MATHEMATICAL PHOTOGRAPHY
The art of Justin Mullins
Next Exhibition
Mathematical Mirrors — great art reimagined in a mathematical landscape
Venue: Lauderdale House in Highgate (free entrance)
Nearest tube: Archway
Dates: Thursday 27 November 2025 until Sunday 21 December 2025
The mathematical photographs in this exhibition are inspired by major works of art, for example those by Monet, Bellini, Dali, Rustici, Warhol and many others. Each photograph sits next to an image of the work that inspired it, like a reflection. In this way, the exhibition space is like a hall of mathematical mirrors — portals between mathematical and physical realities. Some of this work is displayed below (and beyond that is a selection of earlier work). But there is much more at Lauderdale House until 21 December.
Official portrait of the modern Lobster Telephone
Inspired by Salvador Dali's Lobster Telephone 1936, Tate Modern
In this statement, L is the set of modern Lobster Telephones while P is the property of being in this official portrait. In the pure and arcane language of logic, it says that this picture is the official portrait of modern Lobster Telephones. And by the rules of logic, the statement is true. Perfectly, incontrovertibly, puzzlingly true.
Here’s how it works. The original Lobster Telephone was created by Salvador Dali as an example of the Surrealist idea of juxtaposing ordinary objects to create the extraordinary. He did this in the 1930s, so there are no modern examples. In other words, the set of modern Lobster Telephones is empty. That has important implications for the statement that every element in this set has the property of being in this official portrait. Since it is impossible to produce a member of the set for which this is false, the statement must be formally true.
Logicians call this a vacuous truth, a statement so devoid of content that it cannot be proven false. Its seemingly paradoxical nature highlights the profound differences between intuitive thinking in humans and predicate logic in mathematics.
October 2025
Digital print fine art paper
Lamentation over the death of truth
Inspired by Giovani Bellini's Lamentation over the dead Christ (c1475) Vatican Museum
One of the most shocking events in the history of mathematics was the publication in 1931 of a paper entitled "On Formally Undecidable Propositions of Principia Mathematica and Related Systems" by a young mathematician called Kurt Gӧdel. In the paper, Godel showed that systems of logic like arithmetic share a profound flaw that undermines the foundations of mathematical knowledge.
Until then, mathematicians had expected mathematics to be entirely consistent, meaning that it was impossible for a system to contain contradictory statements. They also thought mathematical systems would also be self-contained, or complete, meaning that the truth of any statement made using the language of arithmetic, for example, could be determined using this same language. But Godel used an ingenious method of mathematical self-referencing akin to the famous phrase “This statement is false” to show this was not the case. This mathematical photograph captures the climactic statement, which implies that some truths simply cannot be proven and sealed the fate of mathematicians’ vision of truth.
This is equation is from Godel’s Proof by Ernest Nagel and James R Newman, an essay that appeared in The World of Mathematics in 1956 and was later developed into a short and highly recommended book, where the same equation appears in a slightly modified form.
October 2025
Digital print on fine art paper
The experimenter and their subject
Inspired by The artist and his model, Pablo Picasso 1926, Musée Picasso, Paris
Philosophers have long debated whether the experience of reality is universal—whether my "blue" is the same as your "blue." Physicists and mathematicians, conversely, have traditionally placed their faith in an objective truth revealed through logic and experiment. But the strange laws of quantum mechanics challenge this assumption.
In 1961, physicist Eugene Wigner proposed a thought experiment demonstrating how two observers could have entirely different perceptions of the same event. He imagined a friend in a sealed laboratory who performs a measurement on a quantum particle. For the friend inside the lab, the measurement yields a specific result ”— for example, the particle's spin is "up”— and reality is fixed. But for Wigner, standing outside the lab with no knowledge of the result, the entire system — his friend and the particle — remains in a quantum superposition of all possible states.
This creates a paradox: the friend experiences a definite, measured reality, while Wigner simultaneously observes an indefinite, superimposed one. This discrepancy only resolves when Wigner asks his friend for the result, at which point the superposition collapses for him, and both observers finally share a single reality.
Physicists have recently performed real-world versions of this "Wigner's Friend" experiment. The results suggest that these different, paradoxical versions of reality can coexist at the same time, challenging our fundamental understanding of objectivity, though the implications are still hotly debated.
This quantum puzzle mirrors a theme long explored by artists: the complex and subjective relationship between the observer and the observed. It reflects the dynamic between an artist and their model, and the further paradoxical interactions that arise when a viewer then brings their own perception to the finished artwork.
October 2025
Digital print fine art paper
No 30, 2025
Inspired by Jackson Pollock's No 5, 1948 Private collection New York
Our human experience is shaped by seemingly random events — from life-changing opportunities and coincidences to sudden disasters. Philosophers, historians, and artists have long explored their profound and unavoidable impact.
And yet, the nature of randomness itself remains poorly understood. Even mathematicians struggle, unable to prove if something is random, only that it isn't.
In 2002, physicist and computer scientist Stephen Wolfram published A New Kind of Science, detailing his study of simple computational systems, especially cellular automata. These are simple grids where each cell's state evolves based on simple rules and the state of its immediate neighbours. Despite their simplicity, these systems can generate hugely complex behaviour.
Wolfram’s goal was to understand this complexity. His unexpected discovery was that certain simple, deterministic systems — following a fixed, predetermined sequence of steps — can produce a completely random output.
He concluded that randomness doesn't just emerge from complexity, noise, or unknown inputs. Instead, it is an intrinsic property of ordinary deterministic behaviour, an inherent part of computation itself.
