Beneath the utilitarian purpose of computation, computing is also a source of delight and wonder . Software is not just databases and mail merges or SaaS and spreadsheets; it's creative coding and simulated cities , code poetry and bulletin board systems . It's websites that dazzle and iPhone apps that make the heart…
We’ve trained a model to achieve a new state-of-the-art in mathematical problem solving by rewarding each correct step of reasoning (“process supervision”) instead of simply rewarding the correct final answer (“outcome supervision”). In addition to boosting performance relative to outcome supervision, process…
The myth A few years ago I saw a StackOverflow question (but I cannot find it now): allegedly Andrew Gelman blogged that Bayesian models would not overfit and would only underfit (I also cannot find Andrew’s blog post now but I think what he meant by “Bayesian models only underfits” is that you can never fully model…
In a world-first experimental result, scientists at the University of Sydney have used a quantum computer to coax an atom to behave the same way as a photo-chemical process that underpins the speed of human vision and solar energy harvesting - only at speeds 100 billion times slower than in nature.
The uncanny resemblance between double descent and a 50 year old theory from psychology
Yesterday, we announced adding AI to our recon engine. Today, we're underscoring how reconciliation is a pain point by delving into the math.
A dimension is a physical quantity that can be measured, while a unit is a specific amount of a physical quantity. For example, time is a dimension, which can be measured in temporal units such as hours or seconds.
The following Python function computes the Fibonacci sequence , without loops, recursion or floating point arithmetic:
In this blog post, we explore Spotify's journey from using the Fisher-Yates shuffle to a more sophisticated song shuffling algorithm that prevents clustering of tracks by the same artist. We then connect this challenge to Fibonacci hashing, and propose a novel, evenly distributed artist shuffling method.
Get up close and personal with Schnorr and his now patent-free linear signature algorithm.
We thought we were accelerating fast enough. Turns out we weren't.
Statistical arbitrage (stat arb) is a pillar of quantitative trading that relies on mean reversion to predict the future returns of an asset. Mean reversion believes that if a stock has risen higher it’s more likely to revert in the short term which is the opposite of a momentum strategy that believes if a stock has…
One of my favourite Limited Audience Jokes (although technically it's actually a riddle) goes:
In 2005, id Software released the source code for their 1999 game Quake III Arena under the GPL-2 license. In the file code/game/q_math.c , there is a function for calculating the reciprocal square root of a number which at first glance seems to use a very peculiar algorithm:
A self-contained introduction to Gröbner bases and solving polynomial systems
On April 8, 2020, John Horton Conway developed symptoms of COVID-19. On April 11, 2020, he succumbed to the disease. 1 2 3 4
Generative AI tools like ChatGPT and Midjournery are able to replicate (and often exceed) human-like performance on tasks like taking exams, generating text and making art.
This is the first part of a series of posts on big changes for SymPy with particular focus on speed. What I am going to describe in these posts are:
The fun of owning rural property is that knowing where your land actually starts and ends is a guess usually. Sure, you have a parcel description, and maybe even an online service with “official” GIS boundaries (for us here in New Brunswick, this is GeoNB ). However, since it’s in the middle of the forest, the odds of…
Originally developed by Aristid Lindenmayer in 1968, an L-System is a formalism to generate self-similar structures. Although, L-Systems are capable of generating famous fractals like the Sierpinski Triangle (Axiom: FXF--FF--FF, F → FF , X → --FXF++FXF++FXF-- , angle = 60 ) or the Gosper Curve (Axiom: FX, X →…
Singular Value Decomposition (SVD) is a fundamental concept in linear algebra, and it is particularly important in the field of machine learning for tasks such as dimensionality reduction, data compression, and noise reduction.
Cistercian numerals were invented by the Cistercian order of monks in the 13th century. Giuseppe Frisella explains how the notation system works: A vertical str
This summer, 3Blue1Brown launched the third installment of the Summer of Math Exposition contest. Every year, I’ve been impressed and inspired by the quality of some of the videos in this con…
My last article had tips for for arena allocation . This next article demonstrates a technique for building bespoke hash maps that compose nicely with arena allocation. In addition, they’re fast, simple, and automatically scale to any problem that could reasonably be solved with an in-memory hash map. To avoid…
The phrase “foundations of mathematics” is bandied about frequently these days, but it’s clear that there is widespread confusion about what it means. Some say that a proof assistant must be based on a foundation of mathematics, and therefore that the foundations of mathematics refers to some sort of formal system…
When learning a new programming language, there is usually a table in the documentation that shows the various operators that can be used with numbers.
