Karsten wrote: > > And math develops slowly not because of its economic model, but very > > simply because it is hard. > > Does it and is it? > Time for a biased opinion? One *very* biased opinion coming up... > Is math any harder, say, than chemistry or drug development? > No, but it does not scale as well. Additionally the current mathematical establishment is *very* dysfunctional when it comes to communication... > What about times like WWII and the Cold War era when certain areas of > basic research (nuclear physics, crypto) were heavily funded for > strategic reasons. Is there an incentives problem in math? Are we or > are we not producing an economically efficient level of algorithms and > proofs? The volume of math today is absolutely incredible. But is it working well together? Here is a description of a typical department math talk. A talk is scheduled, and a group of mathematicians shows up at the appointed hour. Most of the mathematicians know they will be lost incredibly quickly, so they thoughtfully have brought themselves something else to do. About 15 minutes into the talk the person at the front is just getting to the actual topic of research (having put it in the context of mathematics in general, the research field, etc), and most people are already lost. Therefore they are reading papers, grading, sleeping - in other words doing what they expected to spend most of the hour doing. The person who invited the speaker is following (after all you invite someone in your own area), and the speaker is going strong... This is standard and accepted. It is also why I could not bear spending the rest of my life in mathematics. The actual structure of the mathematics research community today is that it is split into groups of a dozen or so people per area who have poor communication with outside mathematics. There are some stars, but by and large people are ignorant of what goes on outside their own area, and are unable to explain their research to anyone outside of a select group. Each group is also a bit of an old boys network. Given that nobody else can judge their work, they wind up reviewing each other's papers, recommending each other's students for tenure, etc, etc. Real world tenure decisions are not - indeed cannot - be made on quality for the simple fact that your colleagues at your school cannot read and judge your papers. Thus for the majority, success lies in getting in with a group whose recommendations hold weight... Two books that I recommend, "Why The Professor Can't Teach" and "The Mathematical Experience". The first has been described by several mathematicians of my aquaintance as, "My biography." The other gives a flavor of what sorts of things do get covered in mathematics and briefly mentions the dynamics that I describe above. Cheers, Ben