Similarly, researchers found that in hospitals, the radiologists who ended up with the most desirable networks were the ones with the highest performance nine months earlier. And in banks, star performers attracted bigger networks and were more likely to maintain those ties. Achievements don’t just help us make connections; they also help sustain those connections.

Not long ago, I watched a colleague try to climb the ladder of success solely through networking. For a few years, he managed to meet increasingly influential people and introduce them to one another. Eventually it fell apart when they realized he didn’t have a meaningful connection with any of them. Networking alone leads to empty transactions, not rich relationships.

It’s a lesson I’ve learned in my own career. I once emailed an entrepreneur I admired and got nothing in response. Some months later he contacted me out of the blue, with no memory that I had tried to get in touch before. He had attended a talk I gave and wanted to meet — now he had proof that I could add value.

My students often believe that if they simply meet more important people, their work will improve. But it’s remarkably hard to engage with those people unless you’ve already put something valuable out into the world. That’s what piques the curiosity of advisers and sponsors. Achievements show you have something to give, not just something to take.

Sure, you can fire off cold emails to people you respect — they’re just a click away — but you’ll be lucky if 2 percent even reply. The best way to attract a mentor is to create something worthy of the mentor’s attention. Do something interesting, and instead of having to push your way in, you’ll get pulled in. The network comes to you.

Sociologists call this the Matthew effect, from the Bible: “For unto every one that hath shall be given, and he shall have abundance.” If you establish a track record of achievement, advantages tend to accumulate. Who you’ll know tomorrow depends on what you contributed yesterday.