There is usually one good way to determine the accuracy of a mathematical model: Once a set of equations has been built and solved, if the data generated by the equations agree (or come close to) the real data collected from the system, then we can determine its accuracy. In fact, the set of equations and models are only “valid” as long as the two sets of data are close. If a model result leads to conclusions that are not close to the real-world scenario, then the equations are further modified to correct for the discrepancies as much as possible.

For example, in weather prognostication, meteorologists use various numerical models to make long-term predictions of weather systems (for more information about models and weather prediction, see “Math in the Natural Sciences”). It is interesting to see how meteorologists use a combination of several of the weather models to forecast the weather in certain spots around the United States and the world— mainly because no weather forecasting model has all the right answers. Every day, researchers are tweaking their respective weather models (based on more collected data) in hopes of eventually understanding our weather a bit better.