In this first paper it is shown that during the mid‐1870's when chemistry finally broke free from the shackles of its alchemical past, a process of gradual mathematization ensued. This process has continued apace and at present appears to be accelerating. This has brought attendant difficulties and a plea is made for a better mathematical training for chemists. At the moment applications of linear algebra appear to have special relevance to chemistry and it is pointed out that improved mathematical skills in this area may well result in a reformulation of chemistry within the framework of some appropriate logical structures. Modern theoretical chemistry could perhaps be founded on the theory of sets, or even on the theory of categories, if a higher order of abstraction is called for.