Before Melanie Wood, a Princeton doctoral student, talked about creativity in math in Ward 1 on Tuesday night, she shared a rather humorous experience.
"When I meet new people and tell them I'm a mathematician or a mathematical grad student, I get a lot of different responses," Wood said. The responses ranged from an incredulous "So do you come up with new numbers?" to "Do you study, like, Calculus 9?" to what she called the most frequent response by far: "I can't even balance my checkbook."
Wood dispelled many of the reactions.
"Despite having an excellent calculus teacher, calculus is my least favorite part of mathematics, and if that was all there was to math, I wouldn't be doing math," she said. "Also, I've never actually balanced my checking account. ... I make my boyfriend balance it for me."
Wood, who in 2003 became the first woman to win the Morgan Prize, the nation's top honor in mathematics for undergraduate research, has found that people who ask these questions have had bad experiences with math. They associate math with working out equations and formulas, she said, and since they tend to have such trouble with taxes and balancing their checkbooks, they can't even fathom the rigor of something like "Calculus 9."
But the only sarcastic response, "So do you come up with new numbers?" is actually the most appropriate, Wood said.
"Ironically, these people have actually stumbled onto a much more appropriate response to the fact that I'm a mathematician," she said.
Wood specializes in the theory of numbers.
"I am very interested in the idea of coming up with new numbers," Wood said, adding that numbers have historically been invented by practical people for practical purposes.
Zero is one example, she said. Early man had already invented numbers to count possessions, but there was a problem, Wood said.
"Some mom says to her son, 'Go count how many rabbits are out in the back field so we know what we'll use for dinner,'" but there was no way for the son to communicate that there weren't any rabbits, she explained. "It wasn't that he couldn't count, it was just that he needed a new number, a number that wasn't there," Wood said.
Increasingly complex numbers have been invented, Wood said, often for totally mundane situations. They include negative numbers for overdrawn bank accounts and fractions to divide contested things into equal parts. Even irrational numbers such as pi and the square root of two have had humble applications, such as measuring the diameter of trees or the diagonals of fields.
"People ... discovered these [new numbers] in response to problems and needed solutions to those problems," Wood said. And this leads to the overall role that mathematicians play, she said. They focus on "solving 'open' problems, and inventing new mathematics ... inventing new numbers, new shapes ... [and] new criteria that you can apply [to those problems]."
Open problems symbolize the constant nature of mathematics, as they are quandaries that remain unproven even today. Open math problems abound and encompass innumerable scientific fields. There are "as many [open problems] as there are books that haven't been written," Wood said.
Some of these open problems could lead to dollar signs. The Clay Mathematics Institute of Cambridge has allocated $7 million in prize money to those who can prove seven of the most significant open problems, known as the Millennium Problems.
Tackling open problems requires a creative mind, Wood said, which makes mathematicians more akin to novelists than people might think. While students learn math in an entirely formulaic, predictable manner, Wood said, successful problem-solving actually requires many of the skills needed to write an essay.
"I would say that mathematics is an open field very much in the way literature is an open field," Wood said.
Wood explained that people who think all numbers have already been invented are like those who assume all words have been too.
"These people are wrong about words in the same way they're wrong about numbers," Wood said. People create new words to express new ideas and inventions, and mathematics follows the same path, she said. "When we come across new mathematical phenomena, we develop new numbers to describe what's going on."
Wood's appearance at AU was co-sponsored by the Mathematical Association of America, The American Statistical Association, Women and Mathematics and the Association of Women in Science.
