication systems. In this post, I’ll explain the main idea behind such protocols using the notion of a “one-way homomorphism”. Before diving into the technicalities, though, here’s a useful thought experiment which conveys the main idea.
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