“As the arguments of this book have shown, mathematical understanding is something different from computation and cannot be completely supplanted by it. Computation can supply extremely valuable aid to understanding, but it never supplies actual understanding itself. However, mathematical understanding is often directed towards the finding of algorithmic procedures for solving problems. In this way, algorithmic procedures can take over and leave the mind free to address other issues. A good notation is something of this nature, such as is supplied by the differential calculus, or the ordinary 'decimal' notation for numbers. Once the algorithm for multiplying numbers together has been mastered, for example, the operations can be performed in an entirely mindless algorithmic way, rather than 'understanding' having to be invoked as to why those particular algorithmic rules are being adopted, rather than something else.”