How statistical moments connect the mean, the variance, and higher powers of a distribution

The post Seizing the Moment: The Hidden Silhouette of Data appeared first on Towards Data Science.

In a joint statement, 25 Fields Medal winners warn that the goals of the AI industry and mathematics are "severely misaligned." They argue that mass-producing solved problems with AI undermines the discipline's true goal: understanding. The mathematicians see this as a symptom of a broader threat to intellectual work.

The article Leading mathematicians fear AI is making their field dumber, and warn the rest of us is next appeared first on The Decoder.

Clarifying the math behind Anthropic’s representation workspace

The post Demystifying Anthropic's J-Space: A Mathematical Primer appeared first on Towards Data Science.

Canadian mathematician Jacob Tsimerman, a fresh Fields Medal recipient, has announced the founding of the Mathematical A.I. Safety Institute (MAISI).

The article The Mathematical AI Safety Institute wants to prove AI is safe the way cryptographers prove codes are unbreakable appeared first on The Decoder.

OpenAI's GPT-6 Astra tops the ErdosBench for open math problems, even though chief scientist Jakub Pachocki says math was deliberately not a priority. Instead, OpenAI is pouring resources into recursive self-improvement and alignment research. That supports the theory of an increasingly "spiky" AI development path, with extreme strength in select domains rather than broad progress, at least as long as AI can't improve itself and still needs targeted optimization with human-generated data.

The article GPT-6 Astra gives mathematicians a breather, and OpenAI says that's by design appeared first on The Decoder.

Statistical thinking beyond formulas

The post 10 Statistical Traps We Often Overlook appeared first on Towards Data Science.

The fight over an AI-generated proof of a millennium problem is heating up. Mathematician Tristan Buckmaster accuses OpenAI of academic fraud, CEO Sam Altman rejects the allegations. Terence Tao warns that cases like this could "reverse centuries of tradition in open science."

The article OpenAI's millennium proof dispute raises the question of whether researchers can trust AI labs appeared first on The Decoder.

Mathematician Tristan Buckmaster says an OpenAI researcher pressured him after information about his AI-assisted progress on the Navier-Stokes equations allegedly reached the company. The researcher tried to remove his co-author because he works at Anthropic and threatened Buckmaster when he refused, according to Buckmaster's account. OpenAI then claimed its own breakthrough using the same unusual solution path. Buckmaster had uploaded all his drafts to Codex. OpenAI told him the model didn't look up user data, but when he asked about training, he says he got no answer. OpenAI denies the allegations.

The article OpenAI researcher allegedly pressured mathematician to drop Anthropic co-author from math breakthrough paper appeared first on The Decoder.

We use the equation all the time. But where did it actually come from?

The post The Sigmoid Function: From 'e' to Neural Networks appeared first on Towards Data Science.

A hands-on guide to fine-tuning LLMs for the real world

The post How to Fine-Tune an LLM: An End-to-End Guide appeared first on Towards Data Science.

In a new essay, Terence Tao warns that AI could push mathematics into a crisis on par with the foundational upheaval around 1900. What's being tested this time isn't mathematical truth but the values of the field: what counts as a contribution, what gets rewarded, and who did the work. His rule of thumb: a proof that no human can explain should be considered incomplete.

The article Terence Tao says AI could trigger math's biggest crisis since Gödel appeared first on The Decoder.

Two open problems, exact-arithmetic checking and a proof assistant, over a single weekend.

The post Mathematical Experiments Are Becoming Abundant Through Human-Machine Teaming appeared first on Towards Data Science.

A primer about Semi-Supervised Learning, the approaches taken with different algorithms and the limitations of using unlabelled data.

The post Introduction to Semi-Supervised Learning appeared first on Towards Data Science.

Research-backed cues to detect LLM-generated text along with the mathematical intuition as to 'why'

The post Is This Slop? Detecting AI-Generated Content Without a Model appeared first on Towards Data Science.

The full conjecture is stated over abstract fields, but the counterexample is a concrete 3D function that we can explain and visualize using familiar geometric ideas and a little algebra.

The post A Simplified View of the Jacobian Conjecture appeared first on Towards Data Science.

Using mathematical optimization to solve a pickup-and-delivery problem with time windows.

The post “Los Movimientos”: The Routing Problem That Nearly Broke My Spirit appeared first on Towards Data Science.

The mean keeps making its usefulness felt in all sorts of situations, often in truly non-obvious ways

The post The Most Beautiful Statistic: The History and the Science of the Humble Mean appeared first on Towards Data Science.