Advanced Summer Program for students age 11-14
who show high promise and love mathematics

Message of Executive Director to Alumni

Address delivered by the Executive Director at the closing ceremonies in MathPath 2006

July 29, 2006
University of California
Santa Cruz, CA

Parents, students, staff, and faculty:


This is my annual opportunity to thank people and to lecture to the future mathematicians and scientists on social conduct.

First, I wish to thank Professor Stephen Maurer who has been in the pit with me organizing MathPath 2006 for you. Would you all stand and acknowledge the great professor? [Pause] We are also grateful to Professor Zeitz for helping in many ways, including his inspection visits to locate the camp here this year. I like to acknowledge and thank Mr. Kip Sumner, the Director of the camp, for another year of the wonderful camp. [Pause] I acknowledge and thank the staff headed by Mr. Larry Evans, the volunteer teachers, and our great professors. I thank the University, the helpful staff of the Conference Services, and [Pause] the Mathematics Department for the sponsorship that reduced our cost of this beautiful place.


I would like to coin a new word for this occasion. And that word is “contragenial.” I propose it as the opposite of congenial. Congenial is the adjective of congeniality - the coordination of behavior and cooperation to mutual benefit. The word, congenial, is from Latin [ com – together + genialis – belonging to the genius or fostering spirit]. Congenial means affable, agreeable, amiable, accordant, good-tempered, pleasant, sociable, warm, welcome, compatible, congruous, and consistent. Congenial is what ought to go with you – the genial. ......... Congeniality is clearly not a quality possessed by all. And the absence of congeniality in a genial person often exhibits as a chip on the shoulder. You, by virtue of your higher mental power and industry, will inevitably rise in life and have co-workers and underlings. But if you are not congenial, you will make life difficult for yourself. Since you will become great in life, you will not have people telling you often that you are not congenial. They will often bear it – bear the burden of your discordant behaviour.

Having a chip on one’s shoulder, thinking and behaving as though one is too eminent to be accordant, is not logical. You see, you have one pronounced quality – being good at mathematics. And even that, while it should make you proud, should not delude you into thinking that you are too great to be pleasant to the coworker – especially your underlings. Almost everyone possesses some quality or virtue in a greater measure. Further, ability is like an infinite rod. The extent of your ability has but a finite measure as a portion of this rod. The measure of the ability you do not have is infinite. In this, everyone on earth is equal to you.

Being affable and sympathetic is logical, for what you have is given to you by people. Your very existence and its maintenance. People brought you to this world, people bring you food, people built your dwelling and its comforts, and one day people will bury you. It is all about people. So not being congenial is illogical.

The antonym of congenial is uncongenial. So why would I coin the word contragenial? It is to remind you not to confuse uncongeniality with being genial. How? In mathematics, what does contrapositive mean? The contrapositive of “A implies B” is what? You have been at MathPath for four weeks. Who in the front row can tell us? [Student: NOT B implies NOT A]. Good! Let us consider this statement: A person lives in New York implies the person lives in the USA. The contrapositive is this: A person does not live in the USA implies the person does not live in New York. You have learned that a statement and its contrapositive are equivalent. Why? An Inference Rule of Propositional Logic, which is the beginning part of the mathematics of mathematics, says “A implies B” is equivalent to the statement ((Not A) or B). That is both “A implies B” and ((Not A) or B) evaluate to the same truth value for any assignment of the truth values T or F to the variables A and B. [Pause] But if “A implies B” and ((Not A) or B) are equivalent, then “Not B implies Not A” is equivalent to what? [ A student in the third row: B or ( Not A)] …Yes! But (B or (Not A)) equals ((Not A) or B) which equivalent to “A implies B”. A mathematician proves the contrapositve if it is easier to prove than proving the direct statement.

So, in mathematics, the contrapositive of a statement is equivalent to the original statement. But in English language, contrapositive, being the adjective of contraposition, means an opposite position like in contradistinction. So your math should not confuse you into thinking “contragenial” to be genial. Contragenial is not equivalent to genial or congenial. Contragenial is being ill-tempered, inconsiderate, and unsociable. Being contragenial is being uncongenial.

Three years ago we had a student from Romania. On this occasion at the closing ceremonies of that camp I called you MathPathians. [ Mr. William Meyerson, the graduate student camp counselor, interrupts and says, “It was two years ago.”] ………… There is this beautiful mountain range called the Carpathian Mountains, straddling Romania and Czechoslovakia. Dr. Samuel Johnson, the great 18th century English moralist, essayist, and lexicographer, wrote a wonderful short essay titled “The Vulture” about a bird that nested in the Carpathian mountains. Being so fond of the great Doctor and wanting to acknowledge the good graces of the Romanian student who attended that camp, I then called MathPath alumni, MathPathians. ………. I want the MathPathian to stand out among people by their natural congeniality.

At times you will find it difficult to be congenial - when someone irks you by action or words and your tempers are roused. But do not act on your temper - it will pass quickly like a summer storm. I would ask you to be gentle to the person. Do not fight. Go with the flow. Soon all will be well. Ruth Ginsberg, Justice of the US Supreme Court has said, " It is important to be a good listener, but it also pays to be a little deaf." Deaf to irksome words and numb to the minor injuries done to you.

In the 21st century, some people cushioned frustration by using indecorous words. I want the MathPathian not to use such words, for it is the insecure people who need to use indecorous words. I want more. You see, the vast majority of the peoples of the world inhabit what I call "belief-prisons." They can not escape the prisons of their beliefs - whatever it be. Having or seeing no prospect for advancement they make their beliefs a cause to give up even their lives for. For it gives them the only illusory prospect of life advancement. But you are smart. If you could use a belief sanctuary, I propose this - DO NOT HURT ANYBODY FOR ANY REASON! It is called Nonviolence.


I have no doubt that you will rise in life by sustained work. American education may not be the best in the world, but Americans are the most creative of peoples at this time in history. Let the world make things, but we create the ideas that produce the products. This is what you have inherited and this ….I ask you to foster even as congenial people going forward from MathPath.

I thank your wonderful parents for sending you to MathPath 2006. I now bid farewell to you. But it is just the beginning. Stay in touch with each other either directly or through the Alumni Forum on the website. And write me when you need me. I will reply you promptly as I do to your great parents.
May the future be happy for you!

-- George Rubin Thomas


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