Foundations

Mathematical Foundations

Linear algebra, calculus, probability, statistics and optimisation — the maths behind ML

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Multiply matrices and compute dot products

Probability & Statistics

Calculate conditional probability and Bayes' theorem

Implement gradient descent from scratch

Information Theory

Calculate Shannon entropy and cross-entropy loss

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All Reads (259) Articles (123)Blog Posts (88)Tutorials (29)Research Papers (13)News (6)

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Lord of the Algebras: Groups, Rings, and Semirings in C#

Medium · Programming 🔢 Mathematical Foundations ⚡ AI Lesson 6d ago

Lord of the Algebras: Groups, Rings, and Semirings in C#

This article is part of “Abstract Algebra in .NET” Series Continue reading on Medium »

OpenAI News 🔢 Mathematical Foundations ⚡ AI Lesson 1w ago

On the Navier–Stokes Millennium Prize Problem

We’re sharing an AI-generated solution to the Navier–Stokes Millennium Prize Problem, including a writeup and a formal proof in Lean.

How Did Archimedes Calculate Pi Without Measuring It

Medium · Programming 🔢 Mathematical Foundations ⚡ AI Lesson 3w ago

How Did Archimedes Calculate Pi Without Measuring It

Archimedes trapped π without ever measuring a circle. Continue reading on ThinkArt »

Why Negative Times Negative Is Positive

Medium · Programming 🔢 Mathematical Foundations ⚡ AI Lesson 4w ago

Why Negative Times Negative Is Positive

Six Ways to Understand the Rule Continue reading on ThinkArt »

“Let p be an odd prime” . {Part I}

Medium · AI 🔢 Mathematical Foundations ⚡ AI Lesson 1mo ago

“Let p be an odd prime” . {Part I}

QUESTION. Proofs in number theory often remove the number 2 with the phrase “let p be an odd prime.” Why does mathematics remove its first… Continue reading on

The Hidden Patterns Behind User Behaviour

Medium · Data Science 🔢 Mathematical Foundations 1mo ago

The Hidden Patterns Behind User Behaviour

When I first encountered eigenvectors, they felt disconnected from real work. There were matrices, arrows, and equations, but no obvious… Continue reading on Me

Scrape, small piece on dif of calculators vs generative programs

Reddit r/artificial 🔢 Mathematical Foundations 1mo ago

Scrape, small piece on dif of calculators vs generative programs

submitted by <a href="https://

Bir Yazılımcının Matematik Bilmesi Gerçekten Gerekli mi?

Medium · Data Science 🔢 Mathematical Foundations ⚡ AI Lesson 1mo ago

Bir Yazılımcının Matematik Bilmesi Gerçekten Gerekli mi?

Bir yazılımcının matematik bilmesi gerçekten gerekli mi? Continue reading on Medium »

Emad Mostaque, on camera: "It's a bad time to be a pure mathematician." AI just solved 10 decade-old math problems for $2,000.

Reddit r/artificial 🔢 Mathematical Foundations 1mo ago

Emad Mostaque, on camera: "It's a bad time to be a pure mathematician." AI just solved 10 decade-old math problems for $2,000.

<img src="https://external-preview.redd.it/dm5sY3M5OWM5ZGloMftUNgpf3pPGFfohbBprgndUGypf8lkwKsRK6L4vwuBY.png?width=640&crop=smart&auto=webp&s=0150a56

How √-1 was invented in 16th century Italy

Medium · Data Science 🔢 Mathematical Foundations 1mo ago

How √-1 was invented in 16th century Italy

The Renaissance Italians were the first to discover that allowing √-1 to exist helped solve previously intractable problems Continue reading on Medium »

Hacker News (AI) 🔢 Mathematical Foundations ⚡ AI Lesson 1mo ago

The original URL for this prediction will no longer be available in 11 years (2011)

4D Conformal Field Theory, 5D Gravity, and Stringy Corrections in Extreme Fields

Medium · Data Science 🔢 Mathematical Foundations 1mo ago

4D Conformal Field Theory, 5D Gravity, and Stringy Corrections in Extreme Fields

by Aditiya Widodo Putra, Expert in Mathematics & Astrophysics. Continue reading on Medium »

Splitting €10 three ways: the largest remainder method, and the tiebreak everyone forgets

Dev.to · Eric Mollenthiel 🔢 Mathematical Foundations ⚡ AI Lesson 1mo ago

Splitting €10 three ways: the largest remainder method, and the tiebreak everyone forgets

Split €10 three ways and you get €3.33, €3.33, €3.33. That is €9.99. One cent has gone missing, and...

How to divide by 19 in your head

Medium · Data Science 🔢 Mathematical Foundations ⚡ AI Lesson 1mo ago

How to divide by 19 in your head

Turn division by 19 into repeated division by 2. Continue reading on ThinkArt »

Hacker News (AI) 🔢 Mathematical Foundations 1mo ago

The Entropy of a Markov Chain

I Let AWS Rewrite My DevOps Agent's Prompt: 142 Sessions, +6.2%, and a p-value of 0.38

Dev.to · Gerardo Arroyo 🔢 Mathematical Foundations ⚡ AI Lesson 1mo ago

I Let AWS Rewrite My DevOps Agent's Prompt: 142 Sessions, +6.2%, and a p-value of 0.38

I closed the Episodic Memory article with a line that kept nagging me for months: "there's a point...

