Uhlmann won the East German Chess Championship eleven times and represented the German Democratic Republic (GDR) on several occasions in international tournaments including the Chess Olympiads. He is considered one of the strongest players of his time.
Internationally, Uhlmann was famous for being one of the best King's Indian Defence players. He maintained strong positions throughout his matches and won noteworthy games against notable players such as Bobby Fischer and Boris Spassky.
In 1976, Uhlmann played a match representing GDR against the World Chess Champion Anatoly Karpov which ended in a draw.
Post professional career, Uhlmann authored several chess books and continued to take part in tournaments at a lower level until his death in August 2020.