Math ∩ Programming

Can you find a set of cards among these six, such that the socks on the chosen cards can be grouped into matching pairs?

Table of Contents In a previous article we defined folding functions, and used them to enable some canonicalization and the sccp constant propagation pass for the poly dialect.

In cryptography, we need a distinction between a cleartext and a plaintext.

Table of Contents Last time we defined folders and used them to enable some canonicalization and the sccp constant propagation pass for the poly dialect.

Table of Contents Last time we saw how to use pre-defined MLIR traits to enable upstream MLIR passes like loop-invariant-code-motion to apply to poly programs.

Table of Contents Last time we defined a new dialect poly for polynomial arithmetic.

Problem: Compute 16% of 25 in your head.

Table of Contents In the last article in the series, we migrated the passes we had written to use the tablegen code generation framework.

Table of Contents In the last article in this series, we defined some custom lowering passes that modified an MLIR program.

Table of Contents This series is an introduction to MLIR and an onboarding tutorial for the HEIR project.

Table of Contents Last time, we covered a Bazel build system setup for an MLIR project.

Table of Contents As we announced recently, my team at Google has started a new effort to build production-worthy engineering tools for Fully Homomorphic Encryption (FHE).

Today my team at Google published an article on Google’s Developers Blog with some updates on what we’ve been doing with fully homomorphic encryption (FHE).

Before I discovered math, I was a first year undergrad computer science student taking Electrical Engineering 101.

It’s April Cools again.

In this article I’ll derive a trick used in FHE called sample extraction.

Back in May of 2022 I transferred teams at Google to work on Fully Homomorphic Encryption (newsletter announcement).

This article was written by my colleague, Cathie Yun.

In this article I’ll cover three techniques to compute special types of polynomial products that show up in lattice cryptography and fully homomorphic encryption.

Problem: Compute the product of two polynomials efficiently.

Welcome to the 209th Carnival of Mathematics!

Last time we covered an operation in the LWE encryption scheme called modulus switching, which allows one to switch from one modulus to another, at the cost of introducing a small amount of extra noise, roughly $\sqrt{n}$, where $n$ is the dimension of the

The Learning With Errors problem is the basis of a few cryptosystems, and a foundation for many fully homomorphic encryption (FHE) schemes.

This is a draft of a chapter from my in-progress book, Practical Math for Programmers: A Tour of Mathematics in Production Software.

It’s April Cools!

Previous posts in this series: Silent Duels and an Old Paper of Restrepo Silent Duels—Parsing the Construction Silent Duels—Constructing the Solution part 1 Since it’s been three years since the last post in this series, and the reason for the delay is th…

tl;dr: I’m writing a new book, sign up for the announcements mailing list.

Lately I’ve been studying Fully Homomorphic Encryption, which is the miraculous ability to perform arbitrary computations on encrypted data without learning any information about the underlying message.

I learned of a neat result due to Kevin Ventullo that uses group actions to study the structure of hash functions for unordered sets and multisets.

Welcome to the 197th Carnival of Mathematics!

We’re ironically searching for counterexamples to the Riemann Hypothesis.

Recently I’ve been helping out with a linear algebra course organized by Tai-Danae Bradley and Jack Hidary, and one of the questions that came up a few times was, “why should programmers care about the concept of a linear combination?”

We’re ironically searching for counterexamples to the Riemann Hypothesis.

We’re ironically searching for counterexamples to the Riemann Hypothesis.

We’re ironically searching for counterexamples to the Riemann Hypothesis.

We’re ironically searching for counterexamples to the Riemann Hypothesis.

In a recent newsletter article I complained about how researchers mislead about the applicability of their work.

We’re ironically searching for counterexamples to the Riemann Hypothesis.

We’re glibly searching for counterexamples to the Riemann Hypothesis, to trick you into learning about software engineering principles.

In the last article we set up pytest for a simple application that computes divisor sums $ \sigma(n)$ and tries to disprove the Riemann Hypothesis.

Some mathy-programmy people tell me they want to test their code, but struggle to get set up with a testing framework.

In my book, A Programmer’s Introduction to Mathematics, I describe the Taylor Series as a “hammer for every nail.”

In my book I discuss the importance of context in reading and writing mathematics.

This essay is a slightly modified version of the closing chapter of A Programmer’s Introduction to Mathematics.

The Second Edition of A Programmer’s Introduction to Mathematics is now available on Amazon.

Recently my employer (Google) forced me to switch to Mercurial instead of my usual version control system, git.

A year ago today I self-published “A Programmer’s Introduction to Mathematics” (PIM).

Previous posts in this series: Silent Duels and an Old Paper of Restrepo Silent Duels—Parsing the Construction Last time we waded into Restrepo’s silent duel paper.

At Google, our organization designs, owns, and maintains a number of optimization models that automate the planning of Google’s datacenter growth and health.

Our hero, a mathematician, is writing notes in LaTeX and needs to convert it to a format that her blog platform accepts.