Mathematics

A mathematical claim needs stated assumptions and a reason that works beyond one example.

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Introduction to Mathematics

What makes a mathematical explanation convincing?

Mathematics3h · IntroductionBeginner

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Calculus

How can we reason about continuous change?

Mathematics22h · TopicBeginner

Linear algebra

What do matrices let us see?

Mathematics22h · TopicBeginner

Probability & statistics

How do we reason under uncertainty?

Mathematics22h · TopicBeginner

Statistics foundations

What can a small dataset tell me, and what can it not?

Mathematics22h · TopicBeginner

Functions and models

How does a function represent a relationship?

Mathematics14h · TopicSome background

Proof and counterexample

How can one example disprove a universal claim?

Mathematics14h · TopicSome background

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Karl Friston

Neuroscience and mathematical frameworks for inference, perception and action. Begin with a small probabilistic model before tackling the formal free-energy principle.

Emmy Noether

Mathematical work on algebra and the relation between continuous symmetries and conservation laws. Begin with a precise statement and its assumptions.

Ada Lovelace

Notes on the Analytical Engine, symbolic operations and a worked procedure. Read her contribution alongside the translated text and Babbage’s machine design.

Claude Shannon

A mathematical account of communication under uncertainty. Separate the quantity of information in a model from the meaning or truth of a message.

Abdus Salam

Theoretical physics and electroweak unification. Read the formal framework alongside the predictions and the experiments that can constrain it.

Connect this subject

When does a pattern become an explanation?

Compare symmetry, information and models across mathematics, physics and living systems. Similar vocabulary does not establish identical mechanisms.