If the NY Times book review of S. Wolfram's new book is accurate then Wolfram (who earlier developed very useful software for numerical analysis and methods in calculus) has now been re-born and "sees the truth": that calculus, Lebesgue integrals, differential and integral equations and in general the old methods of obtaining of explicit solutions should now be replaced by algorithms.

I'll give a few examples where mathematical thinking based on Lebesgue and Ito calculus gives quantitative insight while direct algorithmics alone gives just numbers. The examples include CAT scanning, functional magnetic resonance imaging, (fMRI), as well as finance and economics.