JOINT LONDON MATHEMATICAL SOCIETY/ GRESHAM COLLEGE ANNUAL LECTURE Toy here has a special sense: an object of daily life which you can find or make in minutes, yet which, if played with imaginatively, reveal behaviours that keep seasoned mathematicians and physicists puzzled for a while. The lecture will consist of tabletop demos of such toys, together with simple, robust modelling of what is going on. The theme that emerges is singularity. The transcript and downloadable versions of the lecture are available from the Gresham College website: https://www.gresham.ac.uk/lectures-and-events/mathematical-research-from-toy-models Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There are currently over 2,000 lectures free to access or download from the website. Website: http://www.gresham.ac.uk/ Twitter: http://twitter.com/GreshamCollege Facebook: https://www.facebook.com/greshamcollege Instagram: http://www.instagram.com/greshamcollege