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Foundations of AI

What artificial intelligence is, where it came from, and the ideas every other area builds on.

Foundations of AI is one of the core areas in the AI University map of AI. Explore the diagram, then dive into each topic — every subtopic grows into its own deep-dive over time.

flowchart LR
  AI([Artificial Intelligence]):::a --> ML[Machine Learning]:::b --> DL[Deep Learning]:::c --> FM[Foundation Models]:::d
  classDef a fill:#4f46e5,color:#fff,stroke:#3730a3;
  classDef b fill:#6366f1,color:#fff,stroke:#4338ca;
  classDef c fill:#818cf8,color:#111,stroke:#4338ca;
  classDef d fill:#c7d2fe,color:#111,stroke:#6366f1;
timeline
  title A brief history of AI
  1950 : Turing test
  1956 : Dartmouth workshop coins 'AI'
  1980s : Expert systems boom
  1997 : Deep Blue beats Kasparov
  2012 : AlexNet — deep learning takes off
  2017 : Transformers ('Attention is All You Need')
  2022 : Generative AI goes mainstream

Key topics

  • What is AI

    The study and engineering of systems that perform tasks we associate with intelligence — perception, reasoning, learning, and action.

  • AI vs ML vs Deep Learning

    AI is the broad goal; machine learning is the dominant approach (learning from data); deep learning is ML with many-layered neural networks.

  • History of AI

    From the 1956 Dartmouth workshop through symbolic AI, expert systems, the AI winters, the deep-learning boom, to today's foundation models.

  • Intelligence & agency

    Agents perceive an environment and act to achieve goals; rationality, autonomy, and the debate over what 'understanding' means.

  • AGI, ASI & the Turing test

    Narrow AI (today) vs artificial general intelligence vs superintelligence, and how we (imperfectly) measure progress.

  • Math foundations

    Linear algebra, probability & statistics, calculus, optimization, and information theory — the language models are written in.

The three waves of AI

AI has reinvented itself roughly three times. Each wave kept the goal — build systems that act intelligently — but changed the method.

Wave Era Core idea Limitation that ended it
Symbolic AI 1950s–1980s Hand-coded rules and logic ("good old-fashioned AI") Brittle; couldn't handle messy, real-world perception
Statistical ML 1990s–2010s Learn patterns from data instead of coding rules Needed hand-crafted features; plateaued on raw signals
Deep learning & foundation models 2012–today Learn the features and the task from raw data at scale Compute-hungry; opaque; still being worked out

The through-line is less hand-engineering, more learning. Symbolic AI coded the answer; classical ML coded the features and learned the answer; deep learning learns both. Foundation models go one step further — learn general capabilities once, then adapt to thousands of tasks.

The maths you actually need

You do not need a PhD to understand modern AI, but four areas of maths keep showing up:

  • Linear algebra — vectors and matrices are how data and model weights are represented. "Embeddings," "attention," and "layers" are all matrix operations.
  • Probability & statistics — models output distributions, not certainties. Loss functions, sampling, and evaluation are statistical.
  • Calculus — training works by following gradients (derivatives) downhill. Backpropagation is the chain rule at scale.
  • Optimization — the actual act of learning: adjusting millions of parameters to minimize a loss.

Start here

If you learn one thing first, make it vectors and dot products — the dot product of two embeddings measuring similarity is the single most reused idea in the whole field.

Machine Learning · Knowledge & Reasoning · AI Safety, Alignment & Ethics

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