What is a conjecture in maths?

A conjecture in mathematics is a statement that is believed to be true but has not yet been proven or disproven. Conjectures are often based on observations or patterns that mathematicians have noticed, but they lack a formal proof.

Conjectures play an important role in mathematics as they often lead to new discoveries and insights. Mathematicians use conjectures to guide their research and develop new theories. Some famous examples of conjectures in mathematics include the Collatz Conjecture, the Riemann Hypothesis, and the Goldbach Conjecture.

Conjectures can be proven true, proven false, or remain unproven for long periods of time. In some cases, conjectures that were widely believed to be true have been disproven, leading to new understandings of mathematical concepts.

Overall, conjectures are fundamental to the practice of mathematics and continue to drive innovation in the field.