MIT’s Math Test 2010: Calculate the Value of X.

Medium · Data Science 🔢 Mathematical Foundations ⚡ AI Lesson 1mo ago

MIT’s Math Test 2010: Calculate the Value of X.

Taken from Feb. 2010 Past Papers Continue reading on ThinkArt »

MIT’s Math Test 2010: Calculate the Value of X.

Medium · Data Science 🔢 Mathematical Foundations ⚡ AI Lesson 1mo ago

MIT’s Math Test 2010: Calculate the Value of X.

Taken from Feb. 2010 Past Papers Continue reading on ThinkArt »

$How to add feet and inches with fractions (job-site examples)$

Dev.to · Knoxy 🔢 Mathematical Foundations ⚡ AI Lesson 1mo ago

How to add feet and inches with fractions (job-site examples)

How to add feet and inches with fractions (job-site examples) Adding 6′ 3-1/2″ + 2′ 9-3/4″...

$How to add feet and inches with fractions (job-site examples)$

Dev.to · Knox_Studios_little_minion 🔢 Mathematical Foundations ⚡ AI Lesson 1mo ago

How to add feet and inches with fractions (job-site examples)

How to add feet and inches with fractions (job-site examples) Adding 6′ 3-1/2″ + 2′ 9-3/4″...

Medium · Data Science 🔢 Mathematical Foundations 1mo ago

Waveguide Deon Hypothesis of the Electron: Compton Scale, Vacuum Impedance, and the Nature of the…

Gennadii Evseenko Independent Researcher Email: evseenko.gen@gmail.com Continue reading on Medium »

The Quadratic Formula , Explained With Squares

Medium · Data Science 🔢 Mathematical Foundations ⚡ AI Lesson 1mo ago

The Quadratic Formula , Explained With Squares

A 4,000-year-old rectangle-cutting trick that makes the scariest formula in algebra feel obvious Continue reading on ThinkArt »

The Quadratic Formula , Explained With Squares

Medium · Programming 🔢 Mathematical Foundations ⚡ AI Lesson 1mo ago

The Quadratic Formula , Explained With Squares

A 4,000-year-old rectangle-cutting trick that makes the scariest formula in algebra feel obvious Continue reading on ThinkArt »

How do Mathematicians Discover New Things

Medium · Data Science 🔢 Mathematical Foundations ⚡ AI Lesson 1mo ago

How do Mathematicians Discover New Things

Mathematicians do discover formulas, but formulas make up only a small part of mathematics. More often, they are know to discover patterns… Continue reading on

2026 Fields Medal Deep Dive: What Four Mathematicians' Papers Actually Say, and Why AI Needs Math

Dev.to · AICDragon 🔢 Mathematical Foundations ⚡ AI Lesson 1mo ago

2026 Fields Medal Deep Dive: What Four Mathematicians' Papers Actually Say, and Why AI Needs Math

TL;DR: On July 23, the 2026 Fields Medals were awarded. Wang Hong and Deng Yu — both Peking...

Medium · Deep Learning 🔢 Mathematical Foundations 1mo ago

Stochastic Gradient Descent (SGD): The Optimization Algorithm Behind Modern Machine Learning

By Atharv Barage Continue reading on Medium »

Scepticism and Animal Faith (1923)

Medium · Data Science 🔢 Mathematical Foundations 1mo ago

Scepticism and Animal Faith (1923)

Naturalistic Foundations of Knowledge Continue reading on LICENTIA POETICA »

MD Anderson Spent at Least $62 Million on an AI It Never Tested Outside the Building

Dev.to · Alex @ Vibe Agent Making 🔢 Mathematical Foundations ⚡ AI Lesson 1mo ago

MD Anderson Spent at Least $62 Million on an AI It Never Tested Outside the Building

The improvement you measured is a covariance, not a cause In 2013, MD Anderson Cancer Center...

Probability & Distributions: The Complete Math-to-Code Guide for Machine Learning

Medium · Machine Learning 🔢 Mathematical Foundations 1mo ago

Probability & Distributions: The Complete Math-to-Code Guide for Machine Learning

How to reason about uncertainty — the math every model needs before it can guess. Continue reading on Medium »

Probability & Distributions: The Complete Math-to-Code Guide for Machine Learning

Medium · Data Science 🔢 Mathematical Foundations 1mo ago

Probability & Distributions: The Complete Math-to-Code Guide for Machine Learning

How to reason about uncertainty — the math every model needs before it can guess. Continue reading on Medium »

[2] From Maximum Likelihood Estimation(MLE) to Evidence Lower Bound(ELBO): Why Exact Posteriors…

Medium · Deep Learning 🔢 Mathematical Foundations 1mo ago

[2] From Maximum Likelihood Estimation(MLE) to Evidence Lower Bound(ELBO): Why Exact Posteriors…

Continue reading on Medium »

TOPOLOGICAL DYNAMICS ACROSS THREE COSMIC TIERS

Medium · Data Science 🔢 Mathematical Foundations 1mo ago

TOPOLOGICAL DYNAMICS ACROSS THREE COSMIC TIERS

Subquantum Energy-Information Fields & Relational Energy-Informational Networks Continue reading on Medium »

Fast and Simple PCA via Convex Optimization

Dev.to · Paperium 🔢 Mathematical Foundations 1mo ago

Fast and Simple PCA via Convex Optimization

Calculus Isn’t Scary. It’s Just Slopes That Won’t Sit Still.

