The periodic system emerges by intertwining order and similarity relationships among chemical elements, which in turn arise from known substances at a given time that constitute the chemical space. Although the system has been adjusted to accommodate new elements, the connection with the chemical space has been largely forgotten and the question that arises is about the effect of the exponentially growing chemical space upon the periodic system. To what extent advances in chemistry have confirmed or distorted the periodic system? Is the system --icon of chemistry-- a traversal feature of the chemical space? Here we solve these questions by computationally analysing the effect of the chemical space upon the periodic system from the dawn of the 19th century until the present. We found that although the system has undergone several and significant changes across history, it converges towards a stable structure. This dynamics results from advances in chemistry such as the discovery of elements, of forms of chemical combination and the incorporation of new theoretical frameworks. Interestingly, the periodic system is also influenced by socio-political events such as wars. Given the nature of the chemical space, which holds the inertia of more than 200 years of chemical practice, and the limited chemical possibilities for the remaining elements to be synthesised, we hypothesise that the periodic system is going to remain largely untouched in the years to come. We expect our results and methods trigger further research and discussion in the history, pedagogy, philosophy, and ultimately, in the practice of chemistry.