The Uncertain Science of Certainty features acclaimed statistician and epidemiologist Adam Kucharski. Part of the Ethical Matters series, this event delves into the complexities of how we establish and communicate notions of truth in an era rife with disinformation, division and uncertainty.
From the medieval Islamic world to the recent pandemic, scientific progress has relied on different methods of establishing fact from fiction. Today, in the face of ever-increasing disinformation, how we prove things – to ourselves and others – has never felt more urgent. But there is far more to proof than axioms, theories and scientific laws: when demonstrating that an experimental medical treatment works, persuading a jury of someone’s guilt, or deciding whether to trust a new type of financial transaction, weighing up evidence is rarely simple.
Adam Kucharski is a professor at the London School of Hygiene & Tropical Medicine. A mathematician by training, his work on global outbreaks has included Ebola, Zika and COVID-19, and he has advised multiple governments and health agencies. Drawing from his latest book, Proof: The Uncertain Science of Certainty, Kucharski examines the multifaceted nature of evidence across various domains, including science, law, medicine, and economics. He highlights the challenges in determining what constitutes “proof” and how societal trust in evidence can be both built and eroded, traversing from historical scientific methods to contemporary issues like algorithmic bias in the criminal justice system.
What inspired you to investigate the concept of proof? “Alice Stewart, an influential epidemiologist, used this nice phrase that ‘truth is the daughter of time’. But in many situations, whether you’re accused of a crime or thinking about a climate crisis, you don’t want to wait; there’s an urgency to accumulate evidence and set a bar for action. We’re entering an era where questions around information – what we trust and how we act – are increasingly important, and our concepts of what we can prove are shifting as well.” (Kucharski)
Truth’s Triad: Ethos Pathos Logos
The phrase “scientifically proven” is commonly heard in advertisements and pop-sci journalism. Yet, in the philosophy of science, proof in the mathematical or legal sense is not how science typically operates. Scientific claims are never proven in an absolute sense – they are supported to varying degrees by empirical evidence. This is the fundamental difference between science and mathematics. In mathematics, proofs are predominantly deductive: they follow a logical structure from axioms to conclusions. In science, evidence is predominantly inductive: observations lead to generalisations or models, but those models can never be completely confirmed. Efficacy is often weighted through predictive power.
For example, Newton’s laws of motion were once considered fundamental truths. They worked brilliantly to explain planetary motion and terrestrial mechanics. Yet, they were eventually superseded by Einstein’s theory of relativity in contexts where Newtonian mechanics failed – such as near the speed of light or in strong gravitational fields. Newton’s laws weren’t wrong; they were limited in scope. This reveals the heart of scientific progress: theories can be robust and reliable, but never absolutely proven; Like life itself, they are bound by current logical and linguistic limitations.
Far from being a weakness, uncertainty is a defining feature of science because it is a recognition of the real-world complexity that science seeks to describe, explain and forecast. It reflects the openness of scientific inquiry – every theory is potentially falsifiable, and new evidence can challenge the current consensus. Uncertainty shows up in many forms including:
Statistical (Probabilities and Margins of Error: if a drug is effective with 95% confidence, there is 5% chance the result was due to random variation), Measurement (No instrument is perfect. Whether measuring temperature, radiation, or DNA sequences, there’s always some degree of imprecision), Model (Climate models, economic forecasts, or pandemic predictions rely on assumptions. These models are simplifications of complex systems, and their outputs must be interpreted with caution), Theoretical (In frontier areas like quantum gravity or dark matter, scientists propose multiple competing hypotheses, none of which are conclusively confirmed).
The philosopher Karl Popper famously argued that for a theory to be scientific, it must be falsifiable. That is, there must be a conceivable observation that could prove it wrong. This principle underpins the skeptical and self-correcting nature of science: theories gain strength not through confirmation alone, but by surviving repeated attempts at falsification. Yet, not all science is neatly falsifiable. Fields like evolutionary biology, cosmology, and climate science often deal with historical or large-scale systems that cannot be easily experimented upon. In such cases, scientists rely on converging lines of evidence: radiometric dating, fossil records, genetic analysis etc to build robust theories.
