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How to Tell a Mathematician You Love Them (2017)
For those who love numbers, and those who love them.
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Calculating Pi: My Attempt at Breaking the Pi World Record
Before I go into the specifics of my record attempt, it is important for you to have some background information. Over the past few years I have been steadily acquiring server hardware to increase my knowledge of system administration and cyber security. This is not only for personal growth: it has also helped me…
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Projective Geometric Algebra Done Right
[This is part one of a two-part series. The second part can be found here: Symmetries in Projective Geometric Algebra .]
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The Contagion of Concern: Game theory of how anxiety spreads
Founder, Investor, Author
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Optimizing 128-bit Division
When it comes to hashing, sometimes 64 bit is not enough, for example, because of birthday paradox — the hacker can iterate through random $latex 2^{32}$ entities and it can be proven that wi…
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MathJax Turns 3.0
When I launched bit-player.org in 2006, displaying any sort of mathematical notation on the web was torture. I would typeset an equation in LaTeX, convert the output to a JPEG image, upload the image file to a directory on the server, and embed a reference to the file in an HTML img tag. The process was cumbersome and…
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All you need is λ, part one: booleans
Words by Rob Rix.
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Beyond Bézier Curves (2013)
There is a new feature of Pages and Keynote, not mentioned in any of Apple’s publicity nor in any press coverage I’ve seen, that is really very interesting. Perhaps it will even one day prove to ha…
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How to Read a Log Scale
What log scales tell us.
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Simple Image Vectorization
This is an example of an image vectorization algorithm. It shows the bilinear interpolation, polynomial approximation, differential analysis, and iterative algorithms working together to solve a practical problem
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Was Knuth Really Framed?
Recently, the formal methods specialist Hillel Wayne posted an interesting article discussing whether Donald Knuth was actually framed when Jon Bentley asked him to demonstrate literate programming . (Knuth came up with an 8-page long monolithic listing, whereas in a critique Doug McIlroy provided a six line shell…
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Math Symbols Explained with Python
Learn the meaning behind mathematical symbols used in Machine Learning using your knowledge of Python.
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A Graphical Introduction to Lattices
Here is my (extended) family tree: Everyone in the tree shares at least one common ancestor and at least one common descendant. This ...
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Twenty Proofs of Euler's Formula: V-E+F=2
Many theorems in mathematics are important enough that they have been proved repeatedly in surprisingly many different ways. Examples of this include the existence of infinitely many prime numbers , the evaluation of \(\zeta(2)\), the fundamental theorem of algebra (polynomials have roots), quadratic reciprocity (a…
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The field of “useful reals” between rational and real numbers (2019)
Most schools teach number systems the same way. First they teach natural numbers (or “counting numbers”), then integers, rationals, reals, and complex numbers, in that order. Rationals are countable and reals are not, but that’s okay. Once you start taking roots, you need a number system more powerful than a countable…
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Scaling Down Deep Learning
A blog by Sam Greydanus
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How Rainbow Tables Work
I found the creator of Rainbow Table's paper, aimed at cryptanalysts, was pretty inaccessible considering the simplicity and elegance of Rainbow Tables, so this is an overview of it for a layman.
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Mathematical marketing: a piece of calculus to change the way you advertise
If you make $10 profit each time you sell a product, what cost per conversion should you aim for? Answering this question isn't easy, but it can teach us a…
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An Overview of Bayesian Inference (2019)
A few weeks ago I wrote about Kuhn’s theory of paradigm shifts and how it relates to Bayesian inference. In this post I want to back up a little bit and explain what Bayesian inference is, and eventually rediscover the idea of a paradigm shift just from understanding how Bayesian inference works.
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Division by zero in type theory: a FAQ
How can a theorem prover use the convention that 1/0=0 and still be consistent?
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Computational Category Theory in Python III: Monoids, Groups, and Preorders
Parts 1 and 2 are found here and here
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The formula for pi buried in a hydrogen atom
When most people think about pi, they associate the mathematical constant with arcs and circles. Mathematicians, however, are accustomed to seeing it in a variety of fields. But two University physicists were still surprised to find it lurking in a quantum mechanics formula for the energy states of the hydrogen atom.
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Reinventing the Wheel: Discovering the Optimal Rolling Shape with PyTorch (2019)
It is thought that the wheel was invented more than five thousand years ago, yet modern machine learning tools were only developed in the past few decade...
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DARPA’s 23 Challenge Questions
Research in Scientific Computing in Undergraduate Education2020117 points30 commentsMath & Algorithms details
DARPA challenges The Defense Advanced Research Projects Agency (DARPA) has issued 23 mathematical challenges. DARPA says the solution of any one of these challenges would have the effect of “…
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Legible Mathematics: Sketches of interactive arithmetic for programming (2014)
Sketches of an interactive arithmetic for programming by Glen Chiacchieri.