If we had 20 MW to run the brain, we could devote some of it to solving unimportant problems. But we only have 20W, and we have to use it carefully. Maybe it’s the 50% of students at MIT, Harvard, and Princeton who got the answer wrong who really are the smartest.

Just as a climate model with noise can produce types of weather that a model without noise cannot produce, a brain with noise can produce ideas that a brain without noise cannot produce. And just as these types of weather can be exceptional hurricanes, the idea could end up winning you a Nobel Prize.

So if you want to increase your chances of achieving something amazing, I recommend that you go for a walk in the countryside, watch the clouds, listen to the birds sing, and think about what you could eat for the having dinner.

## So, could computers be creative?

Will computers ever be as creative as Shakespeare, Bach or Einstein? Will they understand the world around us as we do? Stephen Hawking has warned that AI will eventually take over and replace humanity.

However, the best-known advocate of the idea that computers will never understand the way we do is Hawking’s former colleague Roger Penrose. In making his assertion, Penrose invokes an important “meta” theorem in mathematics known as Gödel’s theorem, which says that there are mathematical truths that cannot be proven by deterministic algorithms.

But you also need to allow yourself enough time each day to do nothing at all, relax, and let your mind wander. I tell my research students if they want to be sure.

There is a simple way to illustrate Gödel’s theorem. Suppose we make a list of all the most important mathematical theorems that have been proven since the time of the ancient Greeks. First on the list would be Euclid’s proof that there are an infinite number of primes, which requires a really creative step (multiplying the supposedly finite number of primes and adding one). Mathematicians would call it a “trick” – shorthand for a clever, succinct mathematical construction.

But is this trick useful for proving important theorems further down the list, like Pythagoras’ proof that the square root of two cannot be expressed as the ratio of two integers? This is clearly not the case; we need another trick for this theorem. Indeed, as you go through the list, you will find that a new trick is usually needed to prove each new theorem. There seems to be no end to the number of tricks mathematicians will need to prove their theorems. Simply loading a given set of cheats onto a computer will not necessarily make the computer creative.

Does this mean that mathematicians can breathe easy, knowing that their work will not be taken over by computers? Well maybe not.

I argued that we need computers to be noisy rather than fully deterministic, “bit-repeatable” machines. And noise, especially if it comes from quantum mechanical processes, would break the assumptions of Gödel’s theorem: a noisy computer is *not* an algorithmic machine in the usual sense of the term.

Does this mean that a noisy computer can be creative? Alan Turing, the pioneer of the general-purpose computing machine, believed it was possible, suggesting that “if a machine is meant to be infallible, it cannot also be intelligent”. That is to say, if we want the machine to be intelligent, it better be able to make mistakes.