Conrad Anker, member of the Mallory - Irwine expedition 1999, who was the first to have found Mallory's body, has published an article about the event in the National Geographic Magazine, October 1999. Here below we quote only a small part of the article where the question whether Mallory was the first to have reached the Everest top is discussed.

Had Mallory been the first person to stand on top of the world? From what we found with his body and from the difficulties I experienced myself in climbing his route to the summit, I think it's highly improbable, for the following reasons:

• The route is too tough. When Mallory and Irvine were last seen, they were somewhere near the Second Step, a 90-foot-high wall of rock at 28,300 feet. Two weeks after finding Mallory's body, I tried to free climb this sheer wall much as Mallory would have, avoiding a ladder left in 1975. I found it extremely difficult, even with crampons and modern rock-climbing techniques. Climbing roped together without attaching any gear to the rock - standard procedure in their day - would not have gotten Mallory and Irvine up the Second Step.
• Their gear and supplies were insufficient. Without crampons for secure footing and fixed ropes to guide them and aid their descent, Mallory and Irvine would have had to have been superhuman to have summited. Their oxygen apparatus was heavy and prone to malfunction. And their lack of adequate food and drink would have slowed them down and increased their chances for mistakes.
• The timing was off. They were climbing late in the day. If they had made it to the summit, they would have had to bivouac in the open. But Mallory's nose and fingers were not swollen and discolored by frostbite, which leads me to believe that they did not spend the night outside before dying. To me Mallory's missing gloves are a crucial clue. Having turned back above the First Step, Mallory may have taken off his gloves to grip the steep rock as he descended. I think he probably slipped and pulled Irvine off a ledge. The frayed rope still tied to Mallory's waist may have been cut by an edge of rock, sending him tumbling to the snow terrace, then sliding farther to where I found him.