Researched
Calculus (Analysis)
Newton and Leibniz independently develop derivatives and integrals, the tool for describing change exactly.
Open in the interactive tree →Leibniz published his differential calculus in 1684; Newton had developed his version in the 1660s, and the priority dispute lasted decades. The derivative (rate of change) and the integral (summing up) make motion, curves and areas exactly computable. Nearly all later physics, engineering and economics rests on this foundation.
Prerequisites
- Geometry (Euclid)~300 BC
- Zero, Decimals & Algebra~820
- Logarithms (Napier)1614Logarithms and exponentials are basic functions of calculus
- Analytic Geometry (Descartes)1637Newton and Leibniz treated curves as equations in coordinates
Unlocks
- Newtonian Mechanics1687
- Partial Differential Equations1747
- Wave Optics (Young, Fresnel)1801
- Statistics & Least Squares1809
- Fourier Analysis1822
- Non-Euclidean Geometry1829
- Electromagnetism1831-1865
- Analytical Engine & Punch Cards1837
- Gradient Descent1847
- Set Theory & Formal Logic1874
- Prime Number Theorem1896
- Measure-Theoretic Probability1902-1933
- Chaos Theory1963
- Backpropagation1986
- Fermat's Last Theorem Proved1995
- Kakeya Conjecture in 3D2025
- Birch and Swinnerton-Dyeropen
- Hodge Conjectureopen
- Navier-Stokes Problemopen
- Riemann Hypothesisopen
- Yang-Mills Mass Gapopen