Before Matt Centrowitz headed off to college in the early 1970s as one of the fastest milers in the nation, his high school track coach, Brother Bielen, gave him a piece of advice.

“When you get married and have children, put your medals away,” Centrowitz recalled Bielen telling him. “Trust me. There is no better feeling than a child surpassing their parent.”

Several decades later, at the Rio Olympics, Centrowitz celebrated with a mixture of shock and joy as his son, Broadneck High graduate Matthew, became the first American since 1908 to win Olympic gold in the 1,500 meters.

In a recently published book, “Like Father, Like Son: My Story on Running, Coaching and Parenting,” Centrowitz, along with co-authors Nathan Williams and Chris Kwiatkowski, chronicles his own running journey from growing up fatherless in the Bronx to becoming an improbable high school running phenom, befriending track legend Steve Prefontaine at Oregon, qualifying for two Olympic teams, and then, finally, watching his son win an Olympic gold medal.

Centrowitz, 62, spoke last week with The Post about his book between his duties as the cross-country and track and field coach at American University, where he has been since 1999.

This interview has been edited for clarity and length.

Why do you think Bielen’s advice on not displaying your medals is important?

“I’ve found a lot of Olympic champions, their dads smother them to some degree with their accomplishments. They probably meant it as advice slash encouragement, but I think it becomes a wall you have to get through or get over. I think I kept that out of the way so [my children] could develop at their own pace and not have to compare themselves to their father.”

One of the big themes in the book is fatherhood. You had a contentious relationship with your own father. How much did that impact how you wanted to treat your children?

“I knew I wanted to be involved. … But a lot of things I didn’t say in the book. In some areas, this hole was left in me because I was fatherless, but I met a lot of kids where their fathers were in the way. I realized I was better off without one than having a pain-in-the-ass one. There were advantages that I was able to maneuver myself and motivate myself and these [other] kids didn’t have a chance to breathe. Even though the parents loved them, they were still controlling, they were condescending, and whatever [the kids] did wasn’t good enough.”

You didn’t get to compete at the 1980 Moscow Olympics after winning the 5,000 at the U.S. Olympic trials because of the U.S. boycott. Do you feel that Matthew’s gold medal helped you complete your Olympic journey?

“I would say definitely not in the first couple of weeks, but now I do feel that way. [Laughs] The first couple of weeks is all about him, and him achieving it is him and Coach Alberto Salazar and his teammates being part of the Nike Oregon Project — Nike believing in him so much, advertising him so much. I thought about everybody who won during this and invested their energy in him, too. Then I thought about myself last.”

Now you can bask in that glory yourself a little bit, right?

“Yeah, definitely. It took several weeks or maybe a couple of months to feel that way, to be honest with you.”

You dedicated one chapter to Steve Prefontaine, a running legend who resonates with runners of all ages. What did you learn from him?

“I think the way he attacked the races. He was a ferocious competitor that way. Sometimes he wasn’t in top, top shape, but he still went out and attacked the race. I was startled sometimes by just how ferocious he could attack a race. And [even if] the conditions weren’t perfect, he would still go out and give one hell of a performance. He’d give his all for the crowd. The crowd responded, and he’d feed off it. It was a great thing to watch at Oregon, especially at Hayward Field when the fans and him got together and they made it work. It was awesome.”

What would you like the readers to take away from the book?

“Basically, if I had to pick one thing, it’s obviously you’ve got to have fun with the sport. It’s a sport, number one. Not everybody is going to be that successful. I think we can all be successful, given our best. The principles that are in there, you find some balance in your life, you find balance in your training. These are important factors for a successful person, whether you want to be a successful parent, successful businessman. … When I was back East working, it was just work, work, work, and when I went out to Oregon, it was a lot of joy there, and it was a refreshing view of the sport of track. It was something that I never experienced before, and I still enjoy it to this day.”