What is the ruling on climbing Mount Everest, taking into consideration the statistics indicating that approximately 300 people have died out of 14,000 climbing attempts?

The fundamental principle is the permissibility of engaging in sports, including mountain climbing, unless it leads to a religiously forbidden outcome, such as exposing oneself to perdition, or squandering wealth without benefit, or extravagance and wastefulness. Otherwise, it would be religiously prohibited. And the presumption of seeking fame and renown through it is religiously blameworthy. As for showing off (riya') in matters other than acts of worship, it is seeking status, and it can be permissible, blameworthy, or an act of obedience, depending on the intended purpose.