The jokes below try to grab certain ways of mathematical thinking. No offense is intended, these differences in mentality are probably necessary for people in different professions to do their job properly.

**Way of thinking**

- Pour out the water
- How many legs does a sheep have?
- What color are the sheep in Scotland?
- The volume of a little red ball
- Every girl is blonde
- How do you define a mathematician?
- Accuracy

**Social position**

## Way of thinking

### Pour out the water

*How does a mathematician or a physicist prepare tea?*

Both of them pour water into the pot, light the flame, boil the water, infuse the leaves.

*What is the difference in the solution, if the pot is already filled with water?*

The **physicist** lights the flame, boils the water, infuses the leaves.

The **mathematician** pours the water out, thereby reducing the problem to the previous, already solved one.

### How many legs does a sheep have?

Two in front, two in the back, two on the left side, two on the right. That is eight, but we counted each leg twice, so the result is four.

### What color are the sheep in Scotland?

A mathematician, a physicist and an engineer travel on a train in Scotland. They catch a glimpse of a sheep.

*– Sheep in Scotland are black, it seems* – ventures the **engineer**.

*– You can be sure only that there is a black sheep in Scotland* – answers the **physicist**.

*– No, we know only that there is a sheep in Scotland with at least one black side* – corrects the **mathematician**.

### The volume of a little red ball

A mathematician, a physicist and an engineer are asked to measure the volume of a little red ball.

The **mathematician** measures the diameter and calculates the volume.

The **physicist** drops the ball into a tank full of water, and measures how much water poured out.

The **engineer** looks up the volume in the Catalog of Little Red Balls.

### Every girl is blonde

**Proof. **It is sufficient to show that *in every set of girls, any two members have the same hair color.* Indeed, apply this to the set of all girls. Since there exists a blonde girl, every girl is blonde.

We prove the italicized statement by induction on the size of the set. If the size is one, the statement is clearly true. Suppose that the statement holds for every n element set of girls, and consider an n+1 element set: S={Kate, Julie, Ann, Elisabeth,…}. If Kate is dropped from S, then an n element set remains, and by the induction assumption, every girl in this subset has the same hair color, say X. Similarly, if Julie is dropped from S, then in this subset the hair color is uniform. But Ann’s hair is of color X, and so the same holds for Kate. Therefore the hair color is uniformly X in S, too.

### How do you define a mathematician?

A person is a mathematician, if he is willing to think for hours (and builds up a beautiful theory in the process) in order to spare a few minutes of ugly calculations.

### Accuracy

A plane flies over San Francisco in dense fog when the navigation equipment breaks down. The pilot opens the window and shouts:

– *Where am I?*

– *In the air!*

This information was sufficient to find the exact position, and the plane landed safely. How is this possible?

**Solution:** The response was completely accurate and completely useless, so it came from a mathematician. Therefore the plane was above Berkeley.

## Social position

### The student, the assistant and the professor

The **student** has to know everything.

The **assistant** has to know where the appropriate book is.

The **professor** has to know where the assistant is.

### Mathematics and Computer Science

What is the difference between two persons, doing research in the same area of combinatorics, if one works at a Math Department, and the other one at a Computer Science Department?

**Answer:** $50000 per year (in wages).

### The King’s Astronomer

– *Who is this ragged man in my Court?*

– *He is the Royal Astronomer.*

– *What is the job of my Astronomer?*

– *He prepares the maps for Your Majesty’s fleet.*

– *And how can such an important man be so shabby?*

– *Because he receives only five guineas from Your Treasury per year.*

– *He deserves more. Let him receive 100 guineas.*

– *With all respect, I must call Your Majesty’s attention to the fact, that in that case, the position of Royal Astronomer will never be filled by an astronomer.*