121
122
A Nerd’s Way to Walk Up the Stairs (2011)
Mathematics, applications of mathematics to life in general, and my life as a mathematician.
123
Let’s talk about PAKE
The first rule of PAKE is: nobody ever wants to talk about PAKE. The second rule of PAKE is that this is a shame, because PAKE — which stands for Password Authenticated Key Exchange — is actually o…
124
The Strangest Book on the Theory of Computation (2009)
Based on the description of the book in the World Scientific Press catalogue, I asked my university library to order a book entitled Automat...
125
A New Angle on L2 Regularization
Deep neural networks have been shown to be vulnerable to the adversarial example phenomenon: all models tested so far can have their classifications dramatically altered by small image perturbations . The following predictions were for instance made by a state-of-the-art network trained to recognize celebrities :
126
Just teach my kid the math
This is a new thing for me - I'm hosting a blog post by a colleague/friend - James Tanton. You can find James' original post here. One reason it's being re-hosted here is because Medium is apparently blocked in some countries: Egypt Malaysia ..... possibly others. It is astounding to me that mathematics - of all…
127
Limits on Matrix Multiplication
Can 2.3728639 be best? Personal site; note puzzles Josh Alman is a graduate student at a technical school in the Boston area. He is working on matrix multiplication, among other problems in complex…
128
Gravitational attraction of stars and cows
One attempt at rationalizing astrology is to say that the gravitational effects of celestial bodies impact our bodies. To get an idea how hard the stars and planets pull on us, let's compare their gravitational attraction to that of cows at various distances. Newton's law of gravity says that the gravitational…
129
Advent of Code Python Solutions, Explained
I first participated in Advent of Code (AoC) in 2017. My co-workers at Formlabs introduced it to me. This year (2018), quite a lot of Formlabs folks are taking part and we have a nice private leaderboard going. I'm having a lot of fun with it. I've been staying up until midnight to work on the problems as soon as…
130
Twenty Questions Of Maddening, Delicious Geometry
The geometry puzzles that are lighting up Twitter.
131
The Land Before Binary
In the early days of computing, 1 + 1 didn’t always equal 10
132
So You Think You Have a Power Law (2007)
Regular readers who care about such things — I think there are about three of you — will recall that I have long had a thing about just how unsound many of the claims for the presence of power law distributions in real data are, especially those made by theoretical physicists, who, with some honorable exceptions…
133
134
135
136
Worst Puzzle Ever (2009)
It breaks my heart to write this post because the puzzle in question was 1) very expensive and 2) given to me by someone very dear to me who...
137
138
What Made Gödel’s Incompleteness Theorem Hard to Prove
Roughly speaking, Gödel’s Incompleteness Theorem states that there are true mathematical statements that cannot be proven. When I was in 11-th grade, my geometry teacher Mr. Olsen, my friend …
139
Progress on longstanding open problems
For those who haven’t seen it: Aubrey de Grey, better known to the world as a radical life extension researcher, on Sunday posted a preprint on the arXiv claiming to prove that the chromatic …
140
Machine Learning Trick of the Day: Instrumental Thinking
· Read in · 1499 words · All posts in series · [dropcap]This[/dropcap] trick is unlike the others we’ve conjured. It will not reveal a clever manipulation of a probability or an integral or a…
141
The Math Required for Machine Learning
For the past year, I’ve been working on implementing well known model architectures and building web applications, so I have a fair amount…
142
143
144
145
Random Points on a Sphere
John D. Cook, Greg Egan, Dan Piponi and I had a fun mathematical adventure on Twitter. It started when John Cook wrote a program to compute the probability distribution of distances $latex |xy R…
146
Homotopy Type Theory and Higher Inductive Types
In this article, we explore the possibilities allowed by higher inductive types. They enable a much more intuitive formalization of integers and new mind-blowing definitions of the (homotopical) ci…
147
Constraint Solving with MiniZinc
This is part one of a two-part article. Part two is here. A while back somebody told me to check out MiniZinc. Eventually I did and really enjoyed it, so figured I’d write about it here. This is actually going to be a two part article. Right now we’re talking about what it is and how it works, and in the next post…
148
Clojure Numerics: Orthogonalization and Least Squares
How to solve linear systems that have many solutions, or those that have no solutions at all? That's the theme for a thick math textbook, of course, but from...
149
150
Fast, Constant-Time Sphere Indexing
Map any 3D point on or above a triangle-subdivided sphere to a triangle index in constant time, without recursion, table lookups or complicated branching logic.