The everyday answer is conjecture = a guess.
It is an inference or judgment based on inconclusive or incomplete evidence;
e.g. "The commentators made the conjecture that the Conservatives will win the next election".
However in physics and mathematics an idea can have a wealth of what you might call "circumstantial evidence" supporting it before the very strict rules employed, (rigour), allow it to be called a hypothesis or a theory or an axiom or principle.
This is because formal mathematics is based on provable truth; one cannot simply try a huge number of cases and conclude that since no counterexamples could be found, therefore the statement must be true.
Some number theory concepts are very abstruse and progress is only slowly made after several generations. As a result, not every conjecture ends up being proven true or false.
As an example the question - "Is every even number greater than 2 the sum of 2 primes?" - may seem simple and likely. Try a few and they seem to work
4 = 2+2, 6 = 3+3, 8 = 3+5, 10 = 3+7, ... 100 = 53+47, ... and so on.
Well this is called the Goldbach conjecture, dating from 1742, and it is still not conclusively proven.
Try Googling for more examples an discussions.
Regards - Ian
