Reminds me of a quote from a favorite textbook [1] of mine:
> In mathematics, an argument must be airtight; that is, convincing in an absolute sense. In everyday life ... the standard of proof is lower ... evidence plays no role in a mathematical proof. A mathematician demands proof beyond _any_ doubt.
It's interesting how in the sciences, we worship at the altar of the almighty Evidence. However, in math, not even evidence is good enough.
[1] p. 17, _Introduction to the theory of computation, third edition, by Michael Sipser
An alternate way of looking at that is, math requires you to be explicit about basing your statements on observations: now you have probability theory.
The mathematician takes calipers to determine the diameter and uses the formula for area of a sphere.
The physicist fills a bucket completely, places it in a larger bucket, submerges the ball and then measures the volume of the water that spilled.
The engineer reads the part number off the bottom of the ball, and then copies the volume from the data sheet.
An engineer, a physicist and a mathematician are on a train crossing an unknown country. Suddenly, the engineer leaning out of the window says: "in this country the sheep are black!"; the physicist corrects: "in this region of the country, some sheep are black"; the mathematician limits himself saying: "at least from one of their sides."
A physicist, a mathematician and a logician are taking the train to Scotland. As the train crosses the border they see a black sheep on a hillside. The physicist remarks, "Oh look all the sheep in Scotland are black." The mathematician replies, "Oh you can't quite conclude that, the most you can say is at least one sheep in Scotland is black." Then the logician says, "Well really the most you can say is that at least one sheep in Scotland is black on one side."
Engineering is physics with the constraint of money.
The one I know:
An astronomer, a physicist and a mathematician go for a walk in the countryside. They spy a black sheep in the distance.
The astronomer immediately proclaims, "All sheep are black!"
The physicist thinks for a moment and suggests, "Some sheep are black."
The mathematician ponders awhile and says, "There exists a sheep such that at minimum one of its sides is black."
In the first room the engineer is asleep and there is mangled open can of soup on the floor. They wake him up and ask about the soup can. And he says, I got hungry so I smashed the soup can against floor to open it.
Next room the physicist was sleep and the soup can open on the floor with the top cleanly removed. And equations scribbled on every wall. When the wake him up and ask about the soup can he proudly says, I got hungry so I figured out exactly where to hit the can so the top would fly off.
Upon opening the last room they find a bleary eyed mathematician holding the soup can saying 'assume the can is open'
Instead of a can of soup it was a fire that broke out in their respective rooms, the engineer sprays fire extinguisher all over the room, the physicist sprays precisely at the exact point that will extinguish the fire, and the mathematician is satisfied knowing that the problem has a known solution.
xkcd: Certainty [1]
Edit: Here’s the text transcript:
> [A door seen from a hallway, with "Teachers' Lounge" on the glass, next to the door is a sign reading "Award." Inside the door are two teachers talking.]
> Megan: My students drew me into another political argument.
> Cueball: Eh; it happens.
> Megan: Lately, political debates bother me. They just show how good smart people are at rationalizing.
> [The two teachers continue talking. A third one is seen reading a book on a sofa.]
> Megan: The world is so complicated - the more I learn, the less clear anything gets. There are too many ideas and arguments to pick and choose from. How can I trust myself to know the truth about anything? And if everything I know is so shaky, what on Earth am I doing teaching?
> Cueball: I guess you just do your best. No one can impart perfect universal truths to their students.
> Miss Lenhart: ahem
> Cueball: ...Except math teachers.
> Miss Lenhart: Thank you.
(... and, thinking of time-averaging, you all have forgotten "on at least one side, at least once during their lifetime." If programming has taught me anything, it's that variables won't yet constants aren't.)
I'm neither a mathematician nor physicist...but this seems like a category error to me. What the heck does a mathematician care about horses?
An engineer, a physicist, and a mathematician are sitting in a train compartment and travelling through some countryside. Presently they come upon a field, which contains a white sheep.
“Oh look, in this country sheep are white!”, exclaims the engineer. “Oh, how unwarranted!”, exclaims the physicist “in this country, there exists a white sheep, on a specific field.” The mathematician just tut-tuts and curses under his breath. “In this country there exists at least one field, wherein there exists at least one sheep, at least one side of which is white.”
Oh, and another great one I enjoy:
An engineer, a physicist, and a mathematician sign up for a psychology experiment. They are each locked in a room with a tin of baked beans, the idea being that they will have to figure out how to open the tin with no tools in order not to starve.
Sometime later, the experimenters check up on them.
First, they come to the engineer’s cell. There’s a contented engineer sitting in the corner, craters on the wall, and the shrapnel of a totally shredded can strewn around. They ask him what he did. “Oh, I just battered it up against the wall.” Fair enough, they think.
Next, they check in on the physicist. They find him somewhat dishevelled, the walls covered with scratched calculations, and a neatly severed can in the middle of the room. They ask him for his account. “Oh, I calculated that if I emitted a note on a certain pitch, resonance would eventually cleave the can in half. It took me some time to figure out the note, though.” Again, fair enough.
Finally they get to the mathematician, whom they find shrivelled up, sitting cross-legged on the floor in front of an intact can as if venerating it, muttering “assume the can is open, assume the can is open”.
:)
