When I Die…

Did you hear about Tommy Lasorda’s wish? The retired manager of the Los Angeles Dodgers is recovering from a heart attack he suffered in June, and he recently told the L. A. Times:

I’ve already told my wife that when I do go, I want our home schedule attached to my tombstone. I want people who are in the cemetery visiting their loved ones to say, “Let’s go to Lasorda’s grave and see if the Dodgers are playing home or away.”

That could get expensive, since it would have to be updated annually. I suggest one of these instead:

Old baseball players never die; they just go batty.

Old baseball players never die; they just do one more lap around the bases.

Old baseball players never die; they just get traded to the Blue Jays. (Sorry, Toronto!)

This got me thinking about what I’d want on my tombstone when I leave.

Don’t meet my end with gasps and shrieks;
I left you with a book (and blog) for geeks.

Given the likelihood of my eternal destination, I take comfort in the following advice:

Go to Heaven for the climate,
to Hell for the company.

Contemplating what should appear on my tombstone puts me in good company. Many mathematicians have pondered the same question.

At age 18, Carl Friedrich Gauss showed that it was possible to draw a regular 17‑gon with compass and straightedge. Proud of his accomplishment, he later requested that a 17‑gon be inscribed on his tombstone. Although his wish was not granted, a memorial to him in his hometown of Braunschweig, Germany, now bears a small 17‑gon just below his right foot.

Imagine a sphere inscribed in a cylinder whose height is equal to its diameter. Archimedes discovered that the ratio of the surface area of the cylinder to the surface area of the sphere is 3:2 and also that the ratio of the volume of the cylinder to the volume of the sphere is 3:2. Despite his many accomplishments in mathematics, this is the one for which he wished to be remembered. He asked that a cylinder with inscribed sphere be displayed on his tombstone, with the ratio 3:2 inside.

Jacob Bernoulli was so enamored with the logarithmic spiral that he wanted one inscribed on his tombstone. Unfortunately, the engraver mistakenly carved an Archimedean spiral (shown below).

An apocryphal story is that the following poem appears on the tombstone of Diophantus. In fact, this problem appeared in a fifth-century Greek anthology of puzzles.

Here lies Diophantus, the wonder behold.
Through art algebraic, the stone tells how old:
“God gave him his boyhood one-sixth of his life,
One-twelfth more as youth while whiskers grew rife;
And then yet one-seventh ere marriage begun;
In five years there came a bouncing new son.
Alas, the dear child of master and sage
After attaining half the measure of his father’s life, chill fate took him.
After consoling his fate by the science of numbers for four years, he ended his life.”

Good luck solving the puzzle before you meet your end!

Guess Who’s the Best Mathematician of All Time?

Just as Anna Nicole Smith was the premier jeans model in the 1990’s, Carl Friedrich Gauss was the preeminent mathematician of the 1800’s. (Wow, did I really just compare a model known primarily for taking off her clothes and meeting an early demise with a mathematician who made significant contributions in number theory and statistics, as well as astronomy and optics? But the analogy isn’t completely absurd — after all, Carl Friedrich was one of the five hottest mathematicians.)

Recognizing the similarities between these two giants in their fields, it was impossible to resist the urge to create the following poster. Enjoy.

Here’s an up-close look at the Gauss^® symbol:

Name Dropping

Name dropping is the practice of mentioning the name of illustrious or famous people in casual conversation. By implying a connection to that person, the dropper hopes to raise his social status to the level of the droppee.

Wikipedia says that name dropping is “usually regarded negatively.” I say that it’s downright obnoxious… unless, of course, you’re dropping the name of a long-deceased mathematician into conversation for your own amusement. In that case, it is not only acceptable but strongly encouraged.

For instance, imagine that your friend suddenly shows up at your house and announces, “I just proved the parallel postulate!” It would be perfectly appropriate to respond as follows:

Are Eucliding me?

The following is a list of other ways that you might consider working mathematicians’ names into daily conversation. Good luck! And when you use one of these at a cocktail party and you’re the only one who laughs, just remember — it’s not because it isn’t hysterical; it’s just that none of the other attendees are as sophisticated as you.

• I’m ready, willing, and Abel, but I still can’t solve a quintic equation with radicals.
• What’s the sum of the first 100 positive integers? Your Gauss is as good as mine.
• What’s good for pa is good Fermat!
• I just proved the minimax theorem, and I feel like a Neumann.
• Either he Cantor he won’t!
• Did you thay thomething? Noether!
• Banach, Banach. Ba-who’s ba-there?
• Math jokes make me say Hardy har har.
• I’ll figure out the strategy to this game, Conway or another!
• Why, you dirty little Pascal!
• Math is good Fourier soul!
• He wouldn’t see her until his book was published… but he Kepler in his thoughts.

Notes:

• Neils Henrik Abel proved that quintic equations couldn’t be solved with radicals.
• It is claimed that Carl Friedrich Gauss found the sum of the integers 1 + 2 + 3 + … + 100 at an early age by recognizing that there were 50 pairs, each pair adding to 101.
• John von Neumann proved the minimax theorem.
• John Horton Conway did a lot of work in combinatorial game theory.
• Johannes Kepler’s engagement to Barbara Müller almost fell apart while he was finalizing Mysterium.

And, of course, there is this old gem:

A mathematical horse was able to learn arithmetic, algebra, and even Euclidean geometry. But no matter what the trainer tried, the horse just couldn’t master analytic geometry. Moral: You can’t put Descartes before the horse.

