Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") includes the study of such topics as quantity (number theory), structure (algebra), space (geometry), and change (mathematical analysis). It has no generally accepted definition.
Mathematics is essential in many fields, including natural science, engineering, medicine, finance, and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics (mathematics for its own sake) without having any application in mind, but practical applications for what began as pure mathematics are often discovered later.

• Project Euler
• Terence Tao: Updates on my research and expository papers, discussion of open problems, and other maths-related topics.

• Math Is Fun
  • We offer mathematics in an enjoyable and easy-to-learn manner, because we believe that mathematics is fun.
  • The site aims to cover the full Kindergarten to Year 12 curriculum.
• 3blue1brown, by Grant Sanderson, is some combination of math and entertainment, depending on your disposition. The goal is for explanations to be driven by animations and for difficult problems to be made simple with changes in perspective.
• Interactive Mathematics Learn math while you play with it
• At Art of Problem Solving, we are training the intellectual leaders of the next generation. We help students develop the problem-solving skills they need to confidently tackle challenging problems—and not only in mathematics.

• BYRNE’S EUCLID THE FIRST SIX BOOKS OF THE ELEMENTS OF EUCLID WITH COLOURED DIAGRAMS AND SYMBOLS
• Isomorphism -- Mathematics of Programming: This book introduces the mathematics behind computer programming.

• mathworld
• brilliant Build quantitative skills in math, science, and computer science with fun and challenging interactive explorations.
• mathpuzzle
• random.org True random number service
• mathvault - Recommended Math Websites

• Calculus Explained with pics and gifs

• Calculus Made Easy is a book on calculus originally published in 1910 by Silvanus P. Thompson, considered a classic and elegant introduction to the subject.

• Introduction to Linear Algebra for Applied Machine Learning with Python

• Free Linear Algebra textbook is a text for a first US undergraduate Linear Algebra course. You can use it as a main text, as a supplement, or for independent study.
• Introduction to Linear Algebra, free online textbook at Georgia Tech

• Statistics Done Wrong is a guide to the most popular statistical errors and slip-ups committed by scientists every day, in the lab and in peer-reviewed journals. Many of the errors are prevalent in vast swaths of the published literature, casting doubt on the findings of thousands of papers. Statistics Done Wrong assumes no prior knowledge of statistics, so you can read it before your first statistics course or after thirty years of scientific practice.
• Introduction to Probability, Statistics, and Random Processes

• Elementary Number Theory
• PARI/GP is a widely used computer algebra system designed for fast computations in number theory (factorizations, algebraic number theory, elliptic curves, modular forms, L functions...), but also contains a large number of other useful functions to compute with mathematical entities such as matrices, polynomials, power series, algebraic numbers etc., and a lot of transcendental functions. PARI is also available as a C library to allow for faster computations.

• Matplot++: A C++ Graphics Library for Data Visualization
• Manim is an animation engine for explanatory math videos. It's used to create precise animations programmatically, as seen in the videos at 3Blue1Brown.

• WolframAlpha Compute expert-level answers using Wolfram’s breakthrough algorithms, knowledgebase and AI technology
• Mathematica The world's definitive system for modern technical computing
• SageMath is a free open-source mathematics software system licensed under the GPL. It builds on top of many existing open-source packages: NumPy, SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, R and many more. Access their combined power through a common, Python-based language or directly via interfaces or wrappers.
• MathStudio
• Coq is a formal proof management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive development of machine-checked proofs. https://coq.inria.fr/
• Mathway provides students with the tools they need to understand and solve their math problems. With millions of users and billions of problems solved, Mathway is the #1 problem solving resource available for students, parents, and teachers.
• Math Solver
• Mathpix Extract equations from PDFs or handwritten notes in seconds just by taking a screenshot. Paste the resulting LaTeX code into any Markdown or LaTeX editor.

• Awesome Math: A curated list of awesome mathematics resources
• ruanyf/free-books: 互联网上的免费书籍
• 开源/免费数学书大合集