This study was conducted in collaboration with MENSA-Greece, trying to investigate how identified gifted adolescents and adults, representing "different generations of the internet," perceive the use of artificial intelligence (AI) in their life. The extent to which artificial intelligence tools constitute either a positive challenge and experience or not is the main concern of this study. A total of 84 adults (72.6% males) and 60 adolescents (55% males) participated with no previous specific education in artificial intelligence (85.7% for adults, 88.3% for adolescents). Over half of the adult participants (57.2%) held postgraduate degrees, while the adolescents' parents were also highly educated (75% of mothers and 65% of fathers were university graduates). An online questionnaire of 59 main questions and a set of demographic issues and other information was completed anonymously. An overwhelming majority of adolescents reported that they use Artificial Intelligence applications, including for support with their school subjects (73.3%). The participants' beliefs about the influence of AI on their lives clustered into four dimensions: (a) behavioral aspects of AI use (e.g. goal planning, seeking information, risk-taking, etc. (b) cognitive aspects of AI use (e.g. complex problem-solving, discovering of new abilities, development of technological skills, etc.), (c) concerns about the safety of personal data and the reliability of AI-generated information; and (d) scepticism and caution towards AI use. The results are discussed in terms of gender and age cohorts, along with the distinct internet generations they represent.