Here's a summary of your summary: Algorithms are cool. Traditional mathematics isn't enough for modern science; in the future there'll be lots of simulations a

Here's a summary of your summary: Algorithms are cool. Traditional mathematics isn't enough for modern science; in the future there'll be lots of simulations and computer models -- algorithms. But we know how to reason with mathematical formulae, and as yet we have no equally strong "calculus of algorithms". This needs more research.