Re: What is the Difference between Algorithm and Theorem

Posted by DickT on June 25, 2003 at 15:30:08:

In Reply to: What is the Difference between Algorithm and Theorem posted by sol on June 20, 2003 at 23:02:21:

Sol,

Sorry to be so late in replying. I just noticed this in the forest of Kx21 noise.

An algorithm (the name is a form of al Khwarismi, a muslim writer whose algebra textbook was popular in the European middle ages) is a series of steps for arriving at a result. The method of long division as taught in school is an algorithm. First you do this, and then based on what you did before you do that, and so on. An algorithm gives you the answers (if it's a correct algorithm) but doesn't tell you why the answer is so.

A theorem is a logical deduction from a set of axioms and from previous theorems based on those axioms. Mathematicians distinguish lemmas which are theorems that only exist to help prove other theorems, theorems themselves, the main results, and corollaries, which are quick consequences of the theorems. Sometimes theorems are called propositions. Newton, for example, uses both terms in his Principia.

Regards,
Dick

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