Introduction
Compressed sensing: through the kaleidoscope
Eigenvectors: from the mathematical sciences to...an IPO
Mathematical simulations: when the lab isn't big enough
Mathematical sciences inside...tsunamis
Byesian inference: not an enigma anymore
Diffusion tensor imaging: a new view of the brain
Fast multipole method: a long-term payoff
Mathematical sciences inside...the battlefield
Cellular automata: sublimely complex
Graph spectra: sparsest cuts in minimum time
Bioinformatics: interpreting the human genome
Geometry and physics: endlessly intertwined
Probability and statistical physics: connecting microscopic and macroscopic
Mathematical sciences inside...inventions.