Cambridge - The old joke in the field of meganumerology is that it’s not the size of your numbers, but how you use them that counts. But one budding mathematician believes that you need to find the largest numbers before you are able to use them. So Mathew Frederin, Masters student of mathematics at MIT devised a contest to find some suitable numbers to study.
“My real interest is trying to find out which of two numbers is bigger, which isn’t as easy as it sounds when you are dealing with numbers on this scale”, explained Frederin. Finding a novel thesis topic in mathematics isn’t easy either, but thanks to a late night of drinking and playing math games with classmates he came upon the difficulties of determining the relative values of these meganumbers.
“I figured that there must be a systematic method for stratifying these numbers,” Frederin said. “But when I looked through the literature, it looked pretty bare.” Now that he had a thesis topic, he needed a way to gather data. “Computer generated numbers were predictably easy to categorize. So, I needed to find a human source for these numbers, written in the wide spectrum of mathematical notation used to create these numbers.”
The students and faculty at MIT were an obvious resource and at his adviser’s suggestion, created a contest. The rules are simple: Within 15 seconds contestants write on an index card English words or mathematical notation a single whole number that is less than infinity. The highest number gets the $1,000 grand prize with $500 and $250 going respectively to the second and third place winners.
“I sent out grant applications everywhere for the prize money,” said Frederin. “I never knew that the Department of Defense was that interested in the math contests.”
Contestants shouldn’t expect instant gratification for their 15 second effort. “Although it depends on the number of contestants, I fully expect it to take over a year to go through all of the cards and write proofs for the top finishers to discern which is the largest. This is my thesis project, after all.”
Inspiration - http://www.scottaaronson.com/writings/bignumbers.html
2 Comments:
It looks like the contest rules were changed.
http://www-tech.mit.edu/V126/N64/64largenumber.html
I can win a largest number contest if we are allowed only a certain number of digits. For example, let's say that the rules are: Make the largest number you can using only two digits and any mathematical operations you know. Mathematical operations do not count as digits. Any number used as a power does. Your number may not be eqal to infinity and the ∞ sign may not be used.
I would respond to this challenge like this: [(9!^9!)!]!. That is nine factorial raised to the power of nine factorial facorial factorial. A rather impressive number using only two digits, huh? But of course, there are more advanced mathematical operations and notations that I don't really know much about that could make a larger number, but most people (not the most mathematically inclined) might put 9^9. In fact, I know some people who would ignore the part about power and put 9*9, and even some people who would ignore that and the part about mathematical operations and just put 99. I would definately win in that case.
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