Jobs for mathematics graduates

Recently I have spoken to several Italian high-school teachers. Their advice to students proceeding to university is that the important thing is to do something you like. This seems to me to be dangerous advice. It is important not to do something you don't like, if possible. However, a student must consider future job prospects in making a decision. It is no good training for non-existing positions and then demanding that the positions be created afterwards. It is not reasonable to imagine that it is trivial to change after spending three or more years learning skills in one area - this is to discount the value of education. One should realize also that educators in an area have an interest in attracting students independent of job opportunities.

Contrast the following two documents: one is the advice of the Mathematics Department, New York University; the other is a blog by a mathematics graduate:

Mathematics Department, New York University
"Career Opportunities
The study of mathematics can lead to a variety of exciting professional careers. Basic research, engineering, finance, business, and government service are among the opportunities open to those with mathematical training. Moreover, with the increasing importance of basic science and information technology, prospects for careers in the mathematical sciences are very good. Mathematical analysis and computational modeling are important for solving some of the most pressing problems of our time - new energy resources, climate change, risk management, epidemiology, to name a few. We must strive to maintain our technological edge; mathematical skills will be crucial to this effort.
Some more specific business positions include portfolio analysis, design studies, statistical analysis, computer simulation, software design and testing, and other areas of operations research. There are extensive opportunities for mathematics in finance, the actuarial fields, and economic forecasting.
Many laboratories, both government and private, maintain independent research staffs that include mathematicians. Their work often deals with the development of new technology, including research in basic physics and software development, as well as applied mathematics. Numerical simulation, such as weather and climate forecasting, depends heavily on the use of supercomputers.
Practical considerations aside, there is the pleasure of learning, applying, and creating mathematics. Real world issues pose problems that can be studied by formulating and analyzing mathematical models. In some cases applications may lead to new mathematics, and a new branch of the science is born. In other cases abstract theory finds unexpected practical purpose. Working on research problems is exciting; solving difficult problems successfully is, for many, satisfaction enough."

John Armstrong's blog
"All the evidence I see is that mathematics, in and of itself, is worthless in the current job market. It seems to have value solely as training in addition to some other primary field of study. I would love to be proven wrong, but every rejection (most without comment) that passes reinforces this hypothesis."

Update The comment by Sean Carmody that follows is interesting. When a new area which needs mathematical expertize opens there may be opportunities for people with only mathematical degrees but for a limited time. Unfortunately the advice given to new students doesn't mention the limited time, just the successes. I had a similar experience: when I finished a masters degree in mathematics in 1966 (?) I looked at job opportunities. Programming was open to anyone. Now a mathematics student without programming experience has to compete with people with years of experience for such positions.