Enough people love this play that it presumably has some good qualities. But I just couldn't get past the snide, obnoxious characters, and the facile, frequently inaccurate treatment of science and math, which panders to the "science is just the product of fallible human impulses and, like, we don't really know anything for sure anyway, man" attitude that has become the norm among intellectuals and wannabe intellectuals who, for one reason or another, aren't interested in science.
As a presentation of math and science to a lay audience, the play is a failure. It feels as though Stoppard read James Gleick's Chaos (or a similar popular text), misunderstood it, forgot half of it, and then wrote the play on this basis of what remained. When Stoppard tries to write about chaos theory, he fails to mention the central concept -- sensitive dependence on initial conditions (the famous "butterfly effect") and its appearance even in simple systems -- and instead only tells the audience that chaos has something to do with iterated maps.
He mentions that iterated maps can produce fractals that look very much like realistic mountains, leaves, ferns, etc., and implies that the failure of 18th/19th-century dreams of predictability has something to do with the failure to use these realistic, fractal models of objects in physics calculations. (One of the characters proleptically quotes Mandlebrot: "Mountains are not cones, clouds are not spheres.") This, of course, raises the question: if we do have fractals now, is predictability no longer doomed? The answer is no, because (almost) all interesting physical systems exhibit sensitive dependence on initial conditions; but Stoppard does not clarify this. An audience member unfamiliar with the material will leave the play under the impression that physicists like Newton and Laplace were overly optimistic about prediction because they did not know about iterated maps, which (somehow!) are supposed to make prediction harder. Since the idea of an iterated map is very simple (indeed, it is explained in the play), this makes these geniuses look rather stupid.
Of course, they actually did know about iterated maps. (One of the most famous iterated maps is called . . . wait for it . . . Newton's method.) They didn't appreciate the unpredictability of very simple systems, but that unpredictability is a subtle issue, and Stoppard's play doesn't begin to get into it.
There are other errors, too, and they too (uncoincidentally) serve to make early physicists look dumb or oblivious. For instance, at one point one of the characters -- Thomasina, a precocious child who is learning physics -- reads a paper which, given the date and the description of its content, must be Fourier's paper on the heat equation. This paper is famous for introducing Fourier series, but Thomasina seems to think it is remarkable for another reason. She exclaims that Fourier's equations are "not like Newton's equations," for they specify a direction of time, while "Newton's equations" are reversible. This claim comes as quite a surprise, since the heat equation studied by Fourier is simply a continuous version of an equation called . . . wait for it . . . Newton's Law of Cooling. Presumably by "Newton's equations" Thomasina specifically means Newton's three laws of motion. But even there, she's wrong: although in some special cases Newton's laws are reversible, they can also describe irreversible forces, and indeed Newton himself believed that the most fundamental forces were likely to be irreversible. (This would explain the fact that many real-life phenomena, like stirring milk into coffee, seem to be irreversible -- another case where Stoppard seems to imply that early physicists simply ignored something obvious.)
The play views the march of science with an amused sneer: oh, look at these funny plodding people, convinced that they know so much, yet battered this way and that by their culture, swelling with utopian ambition in the Enlightenment, inventing lurid tales of heat death in the age of Romanticism, and once the 20th century rolls around they create "jazzy" math and lose faith in the old verities . . . Now, I'm not denying that scientists are fallible human beings, but Stoppard's sneer is unearned. The issues involved in the development of theoretical physics are esoteric, irreducibly mathematical, and mind-bendingly subtle. This is serious shit. Really, really smart people have been working very, very hard on it for centuries. I'm sure that Stoppard and some parts of his audience would like to imagine themselves as Thomasina, instantly spotting the errors of those grim old scientists and dispatching them with a light, witty touch. Would that that were possible! But science is really hard; when our predecessors have made mistakes they tend to be subtle, recondite ones. Try to catch the masters making obvious blunders and you will just fall on your face, as Stoppard has done.
And Thomasina gripes about having to plot simple mathematical curves like parabolas, because they don't look like real natural forms. Never mind that simple curves are tremendously important in science anyway. Never mind that facts like this are precious and remarkable precisely because they are surprising; if science always conformed to our intuitions (about, say, which shapes are important) it wouldn't have much value. No, Tom Stoppard's audience just remembers its own confusion and displeasure over math in high school and would like its prejudices confirmed. Maybe all those funny curves we had to draw as children really were meaningless! Take that, school! Now let's go home from the theater and never think about math again.
(Also: love/sex is "the attraction that Newton left out"? Seriously??? I know it's just a joke but it's an awful, cringe-inducingly cutesy one. I have a high cutesiness tolerance and this play is too much even for me.)