There is a difference between Ramanujan and a bus ticket collector. Series matter, and bus tickets don't.
If I had to put the recipe for genius into one sentence, that might be it: to have a disinterested obsession with something that matters.
An obsessive interest in a topic is both a proxy for ability and a substitute for determination.
An obsessive interest will even bring you luck, to the extent anything can.
Chance, as Pasteur said, favors the prepared mind, and if there's one thing an obsessed mind is, it's prepared.
The paths that lead to new ideas tend to look unpromising. If they looked promising, other people would already have explored them.
Darwin couldn't turn it off. Neither could Ramanujan.
They didn't discover the hidden paths that they did because they seemed promising, but because they couldn't help it.
That's what allowed them to follow paths that someone who was merely ambitious would have ignored.
What rational person would decide that the way to write great novels was to begin by spending several years creating an imaginary elvish language, like Tolkien, or visiting every household in southwestern Britain, like Trollope? No one, including Tolkien and Trollope.
The bus ticket theory is similar to Carlyle's famous definition of genius as an infinite capacity for taking pains.
It's more promising if you're creating something, rather than just consuming something someone else creates.
It's more promising if something you're interested in is difficult, especially if it's more difficult for other people than it is for you.
In many different areas, reward is proportionate to risk.
If that rule holds here, then the way to find paths that lead to truly great work is to be willing to expend a lot of effort on things that turn out to be every bit as unpromising as they seem.
It's not merely that the returns from following a path are hard to predict.
They change dramatically over time.
1830 was a really good time to be obsessively interested in natural history.
If Darwin had been born in 1709 instead of 1809, we might never have heard of him.
What can one do in the face of such uncertainty?
One solution is to hedge your bets, which in this case means to follow the obviously promising paths instead of your own private obsessions.
But as with any hedge, you're decreasing reward when you decrease risk.
Interest is much more unevenly distributed than ability.
The bus ticket theory also explains why people are less likely to do great work after they have children.
Here interest has to compete not just with external obstacles, but with another interest, and one that for most people is extremely powerful.
It's harder to find time for work after you have kids, but that's the easy part.
The real change is that you don't want to.
The most exciting implication of the bus ticket theory is that it suggests ways to encourage great work.
If the recipe for genius is simply natural ability plus hard work, all we can do is hope we have a lot of ability, and work as hard as we can.
But if interest is a critical ingredient in genius, we may be able, by cultivating interest, to cultivate genius.
For the very ambitious, the bus ticket theory suggests that the way to do great work is to relax a little.
Instead of gritting your teeth and diligently pursuing what all your peers agree is the most promising line of research, maybe you should try doing something just for fun.
And if you're stuck, that may be the vector along which to break out.
What are the most important problems in your field, and why aren't you working on one of them?
If you could take a year off to work on something that probably wouldn't be important but would be really interesting, what would it be?
The bus ticket theory also suggests a way to avoid slowing down as you get older.
Perhaps the reason people have fewer new ideas as they get older is not simply that they're losing their edge.
It may also be because once you become established, you can no longer mess about with irresponsible side projects the way you could when you were young and no one cared what you did.
The solution to that is obvious: remain irresponsible.