Master Mathematics Step by Step
Comprehensive guides, interactive calculators, and thousands of worked examples to help you excel in algebra, calculus, geometry, and more.
๐ The Rich History of Mathematics
Ancient Babylonian Mathematics
The Babylonians developed the first sophisticated number system and created the foundation for algebra. Their base-60 system still influences how we measure time and angles today.
Algebra OriginsEuclid's Elements
Euclid's "Elements" became the foundation of geometry for over 2,000 years. This masterwork introduced logical proofs and the axiomatic method that still shapes mathematics today.
GeometryBirth of Modern Calculus
Isaac Newton and Gottfried Leibniz independently developed calculus, revolutionizing mathematics and enabling the scientific revolution. Their work laid the groundwork for modern physics and engineering.
CalculusProbability Theory
Pascal and Fermat's correspondence about gambling problems led to the birth of probability theory, which now underpins statistics, economics, and data science.
StatisticsFermat's Last Theorem Proved
Andrew Wiles finally proved Fermat's Last Theorem after 358 years, using sophisticated techniques from algebraic geometry and number theory. This achievement marked a milestone in mathematics.
Number TheoryPoincarรฉ Conjecture Solved
Grigori Perelman proved the Poincarรฉ conjecture, one of the seven Millennium Prize Problems, revolutionizing our understanding of three-dimensional shapes and topology.
Topologyabc Conjecture Progress
Shinichi Mochizuki claimed a proof of the abc conjecture using his revolutionary Inter-universal Teichmรผller theory, though the mathematical community continues to verify this complex work.
Number TheoryCollatz Conjecture Breakthrough
Terence Tao made significant progress on the Collatz conjecture, showing that almost all positive integers eventually reach 1 under the 3n+1 process.
Number TheoryAperiodic Monotile Discovery
The discovery of the "einstein" tile - a single shape that tiles the plane only aperiodically - solved a 50-year-old problem in tiling theory, with applications in materials science.
GeometryAI-Assisted Mathematical Discovery
Machine learning models begin assisting mathematicians in discovering new patterns and proofs, marking the beginning of a new era in mathematical research and collaboration between humans and AI.
Applied Mathematics๐ฌ Latest Mathematical Research
Machine Learning Applications in Algebraic Geometry
Recent advances in machine learning have opened new avenues for solving complex algebraic geometry problems, with applications in cryptography and computer vision.
Fractional Calculus in Biological Systems
Fractional derivatives provide new insights into biological processes, from population dynamics to neuron firing patterns, offering more accurate models than traditional calculus.
Bayesian Methods in Educational Assessment
Novel Bayesian approaches to student assessment provide more accurate predictions of learning outcomes and personalized educational pathways.
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Algebra
Master equations, polynomials, and algebraic thinking with step-by-step guides and interactive calculators.
Explore Algebra โCalculus
Understand limits, derivatives, and integrals with visual explanations and practical applications.
Learn Calculus โGeometry
Explore shapes, angles, and spatial relationships through interactive visualizations.
Study Geometry โTrigonometry
Master angles, triangles, and periodic functions with comprehensive examples.
Explore Trigonometry โStatistics
Analyze data and understand probability with practical examples and real applications.
Learn Statistics โCalculators & Tools
Access powerful math calculators for instant solutions and step-by-step explanations.
Use Tools โPopular Examples
Solving Quadratic Equations
Learn to solve $2x^2 - 7x + 3 = 0$ using the quadratic formula with step-by-step instructions.
Finding Derivatives
Calculate the derivative of $f(x) = x^2 \sin x$ using the product rule.
Triangle Area Calculation
Find the area of any triangle using base and height, or Heron's formula.
Popular Resources
๐ง Interactive Mathematical Tools
Specialized Mathematical Tools
Geometry Calculator
Calculate areas, volumes, and properties of geometric shapes
Statistics Calculator
Calculate mean, median, mode, and standard deviation
Calculus Tools
Find derivatives and integrals with step-by-step solutions
Matrix Calculator
Perform matrix operations: addition, multiplication, determinant