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A likeness-informed AI editorial scene of Jordan sorting permutations, stacking matrix blocks, and testing the inside and outside of a closed curve
AI editorial interpretation

Turning transformations into blocks and an obvious picture into a proof problem

The face uses a surviving photograph. Substitutions, canonical form, and the closed curve share one editorial room but remain distinct projects. Jordan's original curve-theorem proof is not treated as the final later standard, nor are all normal forms assigned to one person.

MathVoyage editorial direction · OpenAI image generation · historical photograph identity reference · pre-1889 skyline and generated-text correction · 2026-08-07

Remember the mind, not only the dates

Camille Jordan

AD 1838 - AD 1922
Thinking ground · Paris
Born · Lyon
Nineteenth-Century MathematicsStructure organizing substitutionsBlocks revealing missing eigenvectorsInside and outside a closed curve

The idea to carry forward

Even an “obvious” inside and outside in a picture require definition and proof.

Enter through one scene

AD 1870

Traité des substitutions — organizing group theory

The treatise assembled post-Galois research on permutation groups and algebraic equations into a large system. It became an important vehicle for spreading group theory through research and teaching.

Questions this person helps open

Concept ports to revisit, not another achievement list

These are reverse projections of existing editorial routes, not claims of direct influence or sole invention.

No concept port has yet been reviewed for this person.

Browse every concept route

PROFILE 02 · DEEP VOYAGE

How Camille Jordan’s ideas moved

Instead of memorizing more dates, follow the world that shaped this mind, the scenes that changed its direction, and the questions carried onward.

CHAPTER 01 · PERSON AND PERIOD

What questions surrounded Camille Jordan?

Before the finished achievement, read what this person treated as a problem and where the surviving evidence reaches its limit.

About 1 min read

A mathematician who moved between pictures that look obvious and algebraic forms made computable. Jordan’s name remains attached to the curve theorem, canonical form, measure, and Jordan–Hölder theorem. His 1870 Treatise on Substitutions and Algebraic Equations organized the theory of permutation groups and equations developed after Galois and greatly helped group theory circulate. Calling it the solitary first textbook made directly from Galois’s scattered notes would erase the intervening research network. The attribution and formulation of Jordan form also involve earlier and later work. In 1887 he stated that a simple closed plane curve separates an inside from an outside, but the rigor of his argument was disputed; Veblen supplied a new proof in 1905. The story shows why an obvious-looking claim may still demand difficult definitions and proof.

CHAPTER 02 · TURNING SCENES

3 turning scenes

Follow the moments when the idea moved one step further. Every scene continues through an evidenced place or an honestly labelled time context.

  1. Scene 1 / 3

    AD 1870Paris

    Traité des substitutions — organizing group theory

    The treatise assembled post-Galois research on permutation groups and algebraic equations into a large system. It became an important vehicle for spreading group theory through research and teaching.

    Continue from this scene's place

  2. Scene 2 / 3

    AD 1875Paris· Geographic context

    Jordan form — reading missing eigenvectors through blocks

    Over an algebraically closed field, a square matrix can be represented in blocks built from generalized eigenvectors. Uniqueness is only up to block order, and numerical work must also account for instability.

    Explore this scene's geographic context

  3. Scene 3 / 3

    AD 1887Paris· Geographic context

    Jordan curve theorem — turning the obvious into a proof problem

    The complement of a simple closed plane curve has two connected components, an inside and an outside. Debate over Jordan’s argument was followed by Veblen’s new proof in 1905.

    Explore this scene's geographic context

THOUGHT EXPERIMENT · NOT A FACT CLAIM

Erase Camille Jordan from the map

This is a thought experiment about influence, not a verified historical fact.

Beginners draw a loop and test whether a point lies inside or outside. Intermediate learners simplify matrices into eigenvalue blocks. Advanced learners study the exact hypotheses of the Jordan curve theorem and generalized eigenvectors. Experts compare Jordan’s argument with Veblen’s later proof and examine the layered attribution of canonical form.

STANDING ON SHOULDERS · EVIDENCED CONNECTIONS

What arrived here, and what moved onward?

We do not draw a line merely because two people shared an era. Only connections traced through works, problems, or teaching appear with an explanation and evidence.

Open the full network around Camille Jordan
Camille Jordan

Camille Jordan

Nineteenth-Century Mathematics

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What this person received

Évariste Galois
Influenced byÉvariste Galois

Turning posthumous ideas into modern group theory

Jordan organized post-Galois work on permutation groups and equations in his large 1870 treatise, greatly helping groups circulate as independent objects of study.

Evidence for this connection

Beyond MathVoyage

Curated sources and problems. Bring one discovery back from OEIS, Project Euler, MathOverflow, or arXiv.