2 × 5 Hottest Mathematicians

The WordPress admin page lets me know what terms folks are searching for when they find the MJ4MF blog. This past week, one explorer was looking for “very attractive mathematicians.” It occurred to me that I had nothing to offer this person. Well, let’s rectify that immediately!

I considered posting a list of the 10 Hottest Mathematicians, but I decided not to intermingle boys and girls. There are (at least) two good reasons for keeping them separate. First, my selection method is completely arbitrary, and without objective criteria, I’m not sure how I’d determine whether a man is more attractive than a woman. I mean, I know my preference, but that doesn’t really seem fair. Second, there’s an issue with population sample — there have been far more male mathematicians in history, and a mixed-gender list of the 10 Hottest Mathematicians would undoubtedly have only one or two women.

So instead, here are two separate lists, one of the hottest female mathematicians, followed by a list of the hottest male mathematicians. The lists are, of course, entirely subjective, and I welcome an open debate on the subject.

Hottest Female Mathematicians

Danica McKellar (1975 – )

Yes, I know I’m gonna catch grief for including her on this list. But (a) she’s beautiful, (b) she’s the McKellar in the Chayes-McKellar-Winn theorem, which appeared in a paper she published as an undergrad, and (c) her Erdos number is 4. If you still don’t like her inclusion on this list, then protest by refusing to look at the picture below. (Yeah, right — I double dog dare you to look away!)

Anneli Cahn Lax (1922 – 1999)

She was a gifted mathematician and a first-rate student, but could her beauty have been another reason she was Richard Courant’s only female student?  

Sofia Vasilyevna Kovalevskaya (1850 – 1891)

I’m sure the first female with a full professorship in mathematics in Northern Europe made her male students’ hearts flutter.

• Image of Kovalevskaya

Hypatia of Alexandria (370 – 415)

A woman with truly classical beauty, Hypatia is believed to be the first woman to write about mathematics.

• Image of Hypatia

Sophie Willock Bryant (1850 – 1922)

In addition to an impressive mathematical career, this minister’s daughter published works on Irish history, religion, and philosophy. She was also a rugged outdoorswoman with a penchant for mountain climbing.

• Image of Bryant

Hottest Male Mathematicians

Renato Caccioppoli (1904 – 1959)

With classical European good looks, Caccioppoli was “one of the most interesting and charming mathematical figures of the 20th century.” Perhaps he is all the more attractive because he was so intriguing. A movie about the events leading to his eventual suicide (Morte di un Matematico Napoletano) won seven awards and was nominated for an eighth.

Donald C. Spencer (1912 – 2001)

A former chair of the math department at Princeton once described Spencer as “the most attractive mathematician in America.” Admittedly, he didn’t have much competition for the title in the mid‑1950’s, but who I am to argue with a former chair of the Princeton math department? 

Evariste Galois (1811 – 1832)

This striking young Frenchman had good looks a-plenty. But if that’s not enough for you, how about this? He died in a duel defending the honor of his love. Many women (including my wife) thinks that’s downright sexy.

• Image of Galois

Andrew Wiles (1953 – )

I’ve heard several women refer to him as “an adorable dork.” Bonus points for proving Fermat’s Last Theorem.

• Image of Wiles

Carl Friedrich Gauss (1777 – 1855)

Admittedly, he didn’t age well — but he was quite a looker in his younger years, and his brilliance shone brightly till the end of his days.

• Image of Gauss

Notable and Quotable

Some of my favorite quotes by and about mathematicians:

I like your results. Let’s make it a joint paper, and I’ll write the next one. – Stefan Bergman

Someone told me that each equation that I included in the book would halve the sales. – Stephen Hawking

Amusement is one of the fields of applied mathematics. – W. F. White

The total number of Dirichlet’s publications is not large; jewels are not weighed in a grocery scale. – C. F. Gauss

Any astronomer can predict with absolute accuracy just where every star in the heavens will be at 11:30 tonight. He can make no such prediction about his teenage daughter. – J. T. Adams

Math Clocks

Jiminy. The folks at Clock Zone make a math class wall clock — and I would like to be the first to publicly chastise buy.com, amazon, and anyone else who is selling it. It contains at least two mathematical errors:

SPOILER ALERT: In my rant below, I identify the errors in the clock. If you’d like to identify them for yourself, don’t read any further.

I say “at least” two errors because there may be more. The obvious errors are for 9 (the expression assumes that the exact value of π is equal to the common approximation 3.14) and for 7 (because the equation is quadratic, x = 7 is only one of the answers; the other possible answer is x = ‑6).

More generally, I have an issue with any of the algebraic equations that are meant to represent integers. For instance, the equation 50/2 = 100/x has solution x = 4, but I believe that it is incorrect to say that the equation itself is equal to 4. So perhaps the clock has four errors, if you consider the algebraic equations for 4 and 10 to be erroneous, as I do.

This clock is meant to be a math joke. Edward de Bono in The Mechanism of the Mind (1969) suggested that when a familiar connection (such as seeing the numerals 1‑12 on a clock) is disrupted, laughter occurs as a new connection (seeing mathematical expressions instead of numerals) is made. Sadly, math jokes are supposed to make you laugh… yet this clock makes me want to cry.

To ease the pain, I did a little research and uncovered several clocks of famous mathematicians. I present them here for your enjoyment.

Leonardo da Pisa:

Kenneth Appel:

Rene Descartes:

Karl Friedrich Gauss: