This page is a work in progress. We invite alumni to record some of their memories of the Ross Program, and to fill in missing information in the stories already posted.

## Ross Quotes or *bon mots*

### Recorded in 1970:

- Think deeply about simple things.
- This is food for thought.
- By the end of the summer you will be haggard but happy.
- Even the teacher needs encouragement.
- In proving something, it is not unreasonable to make use of the hypothesis.
- The greatest common divisor is the greatest, common, divisor.
- An approximation to 5 is any number other than 5.
- I am the only one in this room that has the right to make numerical mistakes, and I take full advantage of that right.
- We are always limited by our experience.
- When you arrived here, your view of arithmetic was like that of an experimental physicist: One fact was as good as any other.
- The “negative of c,” or “minus c,” but never “negative c.”
- Our greatest enemy is comfort.
- This is one of the most beautiful and important theorems of number theory.
- We are here because of a common
*weakness*for mathematics, not, as they write in the newspaper, a common strength.

Dr. Ross told many stories about his experiences in life. Many of those stories were repeated often and seemed designed to make a clear point. That point was usually: Don’t give up. Perseverance pays off.

Some of those stories are incorporated in the long post on Ross History.

Some stories were told only once or twice. One of them was the **Michelson anecdote:**

In the late 1920s a lecture at the University of Chicago was given by Nobel Prize winning physicist A. Michelson, who was famous for his 1887 measurements (with E. Morley) of the speed of light. Since the title of that lecture was “The philosophy of light,” the large lecture room was packed with many philosophers as well as scientists. Students (including Ross) had to sit on the floor in the aisles. The distinguished old lecturer began by apologizing for a secretary’s misunderstanding: the correct title was “The velocity of light.” Michelson then gave a technical talk about recent work refining his earlier measurements. Philosophy professors in the audience were unable to escape.

## Stories about Arnold Ross.

**Prologue.**

When was Dr. Ross’s Prologue written? For several years, we thought it first appeared at the German version of the Ross Program in the 1970s, but in 2002 an earlier copy was found (probably from the 1950s). The document posted here is an edited version, composed by Daniel Shapiro and David Pollack around 2005. The original Ross *Prologue* was less focused and was apparently intended for beginning math teachers who are thinking about the best ways to teach young students.

**The Reduced Inventory game.**

For many years this game of axioms in set theory was available only as “Chapter II” in mimeographed copies of Dr. Ross’s unpublished book *Towards the Abstract*. I conjecture that his book project grew out of the program for math teachers that Ross ran at Notre Dame from 1947 to 1963. Many years later that chapter was published as a separate article: Towards the Abstract, in a 1978 issue of *Mathematical Spectrum*.

The game starts with a list of about forty true statements about sets, involving union, intersection, complement, empty set, and universal set. The basic rule of this game is: A statement may be removed from the list if it can be proved from the remaining statements on the list, using standard rules of logic. Successively cross off as many statements as you can. The remaining statements form our list of axioms, sufficient to prove all the original statements. One purpose of this game is to make clear that a particular list of axioms for a theory is a matter of taste rather than an essential feature of the mathematics.

In some years in the 1960s, Ross students were asked to play this game and write down their lists and proofs. A prize (a number theory book) was given to the student with the shortest list of axioms. This is a wonderful exercise, but the minimal list of axioms depends on what exactly are accepted as “standard rules of logic.”

**String tie?**

When did Dr. Ross begin wearing a string tie rather than a cloth tie? One story says that Ross was on a driving trip through the Southwest, saw some string ties, and realized how much easier they are to put on and take off.

## Stories about the Ross Program and its participants.

[as recalled by D. Shapiro]

**Pet beetles.**

In 1966 the Nosker House dormitory was new and Ross students were the first group to live there. The OSU crews had not used much insecticide that summer and many black beetles crawled on the outside of the building. Those beetles were harmless, less than an inch long, and moved fairly slowly. Bob Tax, one of the best students that year, took a liking to those beetles. He captured a few, named each one Ambrose, and kept most of them in an empty coffee can. He would occasionally take one or two to class in a pill bottle, and let it out on his arm or face, nudging the person next to him to witness how cute it looked. In his room, if we were quiet, we could hear them scrabbling away on the bottom of that metal can. For dinner Bob would drop in one Frosted Flake and we would listen to the beetles chewing it. A few people, including a couple of counselors, were disgusted by the Ambrose situation, much to Bob’s delight.

**Knibbling.**

I first learned about knibbling (the “k” is not silent) at the Program in 1966. Get a metal coat hanger, pull on the straight part to get a bend in the middle, and place the hanger on your index finger with the hook part at the bottom. After some adjustment of the end of the hook, you can balance a penny there. Swing the hanger back and forth with increasing amplitude, until you get the hanger (with penny) to go completely around several times. Then slow it down, get it back to swinging, and finally to stop, all without dropping the penny. Learning to do this took some practice, and pennies tended to fly off the hanger at inconvenient times. The Program record was reached when one student managed to knibble a stack of seven pennies without dropping any.

The Program had to pay for the resulting damage to the ceilings in Nosker House.

**Microwaving a watch.**

Each dorm room was equipped with a combination refrigerator/microwave unit. One summer day in 1999, a first-year student (not named here to protect the innocent, but we’ll call him Eric) wondered what would happen if he microwaved his plastic watch. Putting thought into action, Eric got a quick answer to his question: The digital display bubbled and glowed as it rotated, and then noxious colored smoke billowed out, spreading quite a stench. Someone called 911, a fire truck arrived, and the dormitory was evacuated until the smoke cleared. The next day’s riddle: What’s the difference between someone making popcorn, and Eric?

Answer: One watches the microwave, while the other microwaves the watch.

Since then Program leaders tell students: Be careful what you microwave!

## Origin of Ross Program T-shirt design.

Theodore Allen attended the Ross Program in 1978. He is currently a physics professor at Hobart & William Smith Colleges. Here is an edited version of a message he sent in 2005:

“I have been doing calligraphy since the early 1970s. At the Ross Program in Chicago in 1978, Matthew Wiener convinced me to write up a proof of quadratic reciprocity in Gothic lettering. We went downtown and found a silkscreen maker who made us a screen of the proof. We made T-shirts for any students who brought us a shirt.

Several years later, when I was a TA at Caltech (in 1986 or 1987) I saw that Glenn Tesler, one of my students, was wearing a version of that T-shirt! The lettering had gotten ragged on the edges but was still recognizable as my design. Glenn was very surprised to learn that I had done the artwork for the shirt.”

The Ross Program re-started in Columbus in 1979. Only a couple of people continued on from the Chicago program, and one of them had a QR shirt. The counselors arranged to photocopy the lettering from that shirt and got a local T-shirt store to create new Ross shirts. Within a year or two, the QR shirt became a symbol of the Ross Program.

A couple of years later, some counselors decided to redo the lettering because the photocopy process was fuzzy. I think Daishi Harada wrote new calligraphy for the shirt in the same style as before. Perhaps Megumi Harada was also involved with writing that design. That version of the shirt was used for several years. Some time in the early 1990s, Debbie (one of the Ross secretaries) typed up the QR proof using a Gothic font and we used that version. Unfortunately, an error was introduced, with (-1)^{(p-1)/2}(-1)^{(q-1)/2} instead of the correct expression. Those “mint error” T-shirts are now rare and probably valuable.

In 1996, for Dr. Ross’s *Ninetieth Birthday Conference*, someone designed artwork for the back of the shirt, with “Ross Mathematics Program” in an arch at the top and “Think Deeply of Simple Things” across the bottom.

In May 2007 Megumi Harada was kind enough to re-calligraph the T-shirt design, both front and back, in preparation for the Ross Program’s *Fiftieth Anniversary Celebration*. Current T-shirts use that version.

**Z hats.**

For one of the reunions (probably in 2001) we realized that the local T-shirt printing company also offered baseball caps with custom designs. We decided that a capital Z in “blackboard bold” was a great symbol to use, since it stands for the set of integers. Since then the Z-hat has been available for alumni to make a definite fashion statement.

Another aspect was also involved with this design. The “completion” of a ring R is a larger ring typically designated by the R with a caret on top, and the caret symbol is often called a hat. Then Z-hat (in LaTeX: $\widehat{\mathbb Z}$ ) is the completion of Z, equal to the inverse-limit of all factor rings Z/nZ. Around 2005 Karl Zipple always wore his new hat, explaining: “I just don’t feel complete without my Z-hat.”

## Entertainment by the counselors.

In the late 1960s, the counselors had evening story times. They read aloud to the students, typically a short story or some interesting poetry. This task was assigned to counselors on a rotating basis. One of the most memorable of those events was the time Mike Anderson read “The Hunting of the Snark” using a different voice for each character.

Even in the early years there was a Talent Show in which Ross Program participants entertained the whole group with performances of various types. Groups of students sometimes performed imitations or parodies of the counselors and instructors, with varying success.

In 1967 (or 66), Mark Bolotin was instrumental in writing a “comical musedy” in the style of *My Fair Lady*, with number theoretic topics in the songs. For instance, the “Rain in Spain” song became “The GCD is just the GCD”.

A parody of “Try to Remember” song from the Fantasticks included the line: “Try to remember the symbol Legendre, it does not work when q’s composite.”

At a more recent Talent Show, in 2012, Ravi Fernando juggled different sorts of objects. The most memorable object was a Rubik’s cube that he solved while juggling. He has posted a YouTube video of this feat.

## Stories about the Program’s instructors and administrators.

Father **Ivo Thomas** (1912 – 1976) was a highly cultured person, with a deep knowledge of the classics, religion, and mathematical logic. His obituary describes his interesting background and career. He was a professor of classics at Notre Dame, but he taught logic at the Ross Program every summer from 1959 to 1974. Students in Father Thomas’s classes learned that “detachment” is “implication”, and used Polish notation to study various aspects first order logic and modal logic, often with named formulas like “Scotus” and “Tarski.”

We found a good photo of Father Thomas from those days. (We hope to post it here soon.)

Ivo Thomas changed quite a bit in the late 1960s. As the Ross Program group photos show, he wore a suit with a priest’s backward collar in 1966, changing to a regular suit a couple of years later, and then to less formal clothes. In 1972 he was released from priestly duties and married a female colleague at Notre Dame.

In 1967 Father Thomas was apparently asked by Dr. Ross to stop by the dorm and interact with the kids. He showed up one evening and proceeded to teach several of us various string tricks (similar to Cat’s Cradle). We learned how to twist a loop of string into Jacob’s Ladder, Seagull, Fishies, Pyramid, Whale, Vanishing Pear, Two Ptarmigan, etc. The practice of those string figures became a Ross Program tradition for several years.

**Harold Brown** was a math faculty member at OSU and Assistant Director of the Ross Program during the late 1960s. We found a photo of Brown from those years. (To be posted here.) In the early 1970s he made some changes in his life, getting a toupee, a motorcycle, and a divorce. He quit his academic position and becoming a computer scientist associated with Stanford University.

**Hans Zassenhaus** taught *Experimental Number Theory* at the Ross Program for several years in the 1960s and early 1970s. He and Jill Yaqub also collaborated on teaching a course in projective geometry, but Zassenhaus sometimes fell asleep in the back of the room while Yaqub was lecturing. We didn’t joke too loudly about that.

**Kurt Mahler** taught courses in the geometry of numbers at the Program during the late 1960s. He was a professor at Ohio State for several years in the 1970s, and then moved to the Australian National University. He was short and stout, often wore a hat and a dark suit, and used a thick cane to help him walk. (He appears in the Ross group pictures in 1969, 1970, 1971, and 1973.) Mahler had a German accent and used old German script letters as his mathematical symbols when lecturing. He seldom erased anything, getting nearly to the end of the chalkboard just as the bell would ring to end class.

Mahler was a camera buff and took lots of photos wherever he went. He spoke Chinese, and during one quarter at OSU I remember that Mahler taught a graduate course on “mathematical Chinese.”

**Gloria Woods** started working closely with Arnold Ross after his program moved back to Ohio State in 1979. In the 1980s she handled most of the Program’s administration and dormitory supervision, because Arnold was so deeply involved with his wife Bee’s illness.

Gloria grew up in Brooklyn and attended an arts high school with few math requirements. She had planned on a career involving art (mostly water colors). Some years later, at the urging of a boyfriend, she attended a “Moore Method” topology course at a math graduate program at the University of Miami (Florida), and she loved the mathematical ideas. She moved to the math graduate school at the University of Michigan around 1956 – 1958, meeting interesting mathematicians there like Raoul Bott and Steve Smale. Later she transferred to math grad school at Tulane University in New Orleans, where she met Alan Woods, who was a postdoc there. They married and Alan was hired in 1963 by Arnold Ross, who had just become chair at Ohio State.

When asked how she got started at a math graduate program, and why she moved from one math graduate program to another to another, she would reply with a smile: “Oh. You know . . . Boyfriends.”

At the urging of Dr. Ross, Gloria pursued a doctorate in math education and graduated in 1981 with a PhD dissertation that analyzed the teaching methods in the Ross Program.

## Ross Program Jokes

Official Memo: Readjustment to Civilian Life, a document that was probably distributed in 1966.

Riddle: What do integral rabbits eat?

(Lattice.)

**Numberwacky**, by Jordan Pollack (1973):

T’was summer, and the problem sets grew harder and harder on the brain.

Quadratic reciprocity can make one go insane …

**Auto JC**, a flow chart that can substitute for an actual Junior Counselor.

## Games

Wall ball ?

Game of “Mod Ten” ?

Game of 24 ?

No mention was made of Conrad races.