Using a series of equations, Kosinski was able to make a measurable increase in propulsion with the starships USS Ajax and USS Fearless. His warp drive efficiency upgrade experiments brought him to the USS Enterprise-D in 2364, where he was to test different ways of entering warp speed and different intermix ratios. It later was revealed that it was not him but his mysterious assistant, The Traveler, who was affecting the upgrades. (TNG: "Where No One Has Gone Before")
This incident was mentioned, as an example of Jean-Luc Picard's supposed incompetence, by Lieutenant Commander Dexter Remmick when questioning Geordi La Forge. Remmick alleged that, according to Picard's own logs, he had allowed Kosinski to access the Enterprise's engines despite the bridge crew having doubts about the propulsion expert's theories. Although La Forge protested that it hadn't exactly happened that way, Remmick wasn't swayed in his opinion. (TNG: "Coming of Age")
Some of Kosinski's theories were still valid. Ensign Wesley Crusher tested his warp equations aboard the Enterprise while it was docked at Starbase 133 in 2367. Wesley inadvertently created a warp bubble which trapped his mother, Doctor Beverly Crusher, in an alternate universe. In this universe, Wesley contacted Kosinski for assistance when crewmembers began disappearing, but Kosinski was unable to explain the phenomenon. (TNG: "Remember Me")
Background information Edit
Kosinski was played by Stanley Kamel.
In an early draft of the script for "Where No One Has Gone Before", Kosinski was a doctor with the first name "Peter". He was an old friend of Picard's, as they had been roommates at Starfleet Academy. In the same teleplay's stage directions, Kosinski was described as "a rather intense-looking man about Picard's age." 
Whereas, according to the Star Trek: The Next Generation Companion (p. 36), "in the original teleplay, Kosinski was responsible for both the warp effects and the accident; he also had a son who felt he spent more time on his career than with him. The crew was in awe of Kosinski in the original script."
In "Where No One Has Gone Before", Kosinski appears in a Starfleet uniform with no communicator and does not appear to have a Starfleet rank, as he is referred to throughout the episode as "Mr. Kosinski". His collar features a unique rank insignia: a small silver rectangle, and a darker rectangle of the same size. The Star Trek: The Next Generation Companion (p. 37), makes light of this peculiarity as well, noting, "while Kosinski's unexplained square rank pip was never seen again."