Conclusion

Innovative applications like Mathematica need to be understood in the multiple contexts created by the co-evolution of culture and technology. In this regard, metaphoric approaches may be be useful, for example comparing the development of Mathematica notebooks to the early history of cinema. [28] We must also keep in mind the basic principle: Synaptic Law is not Moore's Law! No matter how smart computers get, human synapses still require time to form new connections.

Nevertheless, it is hard to suppress excitement as we reflect on the ideas of visionary thinkers such as Stan Ulam, who wrote forty years ago on the possibility of using computers as a heuristic aid:  

In addition to, and in some aspects quite beyond the above type of use of electronic computing machines, one can conceive more general possibilities for large scale experimentation on problems of pure mathematics or in exploration of tentative ideas in physical theories.... [29]

This statement came from a time of punch-card input and fan-fold paper output from large machines [physically, but puny in terms of today's laptop capacities] that most users never came close to. Today, to students doing their homework with Calculus WIZ, this must not seem such a remarkable idea at all.