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Mathematics

For everyone

The field concerned with numbers, shapes, structures and the relations between them. In mathematics a statement is accepted not by experiment but by being logically derived from accepted axioms, that is, by proof. Statements without a proof are called conjectures.

For specialists

Modern mathematics is usually founded on Zermelo–Fraenkel set theory with the axiom of choice (ZFC) in first-order logic. A theorem's validity is relative to the chosen axiom system. Gödel's incompleteness theorems show that a sufficiently strong consistent system cannot prove its own consistency. Formal verification with proof assistants such as Lean and Coq/Rocq has become increasingly common in recent years.

Claims

The source and nature of mathematical knowledge (discovered or invented?) is debated in philosophy. There are Platonist, formalist, intuitionist and constructivist views.^[1]

Connections

Parent

Humanity

Sub-branches

Babylonian mathematics and Plimpton 322 Euclid's Elements Zero as a number Al-Khwārizmī and algebra Calculus Bayes' theorem and reasoning with probability The Riemann hypothesis (open)Cantor and the sizes of infinity The p-value and the statistical significance debate Gödel's incompleteness theorems The four colour theorem and computer-assisted proof Fermat's Last Theorem Proof of the Poincaré conjecture The fifth Busy Beaver number BB(5)Proof of the geometric Langlands conjecture Proof of the Kakeya conjecture in three dimensions

Philosophy

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New research in this branch

Notable in peer-reviewed journals

Let's Take the Con out of Econometrics — Edward E. Leamer · 2026-10-07 · Journal of Business Cycle Research
The moduli space of multi-scale differentials — Matt Bainbridge, Dawei Chen, Quentin Gendron et al. · 2026-10-20 · Communications of the American Mathematical Society
Free-Monodromic Mixed Tilting Sheaves on Flag Varieties — Pramod N. Achar, Shotaro Makisumi, Simon Riche et al. · 2026-10-16 · Memoirs of the American Mathematical Society
Skeins on branes — Tobias Ekholm, Vivek Shende · 2026-09-08 · Publications mathématiques de l IHÉS

Preprints (may not be peer-reviewed yet)

JT gravity as a conformal scaling limit of random flat combinatorial disks — Morris Ang · 2026-10-29 · arXiv
Multicomplexes in Action: Strong Formality of Compact Hyperkähler Manifolds — Antonio Pio Contrò · 2026-10-29 · arXiv
Central Limit Theorems and Network-Free Inference for Heterogeneous Spatial Autoregressions on Sparse Graphons — Wei Li, Robert Lunde · 2026-10-29 · arXiv
The Number of Tropical Order Types and Coherent Matching Fields — Xavier Allamigeon, Yiyuan Chen, Stéphane Gaubert et al. · 2026-10-29 · arXiv

New papers →

Sources

EncyclopediaHorsten, L.Philosophy of Mathematics. Stanford Encyclopedia of Philosophyplato.stanford.edu archive

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Cite this page

APA

Athena contributors. (2026). Mathematics. Athena: The tree of human knowledge. Retrieved November 1, 2026, from https://latifkedi.github.io/athena/en/d/matematik/

BibTeX

@misc{athena_matematik,
  title        = {Mathematics},
  author       = {{Athena contributors}},
  year         = {2026},
  howpublished = {\url{https://latifkedi.github.io/athena/en/d/matematik/}},
  note         = {Athena: The tree of human knowledge. Accessed: 2026-11-01}
}

Added: September 27, 2026 · Last changed: September 27, 2026 · Page history

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