While technically your statement is true--he remains, and in fact will always be, the first person to reach the South Pole--nevertheless the use of the present tense is not called for unless he is currently at the South Pole at the culmination of his groundbreaking journey, or unless he remains the only person to have made it to the South Pole; in both cases, the 'first-ness' of the journey remains current.
You can think of it as a chain of events that happened in the past: someone made it to the south pole, then someone else, then another person. When speaking of these events, we naturally use the past tense; when referring specifically to their sequence, we would say "he was the first, she was the second, this group was third to reach the South Pole."
Alternatively, if you specifically want to call out the fact that someone will always be at the head of the chronological list of people who visited the South Pole, you can phrase it thus: "He is the first person to have reached the South Pole." (Note, however, that it is customary to use the past tense when referring to dead people, so once this person is deceased you wouldn't say "he is" anymore.)