Researched
Linear Programming (Simplex Method)
Dantzig invents the simplex method in 1947, the standard way to get the best result from scarce resources in logistics, flights and production.
Open in the interactive tree →George Dantzig was looking for optimal deployment plans for the US Air Force and developed a method that solves large systems of inequalities. Karmarkar's interior-point method followed in 1984. Optimization now sits inside supply chains, power grids, markets and the training of neural networks.
Prerequisites
- Zero, Decimals & Algebra~820
- Linear Algebra & Matrices1858The simplex method works by pivoting on systems of linear equations
- Programmable Computer (Zuse Z3)1941
- Game Theory1944Von Neumann linked linear-programming duality to the minimax theorem of games
Unlocks
- Complexity Theory & NP1971Karp's NP-complete list includes integer programming, the hard cousin of simplex LP
- AI Demand Forecasts & Digital Twins2020-2026
More in Mathematics · Atomic & Space Age
- Monte Carlo Methods1949
- Finite Element Method1956-1960
- Chaos Theory1963
- Continuum Hypothesis Is Undecidable1963
- Fast Fourier Transform1965
- Langlands Program1967
- Complexity Theory & NP1971
- Fractal Geometry1975-1982