His most famous example is Rule 30. This simple program for a cellular automaton produces complex, patternless, chaotic behaviour that passes every known test for randomness.
This finding suggests that the possibility of a fully organised, ordered world is a fantasy. Instead, whatever we do, we will always be slaves to the deliberate, deterministic, inescapable march of randomness.
This picture shows Wolfram’s Rule 30 that dictates how cells must be updated to generate a patternless output.
October 2025
Digital print on fine art paper
Slices of pi
Inspired by Andy Warhol's Campbell's soup cans (1962) Museum of Modern Art, New York
The ratio of a circle’s circumference to its diameter is the most culturally alive of all mathematical concepts. Enthusiasts celebrate 14th March as pi day because it is written 3/14 in the American calendar, it has been incorporated into novels such as The Life of Pi by Yann Martel or in the constrained writing of Mike Keith where the lengths of words match the digits of pi, into the 2005 song, Pi, with Kate Bush singing the digits, and the work of visual artists like Martin Krzywinski. In this way, pi has transcended its mathematical origin to become a significant unit of cultural exchange.
October 2025
First nine editions of an infinite series of digital prints on fine art paper
The Pythagorean cathedral 1, 2 and 3
Inspired by Claude Monet's Rouen Cathedral series (c1890s)
October 2025
Digital print fine art paper
Euclid slaying the serpent
Inspired by Giovani Rustici's Apollo slaying the serpent Python (c1530) The Louvre, Paris
Euclid’s Elements is one of humankind’s greatest intellectual achievements and one of the most influential books in history. This work shows Proposition 20 from Book IX, in which he proves the infinitude of the primes. Although the proof is probably not Euclid's alone, it showcases his mastery of axiomatic logic in the most dramatic form.
Rustici was a contemporary of Michelangelo and Leonard Da Vinci. His Apollo slaying the serpent Python shows his mastery of the human form, his technical skill and an acute sense of dramatic theatre.
January 2025
Digital print on fine art paper
Earlier work
Incantation of truth No 1
If I write down a statement, how do you know whether it is true or false?
May 2021
Digital print on smooth fine art paper
30 x 42 cm
Young boy with paper
There are limitless proofs of the Pythagorean theorem but this is the one most often taught in schools. It has probably inspired, bemused and terrorised millions.
March 2019
Digital print on Photorag stock paper
60 x 42 cm
Middle-aged man with paper
Pythagoras' theorem is one of the great relations in mathematics. There are an infinite number of proofs , some 367 of them published in The Pythagorean Proposition by Elisha Loomis. This one — a proof using vector geometry — appears in slightly different form at the end of Loomis' book.
March 2019
Digital print on Photorag stock paper
60 x 42 cm
The shock of sudden death
Entanglement can sometimes end in an unexpected way called sudden death. These matrices show the difference between entangled states that fade away and those that end in sudden death.
March 2019
Digital print on Photorag stock paper
60 x 42 cm
Back to the future
There are no laws of physics that prevent time travel. In the quantum world, the probabilistic nature of these laws means that particles position in time is uncertain and in certain circumstances, can even interact with their former selves. Physicists have devised experiments in which this can happen, in effect creating quantum time travel machines. This work shows the circuit diagram for a quantum time machine.
March 2019
Digital print on Photorag stock paper
30 x 42 cm
About the art of Justin Mullins
For many people, their main experience of mathematics is sheer terror. Show them an equation and cold beads of sweat appear on their foreheads as they succumb to the icy grip of fear. For others, the experience is quite different. Some are bemused or irritated; others feel a surge of curiosity and a powerful sense of achievement when the hieroglyphics have been conquered.
Then there is the sense of beauty, elegance and power that mathematics conveys. Many mathematicians have remarked on this exquisite delicacy as well as on the inevitable counterpoint: a hideous ugliness that can sometimes be suffocating.
All this points to an extraordinary but rarely remarked upon role for mathematics: as a vehicle for social, emotional and cultural experience. That’s where my interest lies.
I am not interested in mathematics as it is often portrayed: as a silver thread of logic that leads from hypothesis to proof. This is a kind of ivory castle of mathematics, a perfect but ultimately unreachable world.
For me, mathematics is a human endeavour—at times it is awe-inspiring and mind-blowing but also infuriating, puzzling, unsatisfactory and often wrong (at least when I think about it). Reuben Hersh describes it refreshingly in his book What is mathematics, really? “Mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context.”
My work attempts to explore this aspect of mathematics. I use it to remember people, things and important moments; to create vignettes of ordinary moments, to make portraits of people I know or snapshots of mathematical landscapes that have inspired or terrified me. I too know the icy grip of fear! For me, my work is an emotional experience, indeed it is a roller coaster ride.
Let me say upfront that I am not a mathematician. I lay no claim to the equations I have selected in my work. Those are the discoveries of the mathematicians, philosophers and scientists who spend their lives exploring the mathematical world and revealing its great wonders. For me they are like the great explorers returning from distant shores with tales of fantastic lands and magical creatures.
If mathematicians are explorers, then my role is that of a photographer who follows their steps. During this journey, I photograph what I find. By that I mean I record it, frame it and later present it.
There is nothing particularly special about this process. In the same way that an ordinary photograph is a snapshot of an area of outstanding natural beauty, a mathematical photograph is a snapshot of mathematical beauty. But photography records much more than that — it is a mirror for society in all its glory and all its ignominy. The mathematical landscape offers a different lens through which to view it.
Justin Mullins is an artist, writer and lecturer. He has been producing and exhibiting his artwork in the UK and US since the 1990s. His art has been covered by New Scientist, The Guardian and various radio and TV shows.
Contact
justin@justinmullins.com