Maths for beginners

Hannah Fry's books, programmes and talks keep returning to a handful of big mathematical themes. You do not need a degree to follow any of them; her whole career is built on making these ideas accessible. Here is what each one means and why it matters.

Probability and chance

Probability is the mathematics of uncertainty. It gives us a framework for thinking about how likely something is to happen, from the roll of a dice to the spread of a disease. Fry's Royal Institution Christmas Lectures (2019) were built around this idea: how to get lucky, how to bend the rules, and what happens when the numbers break down.

At its simplest, probability is a number between 0 (impossible) and 1 (certain). Flip a fair coin and the probability of heads is 0.5 — one half. But real-world probabilities are rarely that clean. The probability that it rains tomorrow, or that a medical test gives the right result, depends on conditions, assumptions and data. Fry's work shows how even small misunderstandings of probability can lead to bad decisions — in courtrooms, hospitals and everyday life.

The Come Fry With Me tour's tagline, "an evening of chance, chaos and questionable decisions", suggests probability will be central. Try our birthday paradox calculator or Monty Hall simulator to explore chance for yourself.

Algorithms and artificial intelligence

An algorithm is a set of step-by-step instructions for solving a problem. Recipes are algorithms. So are the rules for long division. In computing, algorithms sort your search results, recommend what to watch next, set the price of your train ticket and decide whether a bank approves your loan.

In Hello World, Fry explores what happens when we hand important decisions to algorithms — and where things go wrong. She looks at justice (algorithms that predict reoffending), medicine (algorithms that diagnose disease from scans), art (algorithms that generate music) and transport (self-driving cars). The book does not take a simple pro- or anti-technology stance; instead, it asks where the line should be between human judgement and machine calculation.

Artificial intelligence extends this idea: AI systems learn from data rather than following hand-coded rules. They can recognise faces, translate languages and play games at superhuman levels, but they inherit the biases in their training data. Fry's work on AI Confidential, The Future with Hannah Fry and the Google DeepMind podcast all explore these tensions.

Relationships and the mathematics of love

One of Fry's most popular themes is using mathematics to understand human relationships. The Mathematics of Love (2015) covers how mathematical models — originally designed for very different purposes — can illuminate dating, attraction and long-term partnerships.

For example, the "optimal stopping" problem (also called the secretary problem or the 37% rule) suggests that if you date a fixed number of people, you maximise your chances of finding the best match by rejecting the first 37% outright, then choosing the next person who is better than all the ones before. It is a simplified model, but it illustrates how mathematics can frame an apparently emotional decision.

Another example from the book draws on the work of psychologist John Gottman, who found that the ratio of positive to negative interactions in a couple's conversation could predict whether they would stay together. Fry explains how differential equations — the same kind of maths used to model predator-prey relationships in ecology — can describe these dynamics.

Cities and data

Before moving to Cambridge, Fry was Professor of the Mathematics of Cities at UCL. Her research used mathematical models and large datasets to understand urban life: how crime clusters in certain streets, why traffic jams form, how epidemics spread through a city and how people move through transport networks.

This work sits at the intersection of mathematics, data science and urban planning. The idea is that cities, despite their apparent chaos, contain patterns that mathematical models can detect and sometimes predict. Fry's early TED talk, "Is life really that complex?" (2012), introduced this theme by showing how the patterns on a leopard's spots follow the same mathematical rules as the spatial distribution of burglaries.

Game theory and decision-making

Game theory is the study of strategic decisions — situations where the best choice for you depends on what other people do. It shows up in economics, politics, biology and everyday negotiations. The classic example is the Prisoner's Dilemma: two people are better off cooperating, but each has an individual incentive to betray the other.

Fry's upcoming book No One Knows What They're Doing (September 2027) takes on decision-making and uncertainty directly. The title itself captures a theme she returns to often: experts, institutions and algorithms are all working with incomplete information and making the best guesses they can. Understanding the mathematics of decision-making helps us see where those guesses go right and where they go wrong.

Where to go next

If any of these topics interests you, here are some starting points on this site:

• Which Hannah Fry book to read first
• TV and radio programmes — watch the ideas in action
• Podcasts and TED talks — shorter introductions
• Interactive tools — explore probability, expected value and more
• What to expect at Come Fry With Me

Common questions

This page is original explanatory content written for a general audience. Sources for factual claims are linked inline and listed on the relevant hub pages. This site is independent and not affiliated with Hannah Fry.