How Mathematics Evolved from Numbers to the Science of Structure

This article traces the historical transformation of mathematics—from ancient empirical methods through medieval axiomatization and the rise of calculus to modern structural and categorical approaches—highlighting the shift from numerical computation to a science of structures, with emphasis on geometry, group theory, and isomorphism.

group theoryhistoryisomorphism

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How Mathematics Evolved from Numbers to the Science of Structure

Liangxu Linux

Feb 25, 2024 · Fundamentals

Unveiling Liu Qian’s Final Magic Trick: The Hidden Josephus Puzzle

The article explains Liu Qian’s last magic performance by modeling the card shuffling as a periodic ABCD pattern, interpreting it through group theory, and ultimately solving the underlying Josephus problem with a binary‑based formula that predicts the surviving card.

Josephus problembinary representationcombinatorics

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Unveiling Liu Qian’s Final Magic Trick: The Hidden Josephus Puzzle

DataFunTalk

Jan 7, 2022 · Artificial Intelligence

Group-Theoretic Self-Supervised Representation Learning (Lecture)

On Jan 7, 2024, BIT’s “Hundred Lectures” will feature Assistant Professor Hanwang Zhang presenting his group‑theoretic self‑supervised representation learning work, including the IP‑IRM method that iteratively partitions data and applies invariant risk minimization to achieve fully disentangled visual features, with the session streamed via Tencent Meeting.

AIgroup theorymachine learning

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Group-Theoretic Self-Supervised Representation Learning (Lecture)