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A conjecture is a mathematical statement which seems likely to be true but has not been proved to be true under rules of logic. It is usually based on some but not complete evidence.
After finding the sum of the digits of different multiples of 9, we can conjecture that the sum of the digits is always divisible by 9. This conjecture can be proved to be true by algebraic arguments.
A famous problem in mathematics is Goldbach’s conjecture that every even number greater than 2 can be written as the sum of two primes, e.g.
4 = 2 + 2 10 = 3 + 7 = 5 + 5
6 = 3 + 3 12 = 5 + 7
8 = 3 + 5 14 = 3 + 11 = 7 + 7
and so on. Goldbach’s conjecture has so far never been proved.
There are several Mathemapedia articles which explore the idea of a ‘conjecturing ethos’ in the classroom. For example:
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