The Mathematical Roots of AI — From Boole to Transformers

From Boole's 1854 logical algebra, to the 1958 Perceptron, to 1986 backpropagation, to 2017 Transformers, to today's GPT — 170 years of mathematics that turned the dream of machines that learn into reality.

About 25 min·6 nodes

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STEP 1 · Mathematician1854Cork· Publication

George Boole

A largely self-educated teacher and mathematician without a university degree. His 1847 and 1854 works developed an algebraic treatment of logic. Shannon later applied Boolean algebra to the analysis and simplification of relay switching circuits; the historical relation is an adaptation, not a literal identity.

↓Same year

STEP 2 · Concept1854Cork· Publication

Boolean Algebra

An algebra of true/false relations, later connected by Shannon to switching-circuit design and now central to digital logic.

↓94 years later

STEP 3 · Concept1948Bell Labs· Discovery

Information Entropy

A bit-valued measure of average uncertainty in a probability distribution. Building on Nyquist and Hartley, Shannon’s 1948 theory treats source-coding and noisy-channel limits under distinct assumptions; it does not directly measure semantic depth or one file’s compressed size.

↓41 years later

STEP 4 · Concept~1989No location

Universal Approximation Theorem

A neural network with one hidden layer can approximate any continuous function.

↓Next step

STEP 5 · ConceptNo location

Optimization

The mathematics of minimizing or maximizing a stated objective subject to constraints. An optimum exists only after “better” and “feasible” are specified; local versus global, exact versus approximate, computable versus socially desirable remain distinct.

↓Next step

STEP 6 · River2017Lincoln· Journey start

The River of AI and Machine Learning

From Boole to ChatGPT — 170 years toward machines that learn.

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