How is a mathematician?

Definitely a mathematician!

There are two people lost in a balloon. They fly over a hill and saw two people arguing with each other very pungent. Someone needs to ask "you to ask where we are?". Two below and then looked up to debate. The wind blew hot air balloon go, then a new outlook on the bottom: "You're on a balloon!". The man on balloon says "make sure the two below are the mathematicians." "How'd you know?" Asked the companion. 

"First, the mathematicians always bickering” 

"Secondly, they always think carefully before giving the answer” 

"First three: their answer is always extremely accurate “ 

"Fourth: the exact answers are often useless!”

Mathematical Solution

Basic difference between mathematicians and physicists is that, if asked them "how to pull a nails played a half in the wood"? Then physicists will suggest that, if a human is extracted with force N where N is greater than the total friction pressure as well as other pieces of wood on the nails, the nails are removed. 

But mathematicians will first prove that even when nails are closed flooded into the wood it can still spit out. Then they can prove to be closed nails plug half submerged into the wood with their famous phrase "bring back to the original problem "!