You can’t find secrets without looking for them. Andrew Wiles demonstrated this when he proved Fermat’s Last Theorem after 358 years of fruitless inquiry by other mathematicians — the kind of sustained failure that might have suggested an inherently impossible task.

Pierre de Fermat had conjectured in 1637 that no integers a, b, and c could satisfy the equation + c” for any integer n greater than 2; he claimed to have a proof, but he died without Writing it down, so his conjecture long remained a major unsolved problem in mathematics.

Wiles started working on It in 1986, but he kept it a secret until 1993 when he knew he was nearing a solution. After nine years of hard work, Wiles proved the conjecture in 1995. He needed brilliance to succeed, but he also required faith in secrets. If you think something hard is impossible, you’ll never even start trying to achieve it. Belief in secrets is a practical truth.

The actual truth is that there are many more secrets left to find, but they will yield only to relentless searchers. There is more to do in science, medicine, engineering, and technology of all kinds. We are within reach not just of marginal goals set at the competitive edge of today’s conventional disciplines but of ambitions so great that even the boldest minds of the Scientific Revolution hesitated to announce them directly.

We could cure cancer, dementia, and all the diseases of age and metabolic decay. We can find new ways to generate energy that free the world from conflict over fossil fuels. We can invent faster ways to travel from place to place over the planet’s surface; we can even learn how to escape it entirely and settle new frontiers. But we will never learn any of these secrets unless we demand to know them and force ourselves to look.

The same is true of business. Significant companies can be built on open but unsuspected secrets about how the world works•. Consider the Silicon Valley startups that have harnessed the spare capacity all around us but are often ignored. Before Airbnb, travelers had little choice but to pay high prices for a hotel room, and property owners couldn’t quickly and reliably rent out their unoccupied space. Airbnb saw untapped supply and unaddressed demand, where others saw nothing at all. The same is true of private car services, Lyft and Uber.

Few people imagined that it was possible to build a billion-dollar business by simply connecting people who want to go places with people willing to drive them there. We already had state-licensed taxicabs and private limousines; only by believing in and looking for secrets could you see beyond the convention to an opportunity hidden in plain sight. The same reason that so many internet companies, including Facebook, are often underestimated—their very simplicity—is an argument for secrets. If insights that look so elementary in retrospect can support important and valuable businesses, there must remain many great companies still to start.

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