Funnily enough , reading this book about string theory has tied up quite neatly the maths I did at the Open University many years ago. At the time the pure maths did not tie up with anything to do with physics but reading this book from a scientist who has studied both areas very deeply has given me a number of eureka moments.
Late seventies I studied the O.U. Maths Foundation course (M101) , which apart from calculus introduced matrices. Matrices are an important step towards calculating symmetries, which give rise to symmetries in particle physics and the chiral properties in nature. For example a lemon is a mirror image of an orange in terms of their molecular structure but giving quite different smells (check QI for this).
Group theory is also important in the development of determining spin of a particle, and that all fermions , such as electrons, have an angular momentum spin of ½ integer value whereas bosons (such as the proton) have a spin of 1.
The two hypothetical particles, the graviton and the Higgs boson , would have a spin of 0 and 2 respectively.
http://en.wikipedia.org/wiki/Spin_%28physics%29After achieving a good result in the foundation course I did attempt to do the second level pure maths course which introduced vectors, eigenvalues and eigenstates, the Hamiltonian operator, and the Hilbert space. Once again , all these terms become important in the wave equations of Schroedinger and Heisenberg. Reading the Peter Woit book bring all these terms flooding back into my memory, but now I can see why the maths is fundamental to the science.
I also completed the science foundation course the year before and studied physics to third level.
Enough of the brain melting for the morning. Off to Canterbury and Maidstone today and then cinema at Rochester.