"We were 18 years old, ready to live life," said Brown, who became his friend's caregiver, staying by his side at New York City's Rusk Institute after the 1985 accident.
But just six weeks after he had helped raise $25,000 for his friend's new foundation, Brown himself suffered a cruel twist of fate. He, too, was paralyzed after diving into the surf on a Club Med vacation in Martinique. It was Jan. 2, 1988, a bit more than two years after Heumann's accident.
Brown said that he quite literally "saw the light" when he shattered his neck. The undertow threw him head-first against the ocean floor.
"I heard it snap," he said. "I was under water two or three minutes holding my breath to survive. But I thought this was it."
He never lost consciousness and remembered from his friend's accident not to be jostled, so he refused a ride in the bumpy ambulance until he could be airlifted to the hospital. En route, he said he quoted lines from the comedy film, "Fletch" -- "It's all ball bearings."
Just short of his 21st birthday, he lost the use of his legs, but not his sense of humor or his drive.
Today, at 45, Brown says he is doing what he has always done best: facing a challenge.
"There's no ego here -- we're building an army," said Brown, who is director of public impact for the Reeve Foundation. "Spinal cord injuries don't discriminate. In one split second my life changed."
Heumann now sits on the board of the Reeve Foundation.
An estimated 5.6 million Americans live with some form of paralysis, according to Centers for Disease Control and Prevention, and most, like Brown, were injured when they were young.
The Reeve Foundation has become the "hub" of most of the research and advocacy for those who suffer from paralysis. It is named for the actor Christopher Reeve, who was injured in a horseback riding accident and died in 2004. His wife, Dana, worked with him and chaired the foundation; she died in 2006.
Spinal cord research is "painstakingly slow and expensive," according to Susan Howley, executive vice-president of research at the Reeve Foundation. And there are never any quick fixes.
But this is a pivotal time in research and more is being done to improve quality of life and independence for those who are paralyzed.
"It's actually a phenomenally interesting and exciting time in the field of spinal cord research," said Howley. "The old dogmas haven't really been overturned for a very long time."
As recently as two decades ago, an injured adult was never expected to recover. Today, scientists are discovering activity-based exercise or locomotor training that can "remind" the spinal cord how to step and stand again, she said.
But being wheelchair-bound is only part of the medical, psychological and financial challenge of a spinal cord injury.
Depending on the severity of the injury, the yearly expense for treatment can be anywhere from $300,000 to nearly $1 million, according to The University of Alabama National Spinal Cord Injury Statistical Center and the Centers for Disease Control and Prevention.
The lifetime cost of caring for a 25-year-old can range from $1.5 to $4 million.