Creatine supplementation improves cognitive function in older adults and individuals with sleep deprivation or cognitive impairment, but has no significant effect on cognitive performance in healthy young adults.

Study: Effects of high-load, velocity-intentional variable resistance training combined with creatine supplementation on neuroplasticity, oxidative stress, inflammation, physical function, cognitive performance and quality of life in older adults: A randomized, double-blind, placebo-controlled trial

This study found that older adults who took creatine supplements, especially along with exercise, felt better and showed signs of improved brain health. It supports the idea that creatine helps older people think better, but doesn't say anything about young, healthy adults.

Study: Single dose creatine improves cognitive performance and induces changes in cerebral high energy phosphates during sleep deprivation

This study found that taking a large dose of creatine helped people who hadn’t slept much think faster and perform better on mental tasks. It supports the idea that creatine can help when you're tired from lack of sleep.

Study: Single-Dose Creatine Reduces Sleep Deprivation-Induced Deterioration in Cognitive Performance

This study found that taking creatine helped people stay sharper and think faster when they hadn’t slept, which matches part of the claim. It didn’t test healthy people who’ve had enough sleep, so we don’t know if it helps them.

Study: Dose–Response of Creatine Supplementation on Cognitive Function in Healthy Young Adults

This study gave creatine to healthy young people and found it didn’t make them think better, which matches the claim that creatine doesn’t help young, healthy adults. It didn’t test older or tired people, but what it did test supports part of the claim.