# Fun with exams

For the fun of it, the last problem of my take-home recent take-home Advanced Calculus exam read

Problems from a liberal arts Advanced Calculus exam:

(a) Spell Weierstrass.

(b) For whom is the Cauchy Criterion named?

(c) Cite an anecdote of dubious authenticity explaining how Bernhard Placidus Johann Nepomuk Bolzano got his name.

Here are some of the responses

• (b) The “Cauchy Criterion” is named after two Frenchmen named Frank Crashi and Louis Kohppy. Frank, being the greedy one, wanted his name first, but after realizing that would leave them with the “Cra-ppy Criterion” they went for the “Koh-shi Criterion” instead. As for the spelling, well, who knows how the French spell anything?
• (b) Leonhard Euler had a couch with the not so creative name “Couchy,” though it was spelled it “Cauchy” because he was Swiss. Regardless, this was a talking couch that was well versed in analysis. Believe it or not, a great number of Euler’s theorems were ghost written by this couch. However, the “Cauchy criterion” was one of the few results Couchy received credit for.
• (c) Karl and Bernhard were working one day and discovered that every bounded, infinite set of real numbers has at least one accumulation point. When it finally sank in for Bernhard he went totally Bolzano.
• (c) My Bolzano’s got a first name it’s B-e-r-n-h-a-r-d.
My Bolzano’s got a second name it’s P-l-a-c-i-d-u-s.
My Bolzano’s got a third name it’s J-o-h-a-n-n.
My Bolzano’s got a fourth name it’s N-e-p-o-m-u-k.
I’d accumulate it every day and if you ask me why I’ll say
Weierstrass had his way with B-o-l-z-a-n-o.
• (c) Bernhard Bolzano got his name one day from his mathematical buddies while out camping. He was drunk and thought it would be funny if he acted out a nursery rhyme, specifically Jack and the Candlestick. The second jump over the campfire he tripped and landed with his crotch on the campfire. History knows him as Bernhard Bolzano, but his friends knew him as Bernhard Bolzano Campfire.
• (c) A young Berhard Eulke (pronounced “eulke”) had an ongoing debate with a young Leonhard Euler about how Euclid prounced his name. Charles Eulke claimed it was pronounced “you-clid” while Euler contended it was pronounced “oi-clid.” This got Eulke to thinking: he did not want to go down in history with his name always being said wrong. So he changed his name to something no one would have the bolzanos to mispronounce.
• (c) Bernhard Placidus Johann Nepomuk was the first to refer to a neighborhood as a ball. His contemporaries thought this was ridiculous so they started to refer to him as “Bolzano,” which is Italian for balls.
• (c) When the Bolzanos learned they were going to have a son, Mrs. Bolazno got the idea to name the child Berndard, after her husband. When it was time for the baby to be born, mother wanted a middle name for the child, eventually deciding on Placidus Johann Nepomuk Bolazno. When the husband asked his wife about all the middle names the mother replied, “I still not 100% sure who the father is, so I added all their names.”

Once upon a time there lived a young Bohemian boy whose mother had a very, very bad sense of humor. It was so bad, in fact, that she named her young son Anonys, which of course literally means “without a name.” She found this rather funny, but it became a source of great embarrassment for the boy, even though most of his peers were too uncultivated to get the joke. All his young life, Anonys wished for a real name, which he figured would solve all his problems. He eventually reached an uneasy acceptance of his name by making people call him Ano for short.

Ano wanted to be educated, so he studied mathematics. When Ano was in college, he took an Advanced Calculus class taught by a notoriously eccentric and bad-natured Polish professor named Norbert Komplexify, who happened to be the great-great-great-half-step uncle of a modern math professor of the same last name. One day, Prof. K announced that the mid-term exam would be a take-home test. He proceeded to lay down a list of rules concerning what could be construed as cheating, which he ominously entitled The Doctrine of the Doomed. He warned that any breaking of the Doctrine was punishable by unspeakable atrocities.

