As with any major text of literary import, characterisation in this play is one key way in which Stoppard chooses to develop the central themes and messages that he wishes to convey to his audience. These are many and varied, but one you might like to consider is what he says about sex and how he relates that to our human condition, and in particular how science, prized by so many of the characters in this play, is so profoundly inadequate when it comes to trying to understand us as humans and encapsulate us as scientific objects.
Consider how sex is described and how it is used. Sex is described as being "the attraction that Newton left out," perhaps indicating the way that it does not follow any scientific rules or principles. Sex is shown to render sensible and cogent human beings into characters who do stupid things and act in ways that belie their supposed intelligence. Perhaps Septimus captures it best when he describes "carnal embrace" as being "the practice of throwing one's arms around a side of beef." Characters have their urges, and will often go to ridiculous extremes to satisfy them. However Septimus tries to explain sex to Thomasina, there are clear limits to trying to understand sex as a scientific process:
Carnal embrace is sexual congress, which is the insertion of the male organ into the female genital organ for the purposes of procreation and pleasure. Fermat's last theorem, by contrast, asserts that when x, y and z are whole numbers each raised to the power of n, the sume of the first two can never equal the third when n is greater than two.
For Thomasina, as an innocent and impressionable teenager who, at the same time has a keen scientific mind, such prescriptive definitions do not capture the way in which sex and our emotions rule our lives as humans. Consider her own attraction to Septimus, the way that Septimus lives out the remainder of his life after her death, and the way that Mrs. Noakes is an object of attraction to so many of the male characters. Sex and emotions, just like science, are unable to be completely understood and lie at the foot of the reasons for our irrational and unpredictable behaviour as humans.
Probably because the distinctive traits of their personalities are linked to the dialectics of chaos and order in the play.
Yet, although the characters are somehow associated with either newtonian science, with clacissism or a romantic vision of the world, still, the emphasis remains on change and mutability. The characters have a propensity to behave in such or such way but they occasionally turn out to be an odd mixture because of the dynamics of desire and the interplay of ideas that form the structural backbone of the play. As a matter-of-fact, one of the key concepts in the play is the law of entropy which measures the degree of disorder of a system.
Therefore, characterization does convey a message but we should beware of seeing the characters as a mere personification of ideas.