mathematical models
Equations describing reality
Mathematical models are abstract representations of real-world systems using equations, variables, and logical relationships.
Scientists build models to simulate climate patterns, economists model market behavior, epidemiologists model disease spread.
A good model captures essential dynamics while simplifying away irrelevant detail: The mathematical model predicted how the virus would spread through the population.
Models are tools for understanding and prediction, not perfect mirrors of reality—all models are wrong, but some are useful.
- simulationImitation of real processes
- algorithmsFinite instruction sequences
- number crunchingIntensive calculation work
- Monte CarloProbability estimation through randomness
- game theoryStudy of strategic interaction
optimization · risk assessment · chaos theory · equations · curve fitting · graph theory · differential equations · boundary conditions · variables · linear programming · epidemiology · economics · patterns · machine learning · curves · probability · systems · data
- mathaddition, subtraction, multiplication, division, algebra
- ancient astronomyepicycles, stars, deferent, celestial sphere, geocentric
- information theoryentropy, bit, bits, information theory, binary digit
- theoretical physicsquantum mechanics, relativity, general relativity, special relativity, thermodynamics
mathematical modelsintuitive understanding
Knowledge felt, not learned
heuristics · rules of thumb · gut feelings · anecdotal evidence · common sense
mathematical modelsempirical observation
Facts gathered through senses
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