A postulate (also sometimes called an axiom) is a statement that is agreed by everyone to be correct. This is useful for creating proofs in mathematics and science. Along with definitions, postulates are often the basic truth of a much larger theory or law. Thus a postulate is a hypothesis advanced as an essential presupposition to a train of reasoning.
Postulates themselves cannot be proven, but since they are usually self-evident, their acceptance is not a problem. Here is a good example of a postulate (given by Euclid in his studies about geometry).
- Two points determine (make) a line.
Using this postulate and four others like it, Euclid brought a new understanding of geometry to the world, and many people think they are some of the most influential works in geometry (even in modern time).
Sometimes, postulates are not obviously correct, but are required for their consequences. One example is Albert Einstein's postulate that the universe is homogenous. This type of postulate was necessary to make possible some major scientific achievements, but can also be problematic since it is not self-evident.
As a rule of thumb, postulates tend to have the following characteristics:
- Obvious and easy to understand
- Does not contain many words that are difficult to explain
- Few in quantity
- Work together without making any strange result (that is, they are consistent)
- True when used alone (which means that they can be used independently)
Postulates are sometimes proved to be wrong after they have been known for a long time, but this is usually because something new has been discovered, and the original creator could not have known any better.
- "The Definitive Glossary of Higher Mathematical Jargon: Axiom". Math Vault. 2019-08-01. Retrieved 2020-10-08.
- "Definition of POSTULATE". www.merriam-webster.com. Retrieved 2020-10-08.