Three mathematicians walk into a restaurant and sit down at a table. The waitress comes over and asks, “Do all of you want water?” Mathematician 1 says, “I don’t know.” Mathematician 2 says, “I don’t know.” Mathematician 3 says, “Yes.”

An engineer, a physicist and a mathematician are staying in a hotel. The engineer wakes up and smells smoke. He goes out into the hallway and sees a fire, so he fills a trash can from his room with water and douses the fire. He goes back to bed.

Later, the physicist wakes up and smells smoke. He opens his door and sees a fire in the hallway. He walks down the hall to a fire hose and after calculating the flame velocity, distance, water pressure, trajectory, etc. extinguishes the fire with the minimum amount of water and energy needed.

Later, the mathematician wakes up and smells smoke. He goes to the hall, sees the fire and then the fire hose. He thinks for a moment and then exclaims, “Ah, a solution exists!” and then goes back to bed.

There were two men trying to decide what to do for a living. They went to see a counselor, and he decided that they had good problem solving skills.

He tried a test to narrow the area of specialty. He put each man in a room with a stove, a bucket of water, and an empty pot on the stove. He said, “Boil some water in the pot.” Both men filled the pot with water from the bucket and turned on the burner to boil the water.

Next, he put them into a room with a stove, a bucket of water, and a pot full of water on the stove. Again, he said, “Boil the water in the pot.” The first man immediately turned on the burner. The counselor told him to be an Engineer. The second man emptied the pot and proudly said that now the problem is reduced to the previously solved problem. The counselor told him to be a mathematician.

A mathematician, a physicist, and an engineer were travelling in Scotland when they saw a black sheep thru the window of the train.

“Aha”, says the engineer,“I see that Scottish sheep are black.”

“Hmm”, says the physicist, “You mean that some Scottish sheep are black.”

“No,” says the mathematician. “All we know is that there is at least one sheep in Scotland, and that at least one side of that sheep is black!”

An engineer, a physicist, and a mathematician are asked to prove that all odd numbers are prime.

The mathematician says, “3 is prime. 5 is prime. 7 is prime. 9 is not prime. So, it is false.”

The physicist says, “3 is prime. 5 is prime. 7 is prime. 9 is not prime. 11 is prime. 13 is prime. So, to within experimential error, it is true.”

The engineer says, “3 is prime. 5 is prime. 7 is prime. 9 is prime. 11 is prime. 13 is prime…. So, it is true!”

Obviously, there is a rich history to this matter of mathematicians and the obvious. It is necessary and sufficient to present three examples:

This is a certifiably non-original story I tell to all math majors I encounter: One mathematician was showing his new theorem to another. The colleague pointed at the chalkboard and asked how the theorem went from one step to the next. The first mathematician said, “That’s obvious.” The second went to a second blackboard, spent an hour filling it up with complex calculations, then stepped back and said, “You’re right, it is obvious.” —Patrick Lenon

It’s worth recalling the story of the very famous mathematician G.H. Hardy, who in a lecture said about some detail in a proof: “This is obvious.” After a pause, he went on: “Hmm, is it really obvious?” After another pause he left the room to consider the point, returning 20 minutes later with the verdict: “Yes, I was right, it is obvious.” —J.R. Partington

The world’s most famous mathematician, Humpty Dumpty, speaking for fellow mathematicians everywhere, said: “When I use a word, it means precisely what I choose it to mean, neither more nor less.”

Mathematicians always say what they mean, even though they do not mean what they say. Obviously. —Dirk Laurie

Q: What’s yellow and equivalent to the axiom of choice?

A: Zorn’s lemon.

Q: What’s purple and commutes?

A: An abelian grape.

A non-mathematician was at a party where there were both mathematicians and non-mathematicians, and he overheard the “abelian grape” pun. He didn’t get it. So, he wandered over to someone who he knew was a mathematician and said, “I don’t understand this joke I just overheard. Could you explain it? What is purple and travels?”

A mathematics professor who normally only taught graduate level courses had to cover an introductory course. He was showing the class how to do a statistics/combinatorics problem when one of the students asked what “factorial” was. He looked around the class and asked, “You don’t know what factorials are?” It seems they didn’t. So he went over factorials and gave them some problems to try. While they were working on the problems, he wandered around the room to see how they were doing. They were all struggling and having a hard time. He turned to the class and said, “I don’t understand why you are all having such difficulty. I told you—factorials are just a special case of the Gamma function.”

Q: What is an anagram of “Banach-Tarski”?

A: Banach-Tarski Banach-Tarski.

Two professors are giving an oral exam to a student who is not very bright. One of the professors asks him, “Can you give an example of a compact topological space?” The student pauses and says, “The real numbers.” There is a long, painful silence until the second professor asks helpfully, “With what topology?”

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