Medium · Data Science 🔢 Mathematical Foundations ⚡ AI Lesson 1mo ago

Calculus Isn’t Scary. It’s Just Slopes That Won’t Sit Still.

I failed my first calculus quiz in the eleventh grade. Not “did okay but felt bad about it” failed. Actually failed. Red pen, a 4 out of… Continue reading on Me

Accelerating Minibatch Stochastic Gradient Descent using Stratified Sampling

Dev.to · Paperium 🔢 Mathematical Foundations 1mo ago

Accelerating Minibatch Stochastic Gradient Descent using Stratified Sampling

A Classic Maths Puzzle: How Many Cats Are Needed?

Medium · Data Science 🔢 Mathematical Foundations ⚡ AI Lesson 1mo ago

A Classic Maths Puzzle: How Many Cats Are Needed?

The answer might not be what you think Continue reading on Math Games »

So How Does The Koch Snowflake Have Finite Area?

Medium · Data Science 🔢 Mathematical Foundations ⚡ AI Lesson 1mo ago

So How Does The Koch Snowflake Have Finite Area?

Following part one of the series, we will now look at the area of a Koch snowflake starting with an equilateral triangle with a side… Continue reading on Math P

The Truth About 6 ÷ 2(1+2) and PEMDAS

Medium · Data Science 🔢 Mathematical Foundations ⚡ AI Lesson 1mo ago

The Truth About 6 ÷ 2(1+2) and PEMDAS

Why the internet keeps getting it wrong. Continue reading on ThinkArt »

Why This Beautiful Number Pattern Stops at Squares

Medium · Programming 🔢 Mathematical Foundations ⚡ AI Lesson 1mo ago

Why This Beautiful Number Pattern Stops at Squares

A surprising journey from consecutive integers to Fermat’s Last Theorem. Continue reading on ThinkArt »

How Does The Koch Snowflake Have Infinite Perimeter?

Medium · Data Science 🔢 Mathematical Foundations ⚡ AI Lesson 1mo ago

How Does The Koch Snowflake Have Infinite Perimeter?

What is the perimeter of the above Koch snowflake starting from an equilateral triangle with side length 1? Continue reading on Math Games »

It’s The Year 1926. How would you calculate 99¹⁰⁰?

Medium · Data Science 🔢 Mathematical Foundations ⚡ AI Lesson 1mo ago

It’s The Year 1926. How would you calculate 99¹⁰⁰?

The Solution Is Hidden in a Tool We Rarely Use Today Continue reading on ThinkArt »

Are You Smart Enough To Get Into Cambridge University?

Medium · Data Science 🔢 Mathematical Foundations 1mo ago

Are You Smart Enough To Get Into Cambridge University?

Continue reading on Math Mogger »

Beyond the Visible Universe: Are Hidden Dimensions Waiting to Be Discovered?

Medium · Data Science 🔢 Mathematical Foundations 2mo ago

Beyond the Visible Universe: Are Hidden Dimensions Waiting to Be Discovered?

Continue reading on Medium »

Hacker News (AI) 🔢 Mathematical Foundations 2mo ago

GPT-5.6 used a prompt to close a 30-year gap in convex optimization

Part 3: Engineering Deep Dive

Medium · Data Science 🔢 Mathematical Foundations 2mo ago

Part 3: Engineering Deep Dive

part 2 : https://medium.com/@ravikumar_67667/part-2-from-words-to-mathematics-1ea330e7467b?sharedUserId=ravikumar_67667 Continue reading on Medium »

Find ANY Square Root Using Heron’s Formula

Medium · Programming 🔢 Mathematical Foundations ⚡ AI Lesson 2mo ago

Find ANY Square Root Using Heron’s Formula

The Ancient Trick That Finds Any Square Root Almost Instantly Continue reading on ThinkArt »

SAT Conditional Probability Photo Solver

Medium · AI 🔢 Mathematical Foundations ⚡ AI Lesson 2mo ago

SAT Conditional Probability Photo Solver

Conditional probability is one of those SAT math topics where the arithmetic is usually simple, but the wording can change everything. A… Continue reading on Me

Ten Metres That Should Mean Nothing

Hackernoon 🔢 Mathematical Foundations ⚡ AI Lesson 2mo ago

Ten Metres That Should Mean Nothing

Adding ten metres to a rope around Earth raises it by 1.59 metres. The puzzle opens a deeper inquiry into scale, relations and reality.