The painting captures a single figure looking pensive whilst he sits besides a desk. Several books are placed on the table besides him in order to underline his intelligence and interest in study. We can then find some drawings behind him on the wall, all mathematical. The desk is perhaps deliberately reduced in size by the artist compared to how it would have been in real life and the whole composition feels cramped, just as Rivera would have intended. This use of spacial composition is added to by the darkened colour scheme, with strong shadows and dark clothing. The mathematician looks solemn and he stares downwards. His arms are crossed in a negative manner and his clothing is equally devoid of happiness or personal expression. One can imagine this individual to be devoted to his profession, with little time or interest in perfecting his own appearance. One might suggest that he represents the polar opposite of the artist himself, something that makes this paintings particularly intriguing.

The painting itself measures just over a metre in height and around 80cm in width. Rivera had been working within a Cubist manner for several years shortly before this artwork and here we find him moving away from the fractal style of previous years. He had been inspired by a number of artists that he came across whilst living in Paris, which at the time was perhaps the most exciting place for creatives to be. The model that he chose for this portrait was Dr Renato Parescat who is believed to have been a friend of his. Some have argued that this subdued piece represents all that he learned whilst in Europe, at least from a technical sense. Lighting and the angles of perspective are most obvious here and he manages to demonstrate these skills in an understated manner which opposes much of what he would have come across previously within his native Mexico. Rivera is known to have later described The Mathematician as one of his most important artworks of all, albeit whilst attempting to find a buyer for it.

In order to understand the incredible variety of this artist's oeuvre, you might wish to compare The Mathematician with some of his more Mexican-style artworks, such as Nude with Calla Lilies and The Flower Carrier. You essentially have there two very different artists, where colour and style diverge completely, but that illustrates the different influences that impacted his work as he moved to different countries and cultures. The European years were an essential period in his development and he would also have learnt much from his wife, Frida Kahlo, who herself had German roots of her own. It is this fusion of ideas which perhaps made his work so palatable to an international audience and many of his paintings today reside in collections outside of his native Mexico such is the geographic spread of interest in his work.