74 3. MATHEMATICAL CULTURES II
3.3. What is the justification for the statement by the historian of mathematics T.
Murata that Japanese mathematics was not a science but an art?
3.4. Why might Seki K5wa and other Japanese mathematicians have wanted to
keep their methods secret, and why did their students, such as Takebe Kenko, honor
this secrecy?
3.5. For what purpose was algebra developed in Japan? Was it needed for science
and/or government, or was it an "impractical" liberal-arts subject?
3.6. Dante's final stanza, quoted above, uses the problem of squaring the circle
to express the sense of an intellect overwhelmed, which was inspired by his vision
of heaven. What resolution does he find for the inability of his mind to grasp the
vision rationally? Would such an attitude, if widely shared, affect mathematical
and scientific activity in a society?
3.7. One frequently repeated story about Christopher Columbus is that he proved
to a doubting public that the Earth was round. What grounds are there for believing
that "the public" doubted this fact? Which people in the Middle Ages would have
been likely to believe in a flat Earth? Consider also the frequently repeated story
that people used to believe the stars were near the Earth. How is that story to
be reconciled with Ptolemy's assertion that it was acceptable to regard Earth as
having the dimensions of a point relative to the stars?
3.8. What are the possible advantages and disadvantages of eliminating or greatly
reducing the volume of journals, placing all articles on electronic files that can be
downloaded from various information systems?
3.9. Mathematical research is like any other commercial commodity in the sense
that people have to be paid to do it. We have mentioned the debate over taxing the
entire public to support such research and asked the student to consider whether
there is a national interest that justifies this taxation. A similar taxation takes
place in the form of tuition payments to American universities. Some of the money
is spent to provide the salaries of professors who are required to do research. Is
there an educational interest in such research that justifies its increased cost to the
student?
