Alex Smith is 36. He has made more than $173 million in an NFL career that is entering its 16th year. He has a right leg that, less than two years ago, was so badly broken and infected that doctors worried about saving his life, then saving his leg, in that order. Now he intends to play football.

“The guy’s got just incredible mental toughness,” said Greg Roman, his offensive coordinator for a time in San Francisco.

“Just one of the fiercest competitors I’ve ever been around,” said Kyle Whittingham, an assistant at Utah during Smith’s college days.

“He has always had this incredible determination,” said Gordon Wood, Smith’s coach in high school, nearly half his life ago.

Roman inherited Smith when many 49ers fans wanted him run out of town, having failed to live up to the hype that comes with being the first overall pick in the NFL draft. Instead he signed an extension to stay, lost his job to Colin Kaepernick en route to a Super Bowl, yet complained not once. Whittingham watched Smith deal with a new coaching staff led by Urban Meyer, get beaten out for the starting job, yet remain at Utah and become a Heisman Trophy finalist. Wood remembers taking the job at Helix Charter High outside San Diego — where Reggie Bush was already in the backfield, a star in the making — and having an assistant coach say, “We could be pretty good if we could just find a quarterback,” when Smith was right there on the roster.

Which is to say: Smith is steadfast and unwavering, and he has overcome obstacles before.

Now, let’s be clear about a few things: Developing into an excellent high school quarterback when you were once overlooked or hanging in there with Meyer’s Utah staff to get the starting job after an injury and becoming the winningest quarterback in school history or not fleeing from the challenge in San Francisco when most regular people might have sought a fresh start — none of those compare with what Smith is attempting now. Those are all normal athletic adversities. Overcoming them neither makes Smith unique nor means he will ever take a snap in an NFL game again.

“This is like another whole level of determination,” Wood said.

What this process reveals, though, is something of Smith’s character. He simply does not have to do this. Not for money. Not to prove anything to anyone — other than himself.

“I do go back to the challenge in life,” Smith told ESPN’s Scott Van Pelt during a “SportsCenter” interview in May, before he was even cleared to practice. “I got this great big challenge in front of me, and I don’t see how I could turn my back on it.”

Which is not something everybody else would say, not an approach most people would take. But here’s what people who have worked with Smith in the past say: He is not everybody else. He is not most people.

That showed in high school.

“They said: ‘He’s gangly. He’s not real strong. His arm’s weak,’ ” said Wood, who played for Smith’s father, Doug, in high school and at Wyoming, where Smith’s uncle John L. was an assistant. “And that was all true because he was in such a growth spurt. But one of the things I knew right away because I knew the whole Smith family and what kind of people they are: You just knew he was going to be a tough kid and that mentally he was going to be very strong.”

That showed in college.

“He was there three years, and he graduated in three years,” said Whittingham, now Utah’s head coach. “Not everyone can do that. And as far as football smarts go, he was off the charts. Off the charts. As good as I’ve ever seen.”

And it showed in the pros.

“They were ready to run him out of there on rails,” Roman said. “He could’ve left, and he decided to stay, which I thought was incredible. Most people would have just got out of there immediately, but he stayed. Just day in and day out, the guy is a special guy. Such high character.”

In so many ways, what Smith is going through isn’t about the Washington Football Team and its depth chart. He could well end up on injured reserve. He might be more likely to be in the front office than on the field.

Rather, what Smith is going through is about the human spirit. Starter or sub? Make the team or get cut? The result doesn’t matter as much as the effort put in. The trying — that’s what counts.

“When you get closer and closer to it, I think it just fuels it even more,” Smith told reporters via Zoom last month, after he returned to team workouts. “ … I think it’d be like running a marathon and getting close to the end of the race. I think even more of that competitiveness kicks in, and I want to see if I can do it.”

Which leaves the people who knew him back when, who watched him overcome obstacles that are trivial by comparison, say almost in unison and verbatim: “If anyone can do this, it’s Alex.”

“What I think people are doing is they’re looking at how most all of us would be like,” Wood said. “We wouldn’t do it. But what he sees is the thing that’s going to hold him accountable. I don’t know this, but I think he’s thinking, ‘This is what’s going to get me the most healthy for the rest of my life.’ He’s very, very intelligent.”

After he arrived in Washington following a trade from Kansas City in the spring of 2018, Smith played all of 10 games with his new team before the hit against Houston broke his leg and then nearly cost him his limb and his life. Ten games isn’t enough for a fan base to know how its quarterback deals with success or failure. Ten games, in Smith’s case, was enough to suffer a devastating injury, and when he could finally walk again, a former first-round pick had his old job.

That’s the business of football, which is cruel by nature. And yet Smith’s story is already a success story.

“I’m sure he can see the impact on others — to never give up,” Wood said. “He wants to model that behavior. Even if I don’t make this happen, I’m going to be shooting for the stars. He sees that he’s a role model.”

That will be true if Smith somehow plays in the NFL again. But it’s true even if he walked off the practice field today and said, “I’m done.” Smith’s attitude — not a peep, not a complaint, just doing the work — is behavior we all could model.

And so Dwayne Haskins is the starting quarterback for the Washington Football Team. It makes sense that when the season starts a week from Sunday, Kyle Allen would be the backup. And yet by far, Washington’s most intriguing quarterback is Alex Smith.