Osmotic pressure proves to be a useful topic for illustrating the disputes brought to bear on the chemistry profession when mathematics was introduced into its discipline. Some chemists of the late 19th century thought that the introduction of mathematics would destroy that "chemical feeling" or "experience" so necessary to the practice of chemistry. These chemists were critical of the suggestion that mathematically analogous expressions for macroscopic phenomena implied similar kinetic-molecular processes at the microscopic level because they believed that a chemical phenomenon discovered by chemical experience through experiment was a more reliable guide to molecular processes than was mathematics. In general physical chemists of the modern era are also critical of the suggestion that mathematically analogous expressions for macroscopic phenomena imply similar kinetic-molecular processes at the microscopic level but for different reasons. The mathematical analogy between the van't Hoff law and the ideal gas law is regarded as an artefact of the mathematical thermodynamic treatment of osmosis and not as a result of a correlation of kinetic-molecular processes. Some chemists however, albeit a minority, while agreeing with the thermodynamic treatment of osmotic pressure suggest that the mathematical analogy is more significant than being simply a mathematical artefact. They propose a controversial kinetic-molecular model of osmotic pressure which they believe has more educational value than the thermodynamic model. The significance of mathematically analogous expressions for different chemical properties and the desirability of highlighting "unifying chemical principles" for the teaching and learning of tertiary level chemistry are discussed predominantly in the context of historical osmotic studies.