Well, Ano was a good man bound by his faith in God, and so he set out to complete the exam while following in strict adherence to the viciously restrictive rules set out by Prof. K. Soon, however, it became clear that the exam was impossibly difficult. Ano spent two entire days and nights working on the exam, forsaking sleep, food, and all earthly comforts, and still the exam was not finished. Ano began to suspect that evil work was afoot. Ano cautiously asked some of his classmates if they too had found the exam difficult, and they all agreed that Prof. K must indeed be the Devil himself to have contrived such a hideously confusing and bitterly time-consuming exam.

As a matter of fact, Prof. K. was not the Devil, although it was true that Old Scratch had in fact written the exam. Unbeknownst to his students, Prof. K. was in regular communion with Beelzebub, and had in fact purchased the exam from the Devil for a price consisting of the blood of seven virgins and a case of Heineken. (Incidentally, Prof. K. found the Heineken far more difficult to procure than the blood of the virgins, since the Heineken brewing company would not be founded for another 70 years. But he was a man of many devious resources, and he eventually secured the full asking price for the exam.) As Ano grew increasingly frustrated with the exam, his faith began to waver. “How,” he called to Heaven, “could God allow such an abomination as this exam? A righteous God would surely save me from this misery. Have I not suffered enough injustice, living all my years without a real name?”

Well, we’ll never know if God heard him that day, but the Devil certainly was listening, and he saw his opportunity. Lucifer came to Ano and made a deal. Lucifer said, “I will give you enough answers for you to get a passing grade. In return, you will have to go through life with an even dumber name than the one you have now.” Ano, in his weakened and desperate state, reluctantly agreed, secretly believing that there was no way the Devil could come up with a worse name than the one he already had.

The next week, when the exams were returned, Ano learned that he was the only student who had passed, and Prof. K. expressed his wrath toward Ano accordingly. Prof. K. was furious that Ano had somehow managed to pass, since he had gone through so much trouble to ensure that every student would fail. Prof. K. became convinced that Ano had cheated, and had broken the Doctrine of the Doomed set forth at the start of the exam. The good professor therefore called for an interrogation which was to be performed in front of the entire school, in which Prof. K. hoped to force the truth from young Ano. None of the other professors really wanted to come to the interrogation, but they all feared Prof. K. and his association with the Prince of Darkness. The interrogation was grueling and lasted for hours. Eventually, Ano cracked and let on that he had purchased the answers from the Devil. “But in my defense,” he proclaimed, “there was nothing outlined in the Doctrine that explicitly forbade assistance from Satan.”

Prof. K. was outraged that he had made this grievous oversight, but he could not argue with Ano. In his arrogance, he had assumed that he alone had the power to communicate with Satan, and had left out a rule against getting answers from the Devil. So in resignation, Prof. K. hissed, “Well, you’ve got a hell of a lot of balls, Ano, but you’d better watch your back.”

Unfortunately for Ano, the Devil was present at the interrogation, posing as a slightly deaf local reporter, and he was ready to take what Ano owed to him. Old Scratch gleefully recorded the young man’s name as Balls Ano. The name was published in the newspaper the next day, and it stuck. After a few years, “Balls” Ano got sick of explaining his nickname, and decided he’d just change the spelling to Bolzano. In the end, he didn’t really mind because now at least he had a real name.

In later years, Bolzano became regretful of his dealings with the Devil, and he eventually made up four other names for himself to cover up the name created by Satan. He continued to study mathematics under the ridiculously extravagant name of Bernhard Placidus Johann Nepomuk Bolzano. He later went on to develop what is now known as the Bolzano-Weierstrass Theorem.

As for Prof. K., he was really pissed at the Devil for double-dealing, and decided he would write his own exams from now on, thank you very much. As a result, he went insane trying to develop an even harder take-home exam for his next year’s advanced calculus class. He spent the rest of his life locked up, raving about convergence theorems and scribbling epsilons all over his cell walls.

Note: The contents of this account are based on historical facts and should not, therefore, be construed as any form of hostility or aggression toward any of the descendants of the esteemed Norbert Komplexify, though a certain amount of annoyance regarding the length and difficulty of a particular exam may or may not be implied.

I’m not sure if I should be flattered or offended. Or, at the very least, be more discrete about my Faustian test-writing arrangement.