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Reinventing Discovery - Michael Nielsen [1]

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is to pushing a car.” Just 37 days after the project began Gowers announced that he was confident the polymaths had solved not just his original problem, but a harder problem that included the original as a special case. He described it as “one of the most exciting six weeks of my mathematical life.” Months’ more cleanup work remained to be done, but the core mathematical problem had been solved. (If you’d like to know the details of Gowers’s problem, they’re described in the appendix. If you just want to get on with reading this book, you can safely skip those details.)

The polymaths aren’t standing still. Since Gowers’s original project, nearly a dozen Polymath and Polymath-like projects have been launched, some attacking problems even more ambitious than Gowers’s original problem. More than 100 mathematicians and other scientists have participated; mass collaboration is starting to spread through mathematics. Like the first Polymath Project, several of these projects have been great successes, really driving our understanding of mathematics forward. Others have been more qualified successes, falling short of achieving their (sometimes extremely ambitious) goals. Regardless, massively collaborative mathematics is a powerful new way of attacking hard mathematical problems.

Why is mass online collaboration useful in solving mathematical problems? Part of the answer is that even the best mathematicians can learn a great deal from people with complementary knowledge, and be stimulated to consider ideas in directions they wouldn’t have considered on their own. Online tools create a shared space where this can happen, a short-term collective working memory where ideas can be rapidly improved by many minds. These tools enable us to scale up creative conversation, so connections that would ordinarily require fortuitous serendipity instead happen as a matter of course. This speeds up the problem-solving process, and expands the range of problems that can be solved by the human mind.

The Polymath Project is a small part of a much bigger story, a story about how online tools are transforming the way scientists make discoveries. These tools are cognitive tools, actively amplifying our collective intelligence, making us smarter and so better able to solve the toughest scientific problems. To understand why all this matters, think back to the seventeenth century and the early days of modern science, the time of great discoveries such as Galileo’s observation of the moons of Jupiter, and Newton’s formulation of his laws of gravitation. The greatest legacy of Galileo, Newton, and their contemporaries wasn’t those one-off breakthroughs. It was the method of scientific discovery itself, a way of understanding how nature works. At the beginning of the seventeenth century extraordinary genius was required to make even the tiniest of scientific advances. By developing the method of scientific discovery, early scientists ensured that by the end of the seventeenth century such scientific advances were run-of-the-mill, the likely outcome of any competent scientific investigation. What previously required genius became routine, and science exploded.

Such improvements to the way discoveries are made are more important than any single discovery. They extend the reach of the human mind into new realms of nature. Today, online tools offer us a fresh opportunity to improve the way discoveries are made, an opportunity on a scale not seen since the early days of modern science. I believe that the process of science—how discoveries are made—will change more in the next twenty years than it has in the past 300 years.

The Polymath Project illustrates just a single aspect of this change, a shift in how scientists work together to create knowledge. A second aspect of this change is a dramatic expansion in scientists’ ability to find meaning in knowledge. Consider, for example, the studies you often see reported in the news saying “so-and-so genes cause such-and-such a disease.” What makes these studies possible is a genetic map of human beings that’s

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