19-Feb-2012, 11:50 PM

Started this thread to continue on a discussion over at http://nirmukta.net/Thread-Why-negative-...05#pid6305 , that was turning out to be tangential to the topic.

Kanad said

'Never' is too strong a word to be used in this context. Historical geometry was developed mainly for practical use. In Egypt, it was used to build pyramids. In Mesopotamia, mathematics evolved with the purpose of being useful to trade and administration. In India, sulva sutras and other Vedantic mathematics was written to assist in constructing altars for religious rituals. Now, this doesn't mean that all the mathematics of the ancient world was utilitarian. Basic human curiosity would have led some of the mathematicians to consider abstract generalizations of utilitarian geometry. I think it is because of interest in such abstract generalizations that ancient Greek mathematicians pioneered the method of proof. It is also possible that the complex geometrical shapes that ancient Indian priests prescribed for religious altars were due to such curiosity for the abstract and the non-utilitarian.

A reductionist view of the evolution of poetry and music can be an analogy, in my opinion, to the development of mathematics. Poetry (and some forms of music) originally served the purpose of facilitating the transmission of ideas in pre-literate history. This changed over time, in part, due to the growth of literacy. The greatness of many classical poets, even in before writing became prevalent, is because of their treatment of poetry as an intellectual exercise.

Kanad said

Quote:Also, Mathematics is historically never been developed in CONJUNCTION with its applications as you seem to claim.Geometry is pretty old and it was developed and appreciated for its logical consistency. Infact almost all major mathematics concepts have been discovered in era which had no use of idea.

'Never' is too strong a word to be used in this context. Historical geometry was developed mainly for practical use. In Egypt, it was used to build pyramids. In Mesopotamia, mathematics evolved with the purpose of being useful to trade and administration. In India, sulva sutras and other Vedantic mathematics was written to assist in constructing altars for religious rituals. Now, this doesn't mean that all the mathematics of the ancient world was utilitarian. Basic human curiosity would have led some of the mathematicians to consider abstract generalizations of utilitarian geometry. I think it is because of interest in such abstract generalizations that ancient Greek mathematicians pioneered the method of proof. It is also possible that the complex geometrical shapes that ancient Indian priests prescribed for religious altars were due to such curiosity for the abstract and the non-utilitarian.

A reductionist view of the evolution of poetry and music can be an analogy, in my opinion, to the development of mathematics. Poetry (and some forms of music) originally served the purpose of facilitating the transmission of ideas in pre-literate history. This changed over time, in part, due to the growth of literacy. The greatness of many classical poets, even in before writing became prevalent, is because of their treatment of poetry as an intellectual exercise.