The Apogee founder and producer Scott Miller has been sharing a bunch of memories on Twitter of his time working with Remedy on the first Max Payne game. And this includes revealing how the popular bullet-time mechanic was born.
According to Miller, Remedy had already added a slow-motion feature into the game for enemies dying, based on their love of John Woo films, but the producer suggested they tie it into the gameplay and have it be something that Max can activate. Miller even shared the original note where he first jotted down the idea in a follow-up tweet:
For those who can't make out Miller's handwriting, the note in the image reads:
"We need to make the slomo stuff part of gameplay and not just visual. Max needs to be able to activate it! Time slows… Max shoots”
It's a cool bit of game development history, but the conversation quickly turned to the subject of who coined the term "bullet time" originally, as Miller later seemed to take credit for coming up with the classic phrase himself:
As many people pointed out in the replies, Max Payne came out in 2001, two years after the Matrix had already popularized the term.
Miller responded that the term was never included in Matrix promotional material or interviews, at least to his knowledge, but others quickly highlighted the existence of interviews where the Wachowskis used the phrase shortly after the film's release as well as the inclusion of a 6-minute making-of feature on the Matrix DVD from 1999 called "What is Bullet-Time?".
Interestingly, Apogee did hold the trademark for the term for a number of years following the release of Max Payne, but it then abandoned it around the time of Matrix Reloaded. Warner Brothers since registered the trademark, which led to Rockstar having to include disclaimers to that effect in promotional material for Max Payne 3.
Given the number of years Max Payne was in development, it's possible Miller came up with the term independently, but we'd argue it's pretty clear-cut who brought the phrase to general audiences.