After watching a dozen episodes, I decided to give up on this show since it depicts in an unrealistic manner what is mathematical modeling. In the episodes that Charlie would predict the future behavior of individuals using mathematical models, I thought that my profession was being joked about. I am not a mathematician, instead a chemical engineer, but I do work a lot with mathematical models. So I will try to explain to the layman why what is shown is close to "make-believe" of fairy tales.
First, choosing the right model to predict a situation is a demanding task. Charlie Eppes is shown as a genius, but even him would have to spend considerable time researching for a suitable model, specifically for trying to guess what someone will do or where he will be in the near future. Individuals are erratic and haphazard, there is no modeling for them. Isaac Asimov even wrote about that in the 1950's. Even if there were a model for specific kind of individual, it would be a probabilistic (stoichastic) one, meaning it has good chance of making a wrong prediction.
Second, supposing the right model for someone or a situation is found, the model parameters have to be known. These parameters are the constants of the equations, such as the gravity acceleration (9.8 m/s2), and often are not easy to determine. Again, Charlie Eppes would have to be someone beyond genius to know the right parameters for the model he chooses. And after the model and the parameters are chosen, they would have to be tested. Oddly, they are not, and by miracle, they fit exactly the situation that is being predicted.
Third, a very important aspect of modeling is almost always neglected, not only by Numbers, but also by sci-fi movies: the computational effort required for solving these models. Try to make Excel solve a complex model with many equations and variables and one will find doing a Herculean job. Even if Charlie Eppes has the right software to solve his models, he might be stuck with hardware that will be dreadfully slow. And even with the right software/hardware combination, the model solution might well take days to be reached. He solves them immediately! I could use his computer in my research work, I would be very glad.
As a drama, it is far from being the best show. The characters are somewhat stereotyped, but not even remotely funny as those in Big Bang Theory are. The crimes are dull and the way Charlie Eppes solves them sometimes make the FBI look pretty incompetent.
For some layman, the show might work. For others, the way things are handled makes it difficult to swallow!