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Mathematics Exploration Library

mathematical exploration

Mathematics Exploration Library

A personal mathematical garden: explore why concepts exist, what they reveal, and how areas connect. This is not an exam checklist or a textbook summary. Ordinary Markdown is the durable asset; Obsidian is a convenient editor and navigator.

Start Here

Open this folder as your Obsidian vault and begin with Home. Exploration Map organizes ideas; 01 Monthly Explorations records the chronological journey. Week labels are themes, not deadlines. Copy a session's learning prompt into ChatGPT or another learning dialogue; write your own discoveries in the empty sections.

Folders

  • 00 Inbox/: quick questions and unfinished thoughts.
  • 01 Monthly Explorations/: months, weekly overviews and session notes.
  • 02 Concepts/: durable standalone notes in Algebra, Analysis, Topology, Geometry, Probability and Other.
  • 03 Connections/: relationships between ideas and areas.
  • 04 Problems and Experiments/: proofs, calculations, simulations and visual investigations.
  • 05 Mathematical Curiosities/: small observations and surprising facts.
  • 06 People and History/: the people and problems behind ideas.
  • 07 Reading/: sources and reading notes.
  • Templates/: plain Markdown starting points; no plugin required.

Each numbered folder has an ordinary index note, so links such as [[00 Inbox]] work without folder-link plugins. Existing Welcome.md and .obsidian/ settings are preserved. The published starter notes in the parent folder have not been moved or copied into this vault.

Add Notes in Seconds

  • Exploration: copy Exploration Session into a weekly folder, name it NN - Topic.md, and fill in area, month, week and session. Start with a question, a short motivation and a learning prompt. Keep status: unread until you decide to change it.
  • Concept: copy Concept Note into the relevant area, rename it after the concept, and link it to the exploration where it arose. Do not duplicate the explanation in both places.
  • Curiosity: copy Curiosity into 05 Mathematical Curiosities/, give it a short question-like name, and write as little as the observation needs.
  • Connection: copy Connection into 03 Connections/, name the two ideas, and link the notes involved. Record the mechanism, not just that two topics are related.
  • Experiment: copy Mathematical Experiment into 04 Problems and Experiments/; make a prediction before calculating, proving or simulating.

For Month 02, create a sibling folder under 01 Monthly Explorations/. Copy the empty Month Overview and Week Overview templates, then add sessions as needed. Link its overview from the monthly index and update Home manually; no code or settings changes are needed.

Use descriptive concept names and two-digit session prefixes. Repeated names such as Overview.md are safe when links use vault-relative paths with readable aliases, for example:

[[01 Monthly Explorations/Month 01 - Modern Mathematics/Week 02 - Topology/08 - Homotopy|Homotopy]]

Use short [[Concept Name]] links when the name is unique. Link concepts when they exist; do not create empty placeholders just to enlarge the graph. Move useful landmarks into Exploration Map over time.

Session metadata is consistently type, area, month, week, session, status. The initial status is unread; changing it to exploring or revisited is optional. Concept notes start growing. Metadata is a convenience, not a prerequisite for an inbox fragment.

Use $...$ for inline mathematics and $$...$$ for display mathematics. Keep personal notes, sources and attachments as ordinary files. No Dataview, CSS, database or community plugin is needed. Obsidian's built-in Templates feature is optional; manual file copying works just as well.

A Future Website

Markdown, YAML, LaTeX and simple wikilinks remain separate from presentation. A website renderer can map exploration/concept/curiosity types to its views without changing the knowledge itself.

The existing Almost Everywhere website manually syncs from the parent Desktop folder. It publishes only notes explicitly marked status: published with a stable unique slug, and excludes publish: false. The initial exploration library is published. Sessions retain their study state in learning_status, while status: published controls website visibility. New notes remain local unless you explicitly mark them published and give them a stable unique slug. Publishing to Git retains committed material in Git history.

Obsidian Sync, if used, synchronizes this local vault independently. Website publication remains a separate manual choice.