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Since switching from mathematics to biology a little more than two decades ago, Green has witnessed—and has contributed to—a profound transition in biology. Biology used to be one of the least quantitative of the sciences. Its practitioners sought explanations for biological phenomena, whether the behavior of organisms or the interactions of molecules. Most did not need to couch those explanations in mathematical terms or draw on mathematical ideas to arrive at their conclusions.
That has changed. “Phil and I used to go for long walks when we were both associated with Collaborative Research,” says Lander. “Back then, we wondered if there was a need for mathematics in biology. In the mid-1980s, there weren’t a lot of data. Biology was about analyzing the notes in your lab book.
“In the last 20 years, biology has become dominated by huge data sets. Now it’s an exception rather than the rule to publish a paper that does not draw on large databases of biological information. Mathematical analysis has become a fundamental part of biological research. It has turned out to be of equal importance to experimentation.”
The role of mathematics in biology is only going to grow, say Lander, Green, and other quantitatively oriented biologists. As researchers continue to probe genomes for information, and as they begin to build models of biological systems, computer programs and equations will become as common as glassware and pipettes. “There’s a new generation of 21st-century explorers in biology,” Lander says, “and their tools for exploration are computers and mathematics.” 
Photos: Brian Smale
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Modern research calls on biologists to be fluent in analytical methods.
Max Delbrück, the physicist-turned-biologist who became a founding father of molecular biology, often told his students that “if you have to use statistics to interpret your experimental results, they can’t be true.”
That statement wasn’t meant to denigrate the power of mathematics, former colleagues say; it was simply an attempt to provoke students into designing clear-cut experiments. Nevertheless, the remark shows how far biology has come since the mid-20th century, when Delbrück began grappling with the field’s big questions. Researchers today are increasingly using statistics and other analytical tools not just to interpret their results but to arrive at them.
In an essay published last year in PLoS (Public Library of Science) Biology, Joel E. Cohen, a population biologist at the Rockefeller University, called mathematics “biology’s next microscope.” In the coming years, he wrote, mathematics will “reveal otherwise invisible worlds in all kinds of data” just as early microscopes first revealed the microbial and subcellular worlds. Further, Cohen asserts, the explosive pace of biological research will spawn new branches of mathematics just as physics stimulated the development of calculus.
“We’ve gotten so much better at using experimental tools to study complex systems,” says Charles F. Stevens, an HHMI investigator at the Salk Institute for Biological Studies, “that now we need mathematical approaches to make sense of it all.”
“The old way of doing things was that you kept everything fixed, changed one variable, measured one other variable, and then got the relationship between them,” Stevens says. “But now the kinds of questions we’re asking and the kinds of experimental abilities we possess are leading us to measure many things simultaneously, and we just have to have techniques for analyzing and thinking about the data.”
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