Difference Between Conjecture and Hypothesis

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”.