** Conjecture vs Hypothesis **

In science, Conjecture and Hypothesis has two different meaning, but you may have seen in different books that they have used them in a different manner. Both are statements based on observations but not proven.

**Conjecture**

A conjecture is a proposition for which someone assumed to be true. It may be a statement expressing prediction, a judgment, or an opinion based on observations or incomplete evidence. A conjecture is a statement, which is appeared to be true, but has not been either proven or disproven. In mathematics, conjecture is assumed to be an unproven statement or a theorem, which is not disproved or assumed to be true. The Goldbach conjecture: “every even number can be written as a sum of two prime numbers” is a well known conjecture. Conjectures are testable. When a conjecture is proved it become a theorem. The “Four-color conjecture” was a conjecture until Appell and Haken proved that conjecture in 1976. It is now known as “Four-colour theorem”, which is a well-known theorem in Graph theory, a branch of Applied mathematics.

**Hypothesis**

Hypothesis is stronger than conjecture. Hypothesis can be defined as a statement about a part of a theorem that can be tested through experiments or observations. Let us consider a basic theorem in calculus: “If the function f is continuous on closed interval [a,b], then it is Riemann integrable over the interval [a, b]. ”. The hypothesis of this theorem is “f is continuous on [a, b]”, the conclusion is “f is Riemann integrable over [a, b]. In a school experiment if we make a prediction, we should introduce it as a hypothesis. Then we must say, “My hypothesis on this experiment is…”. Very often, in mathematics, the term “conjecture” is substituted by term “hypothesis”. For an example, there is a conjecture called “Riemann hypothesis” in mathematics, which is really a conjecture, and correctly it should be called as “Riemann conjecture”.

• Hypothesis is something that can be tested. However, not all conjectures can be fully tested. • The term hypothesis can be seen in most of the areas. The term “conjecture” is most commonly used in mathematics. • A conjecture can become a hypothesis, then a theory, and then a law. |