Fermat’s Last Theorem
One of the first scientific references in the play, is to Fermat’s Last Theorem. Septimus challenges Thomasina to solve Fermat’s mathematical formula, which famously had been stumping mathematicians for over 300 years. French mathematician Pierre de Fermat claimed to have made a mathematical breakthrough in a note scrawled in the margin of his notebook, but failed to publish his proof before he died. The association between Thomasina’s potential genius and Fermat is deftly underlined when Hannah and Bernard are drawn to Thomasina’s mathematical work by a cryptic note in her notebooks.

Septimus also has a playful riff on Fermat when in the context of his explaining “carnal embrace” to Thomasina, he restates the basic algebra of the theorem, “that when x, y and z are whole numbers each raised to power of n, the sum of the first two can never equal the third when n is greater than 2.” Surely he and Stoppard mean this as a suggestive metaphor for the multiple permutations of passion between the characters in the play.

Fractals
What Thomasina was seeking in her application of algorithms was a mathematical equation that could define the shape of a bluebell or of a leaf. She is exasperated by the limits of classical geometry, which she describes as “nothing but arcs and angles” and which she suggests does not account for the beauty of the natural world. As she says, “mountains are not pyramids and trees are not cones”. Thomasina gathers her work in a document entitled New Geometry of Irregular Forms. In fact, her approach foreshadows what is now called Fractal Geometry, a term that was not coined until 1975 by mathematician Benoit Mandelbrot.

A fractal is a complex, never-ending pattern that repeats itself at different scales, a property known as self-similarity. A fractal object has infinite detail, so that as you zoom in the structure reveals smaller, similar copies of the whole – such as a fern leaf. Mathematicians have developed an iterated function that creates a representation of a fern.

The pattern and beauty of a fern being described in a mathematical formula is a challenging concept. But it is in line with Stoppard’s sympathetic mixing of science and art in the play. Valentine makes Stoppard’s argument that science and art are not binary, when he counters Bernard’s declared preference for poetry over scientific progress: “He’s not against penicillin and he knows I’m not against poetry.” As Stoppard said, “Science and art are more like each other than unlike”, and the play endorses C.P. Snow’s famous exhortation to erase the dogmatic divide between the “Two Cultures”, as he called them.

Chaos Theory
It is a bleak principle. But it may not be that simple – if that is simple – because in another twist, we do recognise some order, some patterns in the inexorable process of dissipation. Which may be where ‘Chaos Theory’ comes into the philosophical mix in the play. Stoppard was inspired by James Gleick’s 1987 book on chaos theory in which Gleick tells us that chaos theory paradoxically identifies mathematical structures within random systems, what are called ‘self-similarities’ – patterns repeating. And of course, within the structure of the play, things from the past are repeating in similar forms.

Stoppard described chaos theory as “a reconciliation between the idea of things not being random on the one hand and yet unpredictable on the other.” It “attempts to systemise that which appears to function outside of any system.” And it applies to any dynamic system where apparent randomness is found to contain order.

As Gleick outlines, ‘mathematical equations could model chaos – tiny differences in inputs could quickly become overwhelming differences in output.’ In systems like the weather where events and patterns ‘almost repeated themselves but never quite succeeded”. A phenomenon simplistically described by the metaphor that the flap of a butterfly’s wings could change the weather.

Metaphorically, in some ways these abstract sounding theories can be applied to our understanding of the world. For example, one small detail in our interpretation of the past will yield a completely different conclusion about what we think occurred, as it did in Bernard’s misinterpretation of the past. Or minute variations in our behaviour at any one time can produce wildly different outcomes in our love affairs or in our lives.

As Valentine outlines it “The unpredictable and the predetermined unfold together to make everything the way it is. It’s how nature creates itself, on every scale, the snowflake and the snowstorm.”

One might also observe that the structure of the play also seems to go from order to some form of chaos, with the strictures of time that separate the two worlds dissolving. The swirls of jam stirred together, disorder out of disorder into disorder.