Diophantus, another Greek, wrote a book about these ideas in the third century A. Algebra was further developed by Abu Abd-Allah ibn Musa Al-Khwarizmi (c. For a long time people were able to predict the motions of some of the heavenly bodies using ad hoc theories derived from observation and philosophical considerations.Claudius Ptolemy wrote the , a famous compendium of this knowledge, in the second century.
In the distant past there were people who lived on the banks of the Nile River.
Each year the Nile overflowed its banks, wiping out land boundaries but providing fertile soil for growing crops.
Traditional mathematics provides a framework for dealing precisely with notions of “what is.” Computation provides a framework for dealing precisely with notions of “how to.” Computation provides us with new tools to express ourselves.
This has already had an impact on the way we teach other engineering subjects.
But the advances that look like giant steps to us will pale into insignificance by contrast with the even bigger steps in the future.
Sometimes I try to imagine what we, the technologists of the second half of the 20th century, will be remembered for, if anything, hundreds of years from now.
For example, one often hears a student or teacher complain that the student knows the “theory” of the material but cannot effectively solve problems.
We should not be surprised: the student has no formal way to learn technique.
In each of these cases there was an advance in human intelligence, ultimately available to ordinary children, that was precipitated by an advance in mathematics, the precise means of expression.
Such advances are preceded by a long history of informal development of practical technique.