## Posts tagged ‘truth’

### 2 Truths and a Lie (Mathematician Version)

Here’s the question that started all of the nonsense that follows:

You come to a fork in the road. One fork leads to the village, the other leads to almost certain death. There are three guards stationed at the fork: two always tell the truth, and one always lies. What one question can you ask to one of the guards to find out which fork leads to the village?

There is a truly logical answer to this question, but my favorite answer is:

Did you know they’re giving away free beer in the village?

and then follow all three of them as they sprint toward the village.

A similar question that got me thinking:

A kind but eccentric king has three beautiful daughters. The eldest daughter always tells the truth, the middle daughter always lies, and the youngest daughter will answer any question randomly, either yes or no. To be sure, you would like to marry the one who always tells the truth; but, you are willing to settle for the one who always lies, because at least you’ll always know where you stand. Under no circumstances would you like to marry the crazy one.

The king offers you the hand of one of his daughters in marriage. He allows you to ask one yes/no question of one of the daughters. What question should you ask to ensure that you don’t marry the crazy one?

Variations of this question have been discussed on Straight Dope and xkcd.

And those two questions got me thinking about the icebreaker game *Two Truths and a Lie*, wherein each person at a social gathering tells two truths and one lie about themselves, and the others have to discern fact from fiction.

So I imagined…

What would happen if the most famous mathematicians in history played

Two Truths and A Liewith one another?

The following is what I suspect some of them might say. (The answers follow below.)

**Isaac Newton**

- Newton’s Cannonball is named after one of my thought experiments.
- The city of Newton, MA, is not named after me, but Newton Township, OH, is.
- The Fig Newton, manufactured by Nabisco, is named after me.

**Rene DesCartes**

- I did not get out of bed most days until 11 o’clock in the morning.
- I posited that boiled water freezes more quickly than other water.
- I started college at the age of 10.

**Abraham de Moivre**

- I noted that I was sleeping 15 minutes longer each day, and using that arithmetic progression, I predicted that the day I would sleep for 24 hours would be the exact day of my death — and I was correct.
- I was unable to garner a university post in England, but I was appointed to a Commission of the Royal Society to determine if Newton or Leibniz was the first to discover the calculus.
- I gained great and immediate notoriety for discovering the normal (bell) curve.

**Euclid**

- My name is a Greek word that means “good glory.”
- Abraham Lincoln would often quote me in his speeches.
- I proved the infinitude of primes using a proof by contradiction.

**Gottfried Wilhelm Leibniz**

- I discovered the calculus.
- I invented the first four-function calculator.
- My vast estate was left to my son after my death.

**Leonardo Pisano (Fibonacci)**

- I love rabbits!
- I sometimes used the name Bigollo to refer to myself, which means “good-for-nothing traveler.”
- The 20th century pianist Liberace created his stage name from a contraction of my book title,
*Liber Abaci*.

**Grace Murray Hopper**

- In 1973, I was the first American and the first woman to be elected a Distinguished Fellow of the British Computer Society.
- I invented the computer language COBOL.
- I received 36 honorary degrees.

**Leonhard Euler**

- All of my work, now collected in
*Opera Omnia*, contains over 70 volumes. - In 1735, Guillaume De L’Isle and I prepared a map of the Russian Empire.
- I was the first to use the notation
*f*(*x*) for a function,*e*for the base of natural logs,*i*for the square root of –1, and π for the ratio of circumference to diameter of a circle.

**Diophantus of Alexandria**

- It is believed that I lived to 84 years of age, based entirely on a problem that appeared in a Greek anthology compiled by Metrodorus.
- I was a potato farmer.
- I proved that 24
*n*+ 7 cannot be expressed as the sum of three squares, for integer values of*n*.

**Evariste Galois**

- I was home-schooled until age 12.
- I was killed in a duel, but history is unsure of the other duelist or the reason for the duel.
- I transcribed most of my ideas for what is now called
*Galois theory*the night before the duel.

The third statement from each mathematician was their lie. Below is explication.

Isaac Newton: The Fig Newton is named after the town of Newton, MA, where it was first manufactured.

Rene DesCartes: Actually, he started college at the age of 8.

Abraham de Moivre: In fact, de Moivre’s discovery of the normal curve went almost unnoticed.

Euclid: While many claim that Euclid’s proof of the infinitude of primes uses a proof by contradiction, Michael Hardy and Catherine Woodgold debunk this belief in *Mathematical Intelligencer*, Vol. 31, No. 4, pp. 44–52. Hardy claims that the proof written by Euclid is simpler and more elegant than the proof often attributed to him.

Gottfried Wilhelm Leibniz: He had neither a vast estate nor a son. He was never married, and he died nearly destitute.

Leonardo Pisano (Fibonacci): Though it would be a great piece of trivia, Liberace’s name had nothing to do with Fibonacci. Liberace was a family name; he was born Władziu Valentino Liberace, but he used only his last name on stage.

Grace Murray Hopper: She received at least 37 honorary degrees, perhaps more.

Leonhard Euler: Euler deserves credit for a lot of things, but he does not deserve credit as the first to use π. That distinction belongs to William Jones who used the symbol in 1706.

Diophantus of Alexandria: Though he claimed that 24*n* + 7 cannot be expressed as the sum of three squares, he had no proof of it.

Evariste Galois: The myth that he basically transcribed Galois theory the night before his death is greatly exaggerated. He wrote a lot that evening, but he published three papers in the year before his death, which collectively contained most of his work.

### Einstein > π

Yes, today is Pi Day.

Whatever.

More importantly, it’s the 134th anniversary of Albert Einstein’s birth. (Isn’t it remarkable that people who celebrate Pi Day don’t think to add a few candles to the pie and sing *Happy Birthday* to Big Al?) It’s interesting that 134 shares the same three digits as Einstein’s birth date, 3/14, and 134 also has the following property:

1 + 3 + 4 = 8

_{8}C_{1}+_{8}C_{3}+_{8}C_{4}= 134

On his birthday, we can honor Einstein by remembering some of his quotes. One of his most famous is about his math ability.

Do not worry about your difficulties in mathematics. I can assure you that mine are still greater.

Slightly less well-known is the following quote by Einstein, also about math.

God does not care about our difficulty with numbers. He integrates empirically.

But special for today, the following is a quote not *from* Eistein, but *about* Einstein. The quote is attributed to a Japanese cartoonist, Ippei Okamoto, and appeared in *Driving Mr. Albert* by Michael Paterniti.

He [Einstein] has a quiet way of walking, as if he is afraid of alarming the truth and frightening it away.

A beautful quote for a beautiful mind. Happy Birthday, Mr. Albert!