So, what do these two great athletes have to do with Formula One? The answer is nothing directly but both achieved greatness in their sport, were knighted and are still revered to this day.
Significantly, they relied on their physicality to achieve that greatness, whereas, while F1 drivers need to be physically fit because of the G-Forces and the energy required to hold the car on the track, as well as enduring two hours of driving, at breakneck speed, they rely on their machinery to win a race and a championship.
Bannister and Walker relied on their physical fitness and strength to succeed, just as Sir Ed Hillary and Sherpa Tenzing Norgay needed the same when conquering Everest in 1952.
Schumacher and Hamilton, and all the world champions before them, have relied on the best racing car possible to achieve their success.
Would Schumacher have succeeded had he not been in a Ferrari that dominated F1 from 2000 to 2004, or Hamilton in the Mercedes that has dominated F1 since 2014?
The answer is probably not to the same degree.
After equalling Schumacher's record total of 91 grand prix wins, by winning the Eifel GP at the Nurburgring, a record of wins he has since increased to 94, Hamilton admitted he doesn't like comments that it was the car and not him that accounted for his success.
"It's not always nice to hear, but I'm not mad at it," he told The Race.
"What I do know is that those that often say those things or make those comments, they just don't know. And I think in general in life, we often can sometimes give the wrong opinion on something when we don't have the full facts. And we don't have the full knowledge of how it really is."
Although the late Ayrton Senna was Hamilton's hero, he raced against Schumacher for three seasons and replaced him at Mercedes when Schumacher retired for a second time at the end of 2012.
"Years ago, I remember when they talked about Michael, turning Ferrari around," Hamilton said. "The fact is it's not one individual. I have not turned Mercedes around. Michael did not turn Ferrari around - as much as I love Michael and he is a legend, it wasn't just him."
"I think the thing with a driver like Michael, and I, our job is to kind of be the rudder. I think there's something that the computer can't simulate. And that's feel, that's yaw, that's the feeling of the car turning and pitching and all these different things,"
"We all have these tools. It's how you use them, how you apply them, do you let your ego get in the way? There are some people that just won't listen, because sometimes you can't see the wood for the trees," he added.
Mercedes boss Toto Wolff, says comments about Hamilton not being the greatest because he is driving the best car, are unfair.
Three-time world champion Sir Jackie Stewart is one who has said Hamilton in his opinion isn't the greatest of all time [GOAT], because he has been in the best car.
Stewart says Juan Manual Fangio was the greatest, because he won his five titles in four different makes, namely Alfa Romeo, Maserati, Damler-Benz (Mercedes-Benz) and Ferrari, but adds the proviso that you can't compare different eras.
"Winning races and winning championships is always a team exercise in this sport, but you need to put yourself in a position that you end up in the best car," Wollf says.
"You can see lots of talents and skilled drivers took the wrong decisions, or not well-advised decisions, and in that respect it was him who joined Mercedes in 2013 and it is him that sits in the car and is able to execute on track with the tools that we provide to him, but it's always the two that are part of this."
"We couldn't achieve the records that we have [without him] and he probably couldn't achieve the records [without] the right car, and full stop."
Wolff says the drivers who say it is the car should try and analyse why they haven't found their way into a Mercedes.
Nico Rosberg got into a Mercedes three years before Hamilton, with Schumacher as his teammate for three years, and beat him. He lost the driver's title to Hamilton in 2014 and 2015 but beat him in 2016 to become world champion and then promptly retired. He knows what it takes to beat Hamilton, and also knows what Hamilton is achieving.
"No-one would have ever thought that Michael Schumacher's titles would be equalled or broken, and yet now he's there," Rosberg told Sky Sports.
"I think it's not only one of the best and successful Formula 1 achievements but it's one of the greatest achievements in sporting history as a whole."
So does Rosberg think that makes Hamilton the GOAT?.
"I'm not going to say here and now say one is better than the other, I think they're there or thereabouts. You'd mention Schumacher, you'd mention Senna, you'd mention Fangio. I would probably filter out those four-Lewis, Senna, Fangio and Schumacher. Who's the best?"
"It's just impossible to say but equally in their own way they've all been just unbelievable."
Former Mercedes executive director Paddy Lowe, says Hamilton's latest victory after qualifying sixth in the Turkish GP on a slippery track, compared to teammate Valtteri Bottas having six spins, being lapped by Hamilton and finishing 14th, should silence Hamilton's critics.
"Taking the race, it was pretty clear he made the difference in that car," Lowe said.
"Yes, it's a good car, but if you compare him to his teammates, and you compare him to the mistakes of many other great drivers in that race, then he produced a perfect performance."
"There are many great drivers who you might say have made a major contribution with their own talent, and they've won championships, single championships, but to win seven requires a very special consistency and endurance."
World Champion in 1996, Damon Hill doesn't consider Hamilton's success is all down to having the best car.
"It is a lot easier if you have the best car, I will say that having had the best car at one time in my career," Hill says.
"But they don't give you the best car forever and in my case, I didn't stay with my team - they probably thought I wasn't worth giving the best car to (any more). With Lewis, they're tripping over themselves to keep him in the car."
"Mercedes have nabbed him at the start of their development as a team because they knew he was the best driver."
After his Turkish victory, Hamilton said: "I want more of these weekends. More tricky conditions like this."
"The more opportunities like this, the more I'm able to show what I'm able to do. And today hopefully you can see ... I think I deserve more respect. I think I have that with my peers, they will know how hard today is, particularly that it is not a car thing."
One of his peers is McLaren driver Carlos Sainz, who will join Ferrari next year.
"I agree with Max [Verstappen] that 90 per cent would probably win in the Mercedes, in the race and qualifying, but if you put half of the field against Hamilton in a Mercedes, then 90 per cent of them would not beat him."
The debate as to whether it is Hamilton or the car that makes the difference may never end, but will it now be "arise Sir Lewis Hamilton"?
Hamilton says when he thinks about that honour, it is "about those unsung heroes, and I don't look at myself as an unsung hero".
He points to people like his grandad who served in the war, or Sir Captain Tom "who got knighted and waited 100 years for that incredible honour" plus "people that are running hospitals, the nurses and the doctors who are saving lives during the hardest time ever."
"I've not saved anybody," he added.
Sir Jackie Stewart was knighted in 2001, three decades after retiring from F1, but he thinks Hamilton deserves to be knighted, noting "he's a seriously topline sportsman in the world and that's a wonderful thing to have."
There is no mention of the Mercedes car in that statement.
