The h-index has become a widely used metric for evaluating the productivity and citation impact of researchers. Introduced by physicist Jorge E. Hirsch in 2005, the h-index measures both the quantity (number of publications) and quality (citations) of a researcher's output. While it has gained popularity for its simplicity and practicality, the h-index is not without its limitations. We examine the strengths and weaknesses of this metric, presenting preliminary experimental results that demonstrate the limitations of the h-index. We also propose a potential solution. The primary aim of this work is to shed light on the shortcomings of the h-index and its implications for ranking scientists, motivating them, allocating funding, and advancing science.