h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

'Information': layman terms is something which informs, gives knowledge, etc. Scientifically, information is a reduction in entropy caused by observation.

'large': layman means something which is big. Scientist means something so big it can be considered to be infinitely big. Similarly with 'small', 'rigid', 'heavy', 'light', etc, etc, etc.

'distance': layman means how far away something is from something else. Mathematician means any function of two inputs which has certain mathematical properties, IE d(X,X)=0 ; d(X,Y)=d(Y,X) ; d(X,Y)+d(Y,Z) <= d(X,Z)

And the classic 'clearly': layman means something which is obvious, mathematician means either -
1) This is true, and if you think about it for a few hours you'll realise it's true too.
2) This is true, and if you think about it for a few weeks you'll realise it's true too.
3) This is true, but I can't work out how to prove it, so I'm going to gloss over it and hope nobody notices.
4) This is false.

There are loads, of course...

One of my lecturers said that the perfect proof to give in exams is to write down everything they give you, then put "therefore" and then what is required. It must follow, you see, or they wouldn't ask you.

In exams, if you are given the starting point and end point then we were told to work from both ends. When you couldn't do the bit in the middle you would put in "it can be shown that" and still get almost full marks.

Wick

On the other hand, I've jumped steps in homeworks at uni because I thought they were obvious and been marked down for it. Not often, though.

sound: strictly means the brain's interpretation of a noise. (Noise being a sound transmitted through a medium). Without a brain there to interpret noises created by an object, there is no "sound". Hence, those studied in the field of acoustics and sound know why "A tree makes no sound when it falls in the woods and there's no one there to hear it."