Physical intuition often provides interesting approaches that then need some mathematical foundation, e.g. the Dirac delta function and the theory of Distributions. Is this type of cross-fertilisation still active? What are the current hot topics? Who is more interested here, the mathematicians or the physicists?
Yes physics is still a motivation to develop mathematics. But computers, robotics and biology are also engines for the development of current mathematics (for example, fuzzy mathematics).
Yes, it is, although there are some claims that the inspiration for math now comes from biology too as the latter becomes more mathematical:
Article Biology is the new physics
Would you say that this means that the importance of physics as driving force is decreasing?
Of course, mathematics is necessary nowadays in most branches of the sciences, but also in economy and industry.
Also, there are ideas from mathematics that are driving the other disciplines.
As to whether the importance of physics as driving force is decreasing, I doubt that (if it does it happens very very slightly).
No doubt, physics has been one of the driving forces for the development in Mathematics. But now-a-days, some other subjects like computer science, biology and economics are equally responsible for its development along with physics. The branches of mathematics like discrete mathematics, optimization theory, bio-mathematics etc., owe more to these sciences than physics. Moreover, Mathematics develop itself as a science and as an independent discipline irrespective of the development in these sciences.
Owing to the economical situation (the poor more and more poor, and the rich more and more rich) mathematics is turning into management science, the mathematicians have become simple employees of the stock markets. Physics is reduced to superstrings, much mathematical but not really evolving.
There are quite a number of intreaguing mathematical topics besides string theory in physics, basic ones, e.g. characterize the exact exchange correlation functional in density functional theory, and more applied ones, e.g. find mathematical approaches to the estimate the errors in ab initio methods for molecules (for 100 electrons, one has to solve a many- body problem in 300 dimensional space) and solids (10^23 or more electrons) - isn't amazing that there are methods for such problems that provide numbers that correlate to experiments :) ?
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