Rethinking proof in a complex world, Kucharski begins with the classic Monty Hall problem, illustrating how even renowned mathematicians like Paul Erdős struggled with probabilistic reasoning. This example sets the stage for a broader discussion on the challenges of interpreting evidence and making decisions under uncertainty – delving into historical shifts in mathematical thinking that highlight how concepts like negative numbers were once controversial due to cultural and philosophical contexts.
Kucharski also explores how figures like Abraham Lincoln employed mathematical principles to strengthen political arguments, demonstrating the interplay between logic and rhetoric, as well as hinting at the value of evidence in light of AI and social media, and how the notion of fact has long been divisive. Another intriguing anecdote recounts a 1920s experiment at Rothamsted Research Station, where statisticians tested whether milk added before or after tea affected taste. This experiment, involving Muriel Bristol and Ronald Fisher, laid the groundwork for modern statistical methods, including the development of the null hypothesis and p-values.
How did the perfect cup of tea inspire the design of clinical trials? “There was a tearoom in Rothamsted agricultural station in Hertfordshire, and in the early 1920s, three statisticians were having a conversation when one of them, Muriel Bristol, observed that tea always tastes better if the milk is put in before the hot water. The other people around the table disagreed, but they thought it was a nice challenge to see how you could work out whether she could tell the difference or not. In the end, they calculated that you need to lay out eight cups, in which half have the milk added before the hot water, and half after, ordered randomly. This produces around 70 possible combinations, meaning there is only a 1.4% chance that Bristol would get that out of all the possibilities correct – which she did…. One of the mathematicians was Ronald Fisher, who would end up writing a landmark book called The Design of Experiments that examined how you can separate an effect from chance or human biases – and this included the principle of randomisation and using probabilities to test the strength of a hypothesis.” (Kucharski)
Error And Ethics: Process Not Product
Science is often packaged for public perception as a collection of facts, but it is more accurately described as a method. Peer review, replication, statistical analysis, and open debate are all parts of the modern scientific process. Scientific consensus emerges over time as evidence accumulates and competing ideas are tested. However the gap between how science works and how it is perceived can lead to confusion even within the industry, and especially during times of crisis. For instance, during the COVID-19 pandemic, changing guidance on masks or vaccines was sometimes interpreted as scientific failure. In reality, it was science working as intended – updating recommendations based on evolving evidence. Demanding absolute certainty before taking action can lead to “paralysis by analysis.”
By nature of the fact that evidence is embedded, data and doctrine are inherently intertwined. Donna Haraway is a feminist scholar of science and technology best known for her influential work A Cyborg Manifesto and her critique of scientific objectivity (her emphasis of the subjective pole inherent to interpretation). In her essay Situated Knowledges: The Science Question in Feminism and the Privilege of Partial Perspective (1988), she challenges the common ideal of “a universal, detached truth”, offering that such claims imagine a “view from nowhere” – and are not only impossible, but politically dangerous. For Haraway, all knowledge is situated: it emerges from specific bodies, cultures, histories, and power relations (the enactive perspective).
From this perspective, the search for proof in science must be understood as a culturally embedded process and practice. Haraway does not reject science, but calls for a more accountable and contextualised way of doing it – one that acknowledges its own partiality, rather than masking it with a veneer of universality. Whereas, traditional science sees uncertainty as a technical limitation to be reduced, Haraway sees an ethical opening.
For example, in feminist science studies, uncertainty becomes a space for dialogue and response-ability: between humans and non-humans, between disciplines, and between different anthropological contexts and worldviews. Haraway’s later work on multispecies relationships (such as in When Species Meet and Staying with the Trouble) exemplifies this shift: she doesn’t look for narrower ways of honing in on certainty and closure, but for more expansive and dynamic ways to “stay with the trouble” of complex entanglements.
