Sir Roger Penrose is one of the greatest living physicists. He also has written a number of books which are extraordinary resources for anyone who would like to learn modern science and mathematics.
These books have significant pre-requisites or require greater commitment of the reader. In many cases they would best be approached as part of a class or study group.
Science and Technology are driving change at an accelerating rate. The consequence of this is that the future we are heading towards will not resemble the past. Some of the coming changes are likely to resemble extrapolations from existing trends, the evolution of recent developments and known theoretical possibilities. Others will doubtless take us by surprise.
One of the best ways to learn Geometry is by interacting with computerized geometry systems. One of the best ways to learn computing is by writing programs which construct and manipulate geometrical objects!
Some computer systems are designed to support learning Euclidean geometry:
Geometric Algebra is a more powerful, expressive, concise and arguably “natural” mathematical language for much of Physics, Computer Science and other disciplines than traditional vector, matrix and tensor approaches.
Anyone who likes the Harry Potter series should at once read
There is excellent practical material on Logic and Rationality atLessWrong
These books and videos present an excellent and practical model for being more effective in our work as well as being more effective in our relationships within the general community.
The videos provide a quick introduction to material which the books go into much more deeply and thoroughly yet the books are short easy reads.