MOST SMALL-BUSINESS EXECUtives only think they have to climb mountains to succeed, but Tom Holzel really does it. In August, Holzel, founder and president of Arcturus Inc., a privately held computer-graphics firm in Concord, Mass., will be high in the Himalayas on a personal mission to solve Mount Everest's greatest mystery.

The mystery is whether two lost British climbers, George Mallory and Andrew Irvine, were the first to scale the highest point on earth -- almost three decades before Sir Edmund Hillary's famed ascent. The remains of the two Brits have never been found.

Mallory and Irvine tackled the 29,028-foot peak in the manner of English squires. They climbed in tweed jackets, puttees, fedoras, and scarves. Their provisions -- carried in picnic hampers by 100 mules -- included champagne and quail.

Holzel's team will trace Mallory's 1924 route all of the way, using space-age gear such as an oxygen system that will keep the climbers at the equivalent of sea level. Based on Holzel's research and the word of a Japanese climber who, in 1979, said he spotted "an English dead" in very old clothing, Holzel expects to find Irvine's body on a snow terrace at 27,000 feet. He theorizes that Irvine turned back while Mallory, who was stronger, climbed on. Mallory, in fact, was last seen within 750 feet of the summit before clouds obscured him. Holzel thinks that Mallory may have reached the top before he died.

Using special metal-detection gear, Holzel will search for a Kodak camera that Mallory carried with him on the ascent. Holzel plans to develop the film "at altitude." Kodak technicians believe the film, frozen now for 60 years, may yield recognizable images. Will it show pictures that Mallory took from the summit?

Holzel's company has sales of $4 million a year. To run Arcturus for the three months he's on Everest, Holzel hired William J. Brown, a marketing vice-president with experience at several other computer firms, and turned the daily operating responsibilities over to him right away. Brown will take charge for good if the worst happens: in this century, one out of every 15 climbers in the Himalayas has died.

Holzel is spurred by his interest in history. "An amateur historian wants to know what happened," he says. "That's what I want to know. What happened to those guys? How close did they get?"

Mallory went for a different reason. In his oft-quoted words, he climbed Everest "because it's there."