Beginning with reference to a classic 1959 C.P. Snow lecture, Stewart argues that mathematics, unlike almost any other field of study, "spans the divide" between the arts and sciences, and makes many interesting points along the way.
Some excerpts to poke your interest…:
"...the mathematical subculture is gravely misunderstood by most members of the public, many prominent scientists, nearly all artists, the vast majority of politicians and almost every bureaucrat on the planet."Set aside some time to read... and think about... the whole piece.
"For mathematics to be useful in today’s society, it has to be invisible. If anyone using a mobile phone had been required first to take a PhD in mathematics, the device would never have appealed to a large enough market to make it worth anyone’s while to manufacture. However, without a significant number of engineers who know some very advanced and apparently esoteric mathematics, mobile phones wouldn’t work."
"If 10 per cent of the $9bn spent on Cern’s Large Hadron Collider had been allocated to research in the mathematical sciences instead, the benefits to society would have been far greater and would have occurred more rapidly. The development of the next generation of supercomputers, a project estimated to cost about $1bn, is struggling to find funding. The result would be a machine with applications throughout the sciences – for example, in climate change and in the design of new materials and alternative energy sources – and it would dominate future computer technology."
"However, the nature and importance of mathematics do not rest solely on its practical uses or its artistic merit. It has an intrinsic intellectual interest and an idiosyncratic beauty. What makes it so hard to grasp the subject’s nature is that it combines many disparate elements in one ever-growing, ever-changing body of knowledge. It is practical, arcane, precise, obscure, abstruse, rooted in nature, rooted in the human imagination; its history spans 4,000 years, and what was discovered long ago is often just as valid and important today. It is absolutely huge, increasing by a conservative one million pages a year, and it is all one thing. Its internal connections link entirely different sub-disciplines in an intricate, dynamically changing web, so that yesterday’s dead end may suddenly become today’s essential technique."