The History of Mathematics

Into Modern Mathematics

What is chaos theory?

Chaos theory is one of the “newest” ideas in mathematics. Developed in the last half of the 20th century, it affects not only math, but physics, geology, biology, meteorology, and many other fields. Modern ideas about chaos began when theorists in various scientific disciplines started to question the linear analysis used in classical applied mathematics, most of which presumes an orderly periodicity that rarely occurs in nature. In the search to discover regularities, the idea of disorder had been ignored. To overcome this problem, chaos theorists developed deterministic, nonlinear dynamic models that explain irregular, unpredictable behavior. By 1961, American meteorologist Edward Norton Lorenz (1917–2008) noticed that small variations in the initial values of variables in his primitive computer weather model resulted in major divergent weather patterns. His discovery of a simple mathematical system with chaotic behavior led to the new mathematics of chaos theory.

The use of chaos theory has enabled scientists and mathematicians to reveal the structure in aperiodic, unpredictable dynamic systems. For example, it has been used to examine crystal growth, the expansion of pollution plumes in water and in the air, and even to determine the formation of storm clouds. One of the reasons chaos theory has come to the forefront of science and mathematics is because of advancements in computers; high-end computers allow for a plethora of variables to enter into the complex chaos equations.


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