In A Cyborg Manifesto (1985), Haraway uses the figure of the cyborg to blur traditional binaries: nature-culture, male-female, machine-organism, object-subject. This is directly relevant to discussions of proof and uncertainty in science, which often rely on similar binaries of: true-false, observer-observed, proven-unproven. In doing so, Haraway shows that these binaries are not natural givens, but historically constructed frameworks that shape how science sees and interprets its world.
The ‘cyborg’, as a hybrid figure, symbolises a more fluid and embodied approach to knowledge which is better equipped to embrace complexity and contradiction. If there is no such thing as true objectivity, and some statements are just more objective than others (an equation or neural circuit as its own definition) then perhaps the rise of terms like “Post-Truth” hint at a moment in time where this inter-relationship and inter-dependency is less fluid and nuanced, becoming entrenched in static and rigid categories that restrict growth and diversity.
When it comes to “situated science” in practice: medicine would foreground patient experience alongside clinical trials, climate science would collaborate with Indigenous ecological knowledge rather than treating it as folklore, and AI research would examine how datasets and algorithms reflect social biases, rather than pretending that they’re neutral. Paradoxically therefore, facilitating (or acknowledging) the integration of these subjective poles, creates a more responsible, reflective, reflexive and critical science that invites extrapolation into the who, what, when, where, how, why. In Haraway’s words, “It matters what stories tell stories”, and science is one of the most powerful storytelling machines in human history.
What is the interplay between proof and politics? “Lincoln was renowned for his speeches and the precise nature of his arguments, and that didn’t come about by coincidence. He made a conscious decision as a lawyer to get a better understanding of what it means to demonstrate something and construct an argument that is logically robust. So he went and taught himself the fundamentals of ancient Greek mathematics, Euclid’s Elements, and he would deploy those principles in his debates. He took advantage of this notion that if you can find a flaw or contradiction, you can cause someone’s entire argument to collapse… A lot of democratic ideas in the foundation of countries like the US attempted a kind of mathematical precision. The statement ‘we hold these truths to be self-evident’ in the US constitution was originally ‘we hold these truths to be sacred’, for example. But Benjamin Franklin crossed it out because he wanted more mathematical certainty behind these ideas, as if they were axioms. And in parallel with mathematics crumbling in its foundations, you saw the US descending into civil war, because the idea that all people are created equal wasn’t self-evident to some people. You had the same tension manifesting in two different ways in two very different fields.” (Kucharski)
Trusting Tentative Tastes: Proof Pudding
Understanding how science (and other disciplines) navigate this delicate balance between evidence and doubt is crucial for interpreting research, public policy, and our daily decision-making. Science may never prove anything with certainty, but it offers our most reliable path to understanding the world. It does so by recognising its own limitations, being open to revision, and anchoring claims in an evidence-base that is open and reflective about its wider ideological context. The history of science is littered with examples of the need to proceed with a mix of curiosity and caution.
The way through may be less about choosing between epistemological camps and more about designing practices that are both reflexive and robust. That means doing rigorous research with transparent methodologies and clear criteria for interpretation – remaining critically aware of the cultural, political, and philosophical scaffolding that supports such frameworks. In areas like psychedelic science especially, where questions of consciousness, healing, and meaning loom large, this dual commitment to evidential integrity and contextual sensitivity works with arising tensions, rather than seeking to resolve or conclude them.
How do we embrace certain uncertainties and constant change? “In the moment, [people] often get distracted: something triggers an emotional response, or aligns with experiences and beliefs, and they share the information on those grounds, without checking the facts… But there are lots of layers to this. Henri Poincaré, a mathematician who did a lot of work in the late 19th and early 20th centuries, described something like this: ‘To doubt everything or to believe everything are two equally convenient solutions; both dispense with the necessity of reflection’… I’ve found that ideas like calculus were also based on physical intuitions about the world: an apple falls, and we can write down the equations that drive its motion. But when you started getting down into it, you could find exceptions where the intuitions weren’t true. As a result, you had this tension with an entire community who wanted to ignore these nuisances – these ‘monsters’, as they called them – while other characters were pushing for an evolution of the field.” (Kucharski)
