Quote Originally Posted by Robb
Having done mathematics graduate school, I'll add this. Mathematicians tend to ask: "I wonder if this thing is true?" This conjecturing is the first step in proving something, which is how research mathematicians make a living. After a while, when you look at a conjecture, you just have a feeling about whether or not it's true. It's almost always correct to go with that gut feeling. After a while, experience and knowledge combine into intuition, and you don't waste time analyzing every factor in a complex setting.

For a mathematician, saying "I feel like this is true" can be a very technical analysis combining dozens of facts and experiences into intuition that generally points in the right direction.

But don't use the word "feel" in an FTR post. I made that mistake once, and lived to regret it.
I'll be in grad school for mathematics before too much longer, and I definitely feel you on that one.

The professor I have for most of my algebra theory classes (groups, rings, etc.) had something really cool to say about this in my first class on groups about a year and a half ago:

At the beginning of each class, she would write a statement on the board that we may or may not know whether it's true or false. Inside of about a minute or two we were supposed to decide if it was true or false, write our answer on a piece of paper and hand it in. If we weren't sure, she told us to flip a coin, if it was heads, consider it to be true, and if it was tails, consider it to be false. Then, if we had a feeling of disappointment about the result of the coin-flip, then that was our intuition telling us that the answer was likely wrong.