# World of Mathematics

> Scholarly English-language reference site covering the six core domains of mathematics — algebra, geometry, analysis, number theory, probability, and applied mathematics — together with profiles of mathematicians, dedicated pages for famous formulas, open problems, and the history of the discipline. Sister site to world-of-physics.com.

World of Mathematics is a static, GDPR-compliant content site. All page content is original prose oriented toward a reader with upper-undergraduate to graduate-level background. Mathematical notation is rendered server-side at build time using KaTeX; the LaTeX source is embedded as `$…$` inline and `$$…$$` display, and is readable directly in the page HTML inside KaTeX's generated markup.

Content is copyrighted unless otherwise noted. Metadata pulled from third-party providers (arXiv, zbMATH, Semantic Scholar, OpenAlex, Crossref) belongs to those providers. There are no stable article DOIs; please cite by URL and access date.

## Mathematical fields

- [Algebra](https://world-of-mathematics.com/algebra/): groups, rings, linear algebra, abstract algebra
- [Geometry](https://world-of-mathematics.com/geometry/): Euclidean, non-Euclidean, topology, fractals
- [Analysis](https://world-of-mathematics.com/analysis/): calculus, real and complex analysis, measure theory
- [Number theory](https://world-of-mathematics.com/number-theory/): primes, Diophantine equations, modular arithmetic
- [Probability](https://world-of-mathematics.com/probability/): probability theory, statistics, stochastic processes
- [Applied mathematics](https://world-of-mathematics.com/applied/): mathematical modelling, optimization, algorithms

## Reference content

- [Formulas](https://world-of-mathematics.com/formulas/): classical and modern mathematical formulas with derivations, history, applications
- [People](https://world-of-mathematics.com/people/): profiles of classical and modern mathematicians
- [Unsolved problems](https://world-of-mathematics.com/unsolved-problems/): Millennium Prize Problems and other major open conjectures
- [History](https://world-of-mathematics.com/history/): the development of mathematics by era
- [Blog](https://world-of-mathematics.com/blog/): editorial articles on foundations, current research, expository topics
- [Research Hub](https://world-of-mathematics.com/research/): aggregated view of six math domains, backed by public APIs

## Interactive content

- [Interactive hub](https://world-of-mathematics.com/interactive/): in-browser mathematical visualizations
- [Euler's identity explorer](https://world-of-mathematics.com/formulas/eulers-identity/): unit-circle slider for e^(iθ)
- [Fourier synthesizer](https://world-of-mathematics.com/formulas/fourier-transform/): build a waveform from harmonic partials
- [Pythagorean triangle](https://world-of-mathematics.com/formulas/pythagorean-theorem/): draggable right triangle with live area squares
- [Gaussian distribution](https://world-of-mathematics.com/formulas/gaussian-distribution/): adjust μ and σ², view density and CDF
- [Quadratic explorer](https://world-of-mathematics.com/formulas/quadratic-formula/): parabola with live roots and discriminant
- [Collatz trajectory plot](https://world-of-mathematics.com/unsolved-problems/collatz-conjecture/): 3n+1 iteration for any starting integer
- [Sieve of Eratosthenes](https://world-of-mathematics.com/number-theory/primes/): animated prime sieve

## Data sources for the Research Hub

- [arXiv API](https://export.arxiv.org/api/query): preprint metadata and abstracts
- [zbMATH Open API](https://api.zbmath.org/): mathematical literature reviews
- [Semantic Scholar Academic Graph](https://api.semanticscholar.org/): paper metadata and citations
- [OpenAlex](https://api.openalex.org/): open scholarly metadata
- [Crossref REST](https://api.crossref.org/): DOI registry metadata
- [CORE](https://core.ac.uk/documentation/api/): open-access repository aggregation
- [DOAJ](https://doaj.org/api/): directory of open-access journals

## Site infrastructure

- [Sitemap](https://world-of-mathematics.com/sitemap.xml): full URL index, refreshed at every build
- [RSS feed](https://world-of-mathematics.com/rss.xml): latest blog and formula articles
- [Robots policy](https://world-of-mathematics.com/robots.txt): crawler directives
- [Contact](https://world-of-mathematics.com/contact/): corrections and suggestions

## Optional

- [Sister site: World of Physics](https://world-of-physics.com): companion reference for physics
- [About the project](https://world-of-mathematics.com/about/): editorial mission and scope
- [Imprint](https://world-of-mathematics.com/imprint/): legal disclosures
- [Privacy](https://world-of-mathematics.com/privacy/): data handling policy