Written in the form of a dialogue between a man in a nursing home and his grandchild, this short story describes an undergraduate research project that produces a surprising answer to one of the most famous open problems in mathematics.
| Contributed by
Sonja Dezman
Sam has to do a report for school. She asks her grandfather what is he proud of. He tell her than when he was young he studied mathematics. He tries to explain what he did. She follows him with the help of Interface — something that she has in her head. Grandfather tells Sam (Kasman tells us) a few things about prime and even numbers. We learn that even numbers can be written as a sum of two prime numbers. [Note: The preceding sentence needs mathematical qualifications. Every even number greater than 4 which has been checked has been found to be a sum of two prime numbers. Whether this is true in general is a famous open problem in mathematics that goes by the name of Goldbach's Conjecture. -ak] Grandfather was working with a professor who was a genius. They tried to answer the question: “Is it always true that an even number is the sum of two primes?”. The story is fictional, but that doesn't mean that it is not important. I think that that the message behind this story is that what may look stupid, not important, and useless now, may be very important and useful at some other time. It also says: “don't underestimate your work and your abilities”! In the story there is also a small but quite interesting part that describes the professor as a genius. It says:”…you could look in his eyes and see flashes from all of the brain activity. He was nice too, very quiet and friendly, not at all stuck up”. It's a wonderful description! Another thing worth mentioning is the use of metaphors (to present abstract mathematics). Instead of saying imagine a 3-dimensional space, a vector bundle, etc. Kasman uses beautiful metaphors. Abstract mathematics could scare us, we would stop reading the story because we wouldn't understand it. Well, in this story, Grandfather says: “Picture a donut”. OK, I (we) can do that. “Imagine that on this donut at each point there is a hair coming straight out of it”. No problem, we can imagine that. “now let's say that the hair are called number lines”. OK, still no problem with that. “When the hair are glued together we get a line bundle”. It goes on and on until we know everything that we need to know. The connection between a donut with hair and mathematics is amazing. I would never had thought of that.
The story is educational, explanatory and fun.
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The Goldbach Conjecture, that all positive even integers are the sum of two primes, is one of the most famous open problems in mathematics. This is not because it is especially important but rather because it is relatively simple to state and yet apparently very hard to prove. Fermat's Last Theorem held a similar status until it was proved in the 1990's by Andrew Wiles and Richard Taylor. For now, it is still completely unknown whether it is true that every even number greater than four is the sum of two primes. Nobody knows how to show it is always true and nobody knows a case in which it does not work. Vector bundles are real mathematical objects and it is conceivably possible that someone could prove Goldbach's conjecture by showing that there is always a vector bundle of rank 2n on a torus that is the direct sum of two vector bundles of prime rank. However, I have no reason to think that such a proof exists; this is pure fiction
BTW: It was never my intention that this story be performed as a play. However, since it was only the words that the characters say -- and not any description of their actions, surrounding or situation -- which convey the story, I found it easier to write it in the form of a dialogue, with each character's "lines" just indicated by their name.
| Contributed by
Tina S. Chang
This story starts slow but picks up when the nurse enters the room. Having it written as a play is a bit discombobulating. Nevertheless I strongly recommend the reader who likes math to go on: the story picks up as soon as the math begins and the ending is great. The description of vector bundles is excellent. The story describes a rare instance where an undergraduate could really do some important mathematics.
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