Time
Time is perhaps the most pervasive theme in the work. Stoppard sets his work in two different time periods and manages to simultaneously reveal the gap between them (literal time), the unknowability of times not our own, as well as the continuities and overlaps between them. The setting and objects are the same in each, and by the end the characters from either era are occupying the same space and essentially in dialogue with each other. Valentine shows how Thomasina was both ahead of her time and limited by it, but the record of her equations makes her timeless. Gus transcends both eras, calling attention to the slippages possible between past and present. Time as embodied in the second law of thermodynamics is brutal and has an endpoint, but a sense that time is mutable and fluid persists. As actual time passes for the audience watching Stoppard's play, the events in the play stop and start, double back on each other, definitively end or open themselves up to the future.
Chaos and Entropy
The rational Newtonian universe cannot hold; instead, as chaos theoreticians and the precocious Thomasina discover, it is always cooling off, always breaking down into disorder. Any order found is in that disorder. This theory is not truly articulated until the 20th century, but Thomasina Coverly sees evidence of it nearly 200 years before. The basic themes underlying chaos theory - disintegration, breakdown, disharmony, patterns amid randomness - are observable in the relationships around her, not to mention the gardens of her own home. Chaos, then, is a component not just of the universe but of every individual thing within it. Sex is chaos, love is chaos, poetry is chaos; however, there is still a sort of harmony present within the disorder.
The Pursuit of Knowledge
Almost every character in the play is in pursuit of some form of knowledge - Bernard and Byron, Hannah and the hermit, Valentine and the grouse, Thomasina and her equations. The characters pursue their interests with varying degrees of deduction, intuition, emotion, and detachment. One of the central conversations is that between Hannah and Valentine, in which Hannah admits that everything they are studying is essentially meaningless, but that it is the pursuit itself that matters and is what makes them human. Wanting to know brings vitality and meaning to life. Stoppard celebrates learning for learning's sake, exhibiting a passion for everything the world has to offer; it's not hard to feel the same sense of breathless excitement while reading/seeing a work that weaves art, poetry, science, sex, history, gardening, and philosophy into one text.
Sex
Sex is present throughout the novel, with Mrs. Chater, Septimus, Byron, Bernard, Chloe, and both Lady Crooms engaging in licentious behavior offstage. Their activities are occasionally a source of amusement and a part of the plot (i.e. the Chater-Byron hypothesis) but sex occupies a more important role than it may initially seem. Sex is chaos - it is what messes up the orderly universe. The apple in the garden ground the whole neat and orderly experiment to a halt. It is unpredictable, confusing, and nonconformist. The heat of bodies is the heat of the universe that cannot be fully contained, nor can it be fully sustained.
The Past
The scholars at Sidley Park desperately want to understand the past by making connections and probing its particulars, but it eludes them. Bernard assumes he has the whole story about Chater and Byron, using scraps of information to put together a theory that ends up being wrong. For her part, Hannah comes a lot closer to knowing what happened, but still, she will never know that Septimus is a hermit because he fell in love with Thomasina and was distraught over her death. The past is not something that is neatly ossified in time and something to play fast and loose with. The people who occupied it were living, breathing individuals with motives perhaps impossible to comprehend. On the other hand, arbitrary divisions between past and present are also useless, as time is not fully linear and the past indelibly factors into the present.
Classical vs. Romantic
There is a debate between the Classical and the Romantic that permeates the text. The Classical, characterized by harmony and order and rationality, seems to be diametrically opposed to the wildness, irrationality, irregularity, and emotional Romantic. This plays out in the Sidley Park garden, in which the latter replaces the former, but also in the characters' temperaments and scholarly styles (i.e., Bernard is passionate and intuitive while Hannah is cool and cerebral) as well as the science of the text, in that Newtonian order is supplanted by chaos theory. In terms of people, Stoppard's message seems to be that a bit of both is necessary.
Nature
Nature is, to an extent, unknowable in the same way as the past. One can attempt to tame it, to order it, and to understand it, but it will more often than not refuse to conform to our expectations. The grouse population is too "messy" for Valentine, and weather can't be predicted. The landscape of Sidley Park in its purer, Romantic form is wild, untameable, fraught with tension and home to "carnal embrace," hermits, geniuses, and threat of violence. It also represents the raw embodiment of the passions of humankind.
