6 $\begingroup$ In mathematics, probability means how likely a random event is to occur. But I've also heard mathematicians use this word in other cases too. Here are some examples to make you understand what I mean: For example, They say The Collatz conjecture is "probably" true. There is no random event happening here because the conjecture is either true or false. But when this conjecture is tested for many numbers and there is no counter example, it means that there is a high chance that the conjecture always works. Here is another example: There was a combination question that was about calculating the number of ways that we can sort letters A,B,C and D so that A always comes before B. I solved that and my answer was $\binom 42 \cdot 2$. Then I accidentally realized that this is equal to $\frac {4!}{2}$. So I guessed that "probably" another way of solving the question exists that leads to the second answer, and it did exist. These statements (e.g: "The Collatz conjecture is probably true") are not mathematical statements. But they are not useless and worthless statements either, and sometimes can help us. So what exactly are they? probabilityterminology Share Cite Follow edited 20 hours ago Blue 80.4k1414 gold badges124124 silver badges247247 bronze badges asked 20 hours ago madfd adfdmadfd adfd 33011 silver badge99 bronze badges $\endgroup$ 7 3 $\begingroup$ A probability can also be interpreted as just a number indicating how strongly you believe something. See the book Probability: The Logic of Science for example. $\endgroup$ – littleO Commented 20 hours ago 15 $\begingroup$ I don't think a mathematician is using "probably" in any way different from the way the average person uses "probably" here. $\endgroup$ – Jair Taylor Commented 19 hours ago 2 $\begingroup$ It’s a colloquial way of saying ‘I’m happy to bet you $100 it turns out to be true.’ $\endgroup$ – A rural reader Commented 18 hours ago 1 $\begingroup$ There is a simple heuristic probabilistic argument that gives that the expected ratio between two consecutive odd numbers in the trajectory is $3/4$, so that divergent trajectories are unlikely. $\endgroup$ – Fabius Wiesner Commented 18 hours ago $\begingroup$ It can be solved by a quantum computer as it's expecting output (true/false) and an oracle (Collatz conjecture algorithm), returning input probabilistically (every possible integer that says the output is true/false). Therefore you have the answer probabilistically. $\endgroup$ – Muhammad Ikhwan Perwira Commented 8 hours ago  |  Show 2 more comments