Essay/Logic Philosophy tool kit Thinking like a philosopher need not be a strange and arcane art, if you get started with these tricks of the trade Alan Hájek

Essay/History of Ideas Infinity and beyond Georg Cantor showed that some infinities are bigger than others. Did he assault mathematical wisdom or corroborate it? A W Moore

Video/Mathematics A brilliant ‘geometric ballet’ of sound, shape and symmetry on the theme of 180° 5 minutes

Essay/Mathematics How to play mathematics The world is full of mundane, meek, unconscious things embodying fiendishly complex mathematics. What can we learn from them? Margaret Wertheim

Essay/Logic What is logic? Is logical thinking a way to discover or to debate? The answers from philosophy and mathematics define human knowledge Catarina Dutilh Novaes

Video/History of Science Energy is like children’s toys: often hiding out of sight, but never actually lost 3 minutes

Essay/Mathematics Future tension Facts about the past and present are either true or false. Can knowledge of the future offer the same degree of certainty? Anthony Sudbery

volume_up play_arrow pause Idea/Logic On vagueness, or, when is a heap of sand not a heap of sand? Timothy Williamson

Essay/Mathematics The problem with p-values Academic psychology and medical testing are both dogged by unreliability. The reason is clear: we got probability wrong David Colquhoun

Video/Mathematics Mesmerising fractals and space-filling curves give a window into infinity 3 minutes

Essay/Economics The new astrology By fetishising mathematical models, economists turned economics into a highly paid pseudoscience Alan Jay Levinovitz

Video/Mathematics The pleasure of being fooled: inventor Mark Setteducati makes maths into magic 4 minutes

Video/Beauty & Aesthetics Discover the secret geometry of beauty – the mathematics of form and pattern 4 minutes

Video/Mathematics Aerodynamics researchers play with air and water to make amazing flying machines 4 minutes

Essay/Epidemiology The calculus of contagion In the battle against disease, the difference between a raging epidemic and a passing fever comes down to a single number Adam Kucharski

Essay/Logic What are the chances? From a big lottery win to a disaster like the Titanic, unlikely stuff happens all the time. But can we summon it at will? David Hand

Video/Philosophy of Science The elegance of mathematics meets the breathtaking complexity of nature 4 minutes

Essay/Beauty & Aesthetics Beauty ≠ truth Scientists prize elegant theories, but a taste for simplicity is a treacherous guide. And it doesn’t even look good Philip Ball

Video/Beauty & Aesthetics Maybe I’m not even here, and other crazy, beautiful stuff physics told me 3 minutes

Essay/Logic The mathematical world Some philosophers think maths exists in a mysterious other realm. They’re wrong. Look around: you can see it James Franklin

Essay/Knowledge A drop in the sea What are the odds that Jesus rose or Moses parted the waves? Even with the best witnesses, vanishingly small Lawrence Shapiro

Essay/Physics A binding light Laser beams can tie themselves in knots, just like electrical cords. But what does this tendency to tangle illuminate? Anton Desyatnikov

Essay/Mathematics The sultan’s Sudoku Order and conformity make for satisfying number puzzles, but eerie countries. Welcome, Daniel Tammet, to Oman Daniel Tammet