This is the most famous version, created by physicist and YouTuber Dominic Walliman (Domain of Science). It is a colorful, high-level infographic that summarizes all of mathematics from its foundations to modern applied branches.
Key Features: Divided into Pure Mathematics (Numbers, Structures, Spaces, Change) and Applied Mathematics (Physics, Computing, Statistics). Where to find it:
High-Res Image/PDF: Often hosted on platforms like the Internet Archive or available as a high-resolution download via Flickr.
Educational Use: Walliman provides versions for non-commercial educational use through his DFTBA store and social platforms. 2. Quanta Magazine’s Interactive Map
Quanta Magazine offers a more academic and research-focused Interactive Map of Mathematics.
Key Features: It focuses on three core pillars—Numbers, Shapes, and Change—and shows how they branch out into modern research areas like the Riemann Hypothesis and Einstein’s Equations.
PDF Status: This is primarily an interactive web experience, but it is often used as a visual reference for how abstract concepts interweave. Core Branches Included in These Maps
Most "Map of Mathematics" PDFs are structured into these standard categories: 📐 Pure Mathematics
Foundations: Mathematical logic, Set Theory, and Category Theory.
Numbers: From natural numbers and integers to complex and octonion numbers. map of mathematics pdf
Structures: Algebra (Linear and Abstract), Number Theory, and Combinatorics. Spaces: Geometry, Topology, and Trigonometry.
Change: Calculus (Integrals and Differentials) and Dynamical Systems. 💻 Applied Mathematics
Physics: Mathematical physics and the "Theories of Everything".
Computer Science: Complexity Theory, Cryptography, and Machine Learning.
Data & Decisions: Probability, Statistics, Game Theory, and Optimization. Academic PDF Alternatives
If you are looking for a more text-heavy or formal document rather than an infographic, consider these resources: Go to product viewer dialog for this item.
Mathematics Poster Set - 6 Printable STEM Wall Art Designs | Digital Download for Classroom or Homeschool
Map of Mathematics is a highly acclaimed visual tool and conceptual framework designed to help learners and enthusiasts navigate the vast, often intimidating expanse of mathematical fields. While there are several versions, the most prominent was popularized by physicist Dominic Walliman Overview and Purpose The map serves as a holistic visual guide
that categorizes the entire field of mathematics into two primary domains: Pure Mathematics (the study of math for its own sake) and Applied Mathematics (math used to solve real-world problems). Pure Mathematics This is the most famous version, created by
: Explores numbers, structures (algebra), space (geometry/topology), and change (calculus/analysis). Applied Mathematics
: Highlights connections to physics, chemistry, biology, computer science, and engineering. Foundations
: Digs into the philosophical and logical roots, such as set theory and Gödel's incompleteness theorems. Educational Value
Reviews from students and educators often highlight its utility in transforming abstract concepts into accessible formats. Contextual Learning
: It helps students see "the big picture," showing how high school algebra connects to advanced topics like group theory or cryptography. Reduced Frustration
: By acting as a roadmap, it clarifies prerequisite knowledge, which can reduce learner anxiety when encountering complex new topics. Visual Memorization
: The use of infographics and diagrams aids in long-term retention and recall compared to traditional text-heavy textbooks. Critical Perspectives
While widely praised for its breadth, some advanced users have noted its limitations: Simplification : Critics on platforms like
argue that representing math in a 2D plane is inherently biased and incomplete, as it cannot capture every nuanced connection between fields. Students: to help them navigate the mathematical curriculum
: Some undergraduate-level jargon may still be difficult for complete beginners to parse without the accompanying explanatory video. Where to Access The Map of Mathematics
A Comprehensive Map of Mathematics: A Visual Guide to Mathematical Disciplines
Abstract
Mathematics is a vast and diverse field, encompassing various branches, subfields, and disciplines. The sheer breadth of mathematical knowledge can be overwhelming, making it challenging for students, researchers, and professionals to navigate the landscape of mathematical concepts. This paper presents a comprehensive map of mathematics, providing a visual representation of the relationships between different mathematical disciplines. The map is designed to facilitate exploration, discovery, and understanding of the mathematical universe.
Introduction
The map of mathematics is a graphical representation of the various branches of mathematics, showcasing their interconnections and relationships. The map is not exhaustive, but it covers the main areas of mathematics, including pure mathematics, applied mathematics, and interdisciplinary fields. The map is intended to serve as a guide for:
The Map
The map of mathematics can be broadly categorized into several main areas:
A complete PDF should include:
The “Map of Mathematics” is a conceptual and visual representation of the vast, interconnected landscape of mathematical disciplines. Originating from popular online videos (notably by Dominic Walliman), the map has become an essential pedagogical tool for students, educators, and enthusiasts. A PDF version of this map serves as a portable, high-resolution reference that organizes the entire field of mathematics into logical territories, showing how abstract concepts connect to real-world applications.
This report explores the structure, utility, acquisition, and study strategies for using a Map of Mathematics PDF.