Do humans have a free choice of which actions to perform? Three recent developments of modern science can help us to answer this question. First, new investigative tools have enabled us to study the processes in our brains which accompanying our decisions. The pioneer work of Benjamin Libet has led many neuroscientists to hold the view that our conscious intentions do not cause our bodily movements but merely accompany them. Then, Quantum Theory suggests that not all physical events are fully determined by their causes, and so opens the possibility that not all brain events may be fully determined by their causes, and so maybe - if neuroscience does not rule this out - there is a role for intentions after all. Finally, a theorem of mathematics, Godel's theory, has been interpreted to suggest that the initial conditions and laws of development of a mathematician's brain could not fully determine which mathematical conjectures he sees to be true. Papers by Patrick Haggard, Tim Bayne,