In our Oxford Mathematics Christmas Lecture Alex Bellos challenges you with some festive brainteasers as he tells the story of mathematical puzzles from the middle ages to modern day. Alex is the Guardian’s puzzle blogger as well as the author of several works of popular maths, including Puzzle Ninja, Can You Solve My Problems? and Alex’s Adventures in Numberland.

Simon Baron-Cohen, Professor of Developmental Psychopathology, Cambridge, and Director of the Autism Research Centre, gives the 2016 Charles Simonyi Lecture on new research into autism.

From early mathematical inspiration at school in Duffield, Derbyshire, Nigel recalls his often unplanned progress via Jesus College, Oxford, Princeton, Cambridge and Warwick, before his final return to Oxford. Along the way such luminaries as Michael Atiyah and Simon Donaldson play their part as Nigel talks about time spent with physicists in Cambridge, the Eureka moments when the answers take shape, to his final reflections on a career where the name Hitchin is attached to so many of the tools of modern geometry and which culminated in the award of the 2016 Shaw Prize.

What can fashionable ideas, blind faith, or pure fantasy have to do with the scientific quest to understand the universe? Surely, scientists are immune to trends, dogmatic beliefs, or flights of fancy? In this lecture, based on his new book, Roger will argue that fashion, faith, and fantasy, while sometimes productive and even essential, may be leading today's researchers astray, most notably in three of science's most important areas - string theory, quantum mechanics, and cosmology. Yet Roger will also describe how fashion, faith, and fantasy have, ironically, also been invaluable in shaping his own work.

Roger Heath-Brown is one of Oxford's foremost mathematicians. In this interview with fellow Oxford Mathematician Ben Green, Roger reflects on his influences, his achievements and the pleasures that the subject of mathematics has given him. Roger Heath-Brown's work in analytic number theory has been critical to the advances in the subject over the past thirty years and garnered Roger many prizes. On the eve of his retirement Roger spoke to Ben Green, Waynflete Professor of Mathematics in Oxford and himself a leading figure in the field of number theory.

In this lecture Professor Alison Etheridge explores some of the simple mathematical caricatures that underpin our understanding of modern genetic data. How can we explain the patterns of genetic variation in the world around us? The genetic composition of a population can be changed by natural selection, mutation, mating, and other genetic, ecological and evolutionary mechanisms. How do they interact with one another, and what was their relative importance in shaping the patterns we see today?

Oxford Students discuss the Prime Number Theorem. Prime numbers have fascinated mathematicians since there were mathematicians to be fascinated, and The Prime Number Theorem is one of the crowning achievements of 19th century mathematics. The theorem answers, in a precise form, a very basic and naive-sounding question: how many prime numbers are there? Proved in 1896, the theorem marked the culmination of a century of mathematical progress, and is also at the heart of one of the biggest unsolved problems in mathematics today. Host: Aled Walker, 2nd year DPhil, Mathematics, Magdalen College Guests: Simon Myerson, 4th year DPhil, Mathematics, Oriel College: Sofia Lindqvist, 1st year DPhil, Mathematics, Keble College, Jamie Beacom, 1st year DPhil, Mathematics, Balliol College.

Science is giving us unprecedented insight into the big questions that have challenged humanity. Where did we come from? What is the ultimate destiny of the universe? What are the building blocks of the physical world? What is consciousness? 'What We Cannot Know' asks us to rein in this unbridled enthusiasm for the power of science. Are there limits to what we can discover about our physical universe? Are some regions of the future beyond the predictive powers of science and mathematics? Are there ideas so complex that they are beyond the conception of our finite human brains? Can brains even investigate themselves or does the analysis enter an infinite loop from which it is impossible to rescue itself? To coincide with the launch of his new book of the same title, Marcus du Sautoy will be answering (or not answering) those questions

The Oxford Mathematics Christmas Public Lecture 2015 examined an aspect of Christmas not often considered: the mathematics. Delivered by Marcus du Sautoy, Simonyi Professor for the Public Understanding of Science. The Oxford Mathematics Christmas Lecture is generously sponsored by G-Research - Researching investment ideas to predict financial markets.

The understanding of the possible geometries in dimension 3 is one of the triumphs of 20th century mathematics. In this talk Martin Bridson explains why such an understanding is impossible in higher dimensions. When one wants to describe the symmetries of any object or system, in mathematics or everyday life, the right language to use is group theory. How might one go about understanding the universe of all groups and what kinds of novel geometry might emerge as we explore this universe? Martin Bridson became Head of the Mathematical Institute on 01 October 2015. To mark the occasion he gave this Inaugural Chairman's Public Lecture.

Professor Melissa Franklin talks about her experiences working towards the discovery of the Higgs Boson and her work today at the Large Hadron Collider This entertaining lecture by experimental particle physicist, Professor Melissa Franklin (the first woman to achieve tenure in the Harvard Physics Department), is the latest in the Charles Simonyi annual lecture series. This series was set up in 1999 in order to promote the public understanding of Science