What does theorem mean in math




















Note that, by contrast, common claims are often granted "fact" status after only a single observation or inference! Because of the difference in the levels of testing, the "facts" of everyday life are actually much more likely to be incorrect than are our scientific models.

As our hypotheses are being tested and refined until our level of confidence in them is very high, we seek a set of principles which provide a coherent explanation for the various laws and facts which we've assembled.

This kind of detailed explanation of some aspect of reality, incorporating all of the various well-tested hypotheses and mathematical models and explaining the various facts and laws that we've observed, is what we call a scientific theory. This is quite a different kind of thing entirely from what one might call a "theory" in day-to-day life.

Our usual non-technical meaning of "theory" is much closer in meaning to the scientific term "hypothesis", that is, a simple idea which can be tested. For example, a detective might have a "theory" about who committed the murder, or a student might have a "theory" about the best way to get a good grade.

These are not "theories" in the scientific sense! A single individual never creates an entire scientific theory alone, for scientific theories are much too large and complex. Even theories which have an individual's name associated, such as "Einstein's theory of General Relativity" or "Darwin's theory of Evolution" are not the work of a single individual but are the cumulative results of the collaboration of many individuals over time.

A scientific theory is an extensive body of knowledge which brings together a great number of well-tested hypotheses and mathematical models, weaving them into a coherent explanation for the facts and laws we can observe. An everyday hypothesis is no more a scientific theory than a single bolt is an automobile. A common related confusion is the idea that scientific theories are waiting to be tested and proved before becoming accepted as a fact or a law.

This is a serious misunderstanding -- the ideas that make up a scientific theory are already as well-tested as the current technology permits before they achieve the status of a Scientific Theory. Theorems are proved, not theories. In mathematics, before a theorem is proved, it is called a conjecture. In the sciences, only well-tested hypotheses can become part of a theory. In this way, the term "scientific theory" is very poorly chosen, because for most of the population, the word "theory" suggests weakness and doubt when in a scientific theory there is only well-earned confidence.

In other words, to say that something is a "scientific theory" is to say that it is backed by all available evidence and that our confidence in its correctness as a description of reality is as strong as it can get with our current ability to test it.

Theories do not get proved and become facts or even theorems; if a model or hypothesis is part of a scientific theory, then it already is as "proved" as it can ever get.

It is true that scientific theories are not static and absolute; as technology matures, we constantly find new ways to refine our previous ideas. Occasionally, there are so-called "paradigm shifts" in which a new theory replaces and older one, but in every such case the new theory must be able to explain why the old theory matched up with observations as well as it did. For example, relativity was only able to replace Newtonian mechanics as the accepted scientific theory of gravitation because at low speeds and in low gravitational fields, relativity looks a lot like Newtonian mechanics.

This confusion between the ordinary and scientific meanings of the word "theory", between "simple guess to be tested" and "extensive collection of thoroughly tested and confirmed hypotheses which together provide an explanation of observed facts and laws", forms the basis for a Monty Python sketch -- a character has "a new theory about the Brontosaurus", namely "that all Brontosauruses are thin at one end, thick in the middle, and thin at the other end. A more serious consequence of the confusion of the two meanings is the ability of ideologically motived groups to exploit this confusion, misrepresenting very well-tested and robust scientific theories as "only a theory".

This creates the false impression that there are serious doubts about the theory, when in fact the models and hypotheses which comprise the theory are known to be accurate descriptions of reality with a very high level of confidence. MacTutor History of Mathematics Archive. Malkevitch, J. Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, Weisstein, Eric W. Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more.

Walk through homework problems step-by-step from beginning to end. Hints help you try the next step on your own. Unlimited random practice problems and answers with built-in Step-by-step solutions.

Practice online or make a printable study sheet. Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. MathWorld Book. McKenzie and geophysicist Robert Parker used this theorem to calculate the dance of the lithospheric blocks — the plates. Mathematics searches for new theorem s to build upon the old. In the decade or so since he started learning about this approach, it has helped him prove a wide range of theorem s.

Infinite Monkey Theorem has also landed praise in national publications including Wine Spectator as recently as last year. This, however, is not a question of the method of the social science, but a theorem of the science itself. This was M. Comte's opinion; but it is by no means implied in his fundamental theorem.



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