When and why did the postdoctoral position originate? Does anyone know when and how the system of post-doctoral studies after a Ph. D. originated? I've heard in a few places that there was a time when there was no such thing as a post-doc, and people used to go for faculty positions right after their Ph. D.'s. Is this true? When and why did it change? What does the post-doctoral position achieve?
 A: Well, in Italy Ph.D. programs started about in mid-80s (1980s, I mean), so strictly speaking we had no post-doctoral positions or fellowships before that. :-)
A: Some anecdotal evidence I heard from the older generation is that post docs in the sciences and mathematics didn't really appear (in the United States) until the Eisenhower era. During the cold war there was a big push by the government to invest in basic research, so suddenly everybody got more money to hire more graduate students. Unfortunately, the faculty positions are not opening up as fast. So you have a problem with supply bigger than demand. The expectation was that (a) more professorships will be created and (b) due to the explosion of interest in basic research, partly driven by the invention of the atomic bomb, industry will start hiring more PhDs. So it was expected that the over-supply of PhDs is a temporary problem (so does not need "curing" at the source) and a simple stop-gap (the post doc position) is enough. 
How much of this is actually true, I am not certain. 
A: It is important to understand that the postdoc was not designed to "achieve" anything. It is simply a product of the system's incentives. There is no central planner.
In the US a professor at a research university gets tenure and promotion based on the number of publications and grant dollars he has. As you know, a postdoc or PhD student can write several good papers' a year in which the advisor (professor) shows up a second author. So, someone who can fund 10 students will have 10 times as many publications as someone with 1 student. The more publications you have the easier it is to get funding, so we have a positive feedback loop where the top performers get a continually larger share of the money and talent.
Because of this, a professor would rather hire 2 postdocs at \$40K/year than 1 postdoc at \$80K/year since we know that more money does not translate into more papers. In the sciences and math new PhDs are happy to take the job of a postdoc at very low wages, for several reasons:


*

*Some really really want that tenure-track job, so are willing to endure the costs.

*Some have few other job prospects

*For many foreign students (India, China) the postdoc salary is much higher than anything they could get in their country, and has the added benefit (for some) of a student visa to the US with the prospect of full citizenship to come. It is much easier to become a US citizen if you have a PhD and are employed in the US.


More than half of US Science and Math PhD students and postdocs are foreigners, so point 3 is a big effect.
There are virtually no postdocs in Law, Medicine or Finance, since someone with a law degree, medical degree, or finance PhD commands a starting salary above \$150K/year in the marketplace, so they are not willing to take a postdoc for such comparatively low wages. In Computer Science the postdoc is still somewhat rare since starting salaries for PhDs in CS are around \$100K in industry. Thus, point 1 also seems important.
A: This is really a blog question, with no single answer.   There are 150+
Ph.D. programs in mathematics in the U.S., plus various institutes.  As
noted already, there is no central planner.   Before the 1960s there
were relatively few mathematicians in the U.S.   Those doing active
research in universities did a lot of routine teaching and were low paid.
But then higher education mushroomed for many reasons, with new programs
and universities all over the place.   The Ph.D. program here at UMass
(earlier Mass. Agricultural College) started in the mid-1960s.   Hiring
everywhere of new Ph.D.'s was frenetic and worked mainly through the old
boy network.   As the market settled down and recessions occurred, 
temporary postdoc positions became more common.   Some at the prestigious
universities were institutionalized, others were an afterthought and most
often on a 1-2 year basis.   At UMass almost everyone in the 1970s was
on a tenure-track, with just a few non-Ph.D. "lecturers" on contracts.
It's cheaper for administrators to hire non-Ph.D. people just for teaching
service courses, so here it was difficult to persuade the provost and others
that postdocs are standard for research-based math programs.  Our main
postdoc burst occurred after two state early retirement incentives removed
most of the senior faculty.   Now postdocs are sporadic and hard to authorize
here, though the department still wants them.   (There are still a few
lecturers, who have full faculty benefits but no tenure.   We'd have more
if they didn't undercut faculty teaching ratios and if UMass had built
bigger lecture halls.)   The statistics part of the UMass department still
tends to hire new Ph.D.'s on tenure tracks due to market pressures from
nonacademic employers.  No conspiracies, but lots of pressures on the system.
A: In know that there is some variation among fields for when post-docs became popular.  My understanding is that the "post-doc" institution as a whole began around the beginning of the last century, but didn't become common until many decades later.  In the physics (and, I think, math) world, there was an explosion of post-docs in the US after WWII.  During the war, the government had created many national labratories, and most of the top physicists took time away from their other academic pursuits to help in the war effort.  When the war ended, the government was still very interested in funding physics research (Cold War!) in particular, and academics in general (G.I. Bill!).  Thus, in the US anyway, the middle of the 20th century saw a dramatic rise in both the demand and supply for researchers.  But the number of professorships didn't match pace, hence the growing number of post-docs.  Moreover, many of the leading senior physicists at the time (Oppenheimer, Bethe, etc.) strongly encouraged the creation of post-doc positions as a way for the young people (Feynman, Dyson, Schwinger, etc.) to communicate their theories.  As is often said: the best way to send an idea is to wrap it in a person.
This story is very well told in D. Kaiser, Drawing theories apart: the dispersion of Feynman diagrams in postwar physics, University of Chicago Press, 2005.
One other comment is important to make.  The structure of the academy (and in particular the names of ranks) can vary wildly from country to country, so that "assistant professor" in some countries means "post-doc" in others.  For example, Denmark in the last decade has made a conscious shift away from the "German" model, in which there are very few "professors", each of whom over see many full-time senior researchers, and towards a more "American" model where the rank "(full) professor" is more freely given.
A: I think the why part is easy. University administrations like cheap labor and are risk averse when it comes to giving permanent jobs, and the people who already have permanent jobs like cheap labor because then their teaching load goes down. The real question is why people take post-docs. I think the answer is that people really want to do good mathematics and they think (often correctly, often not) that having access to the top people will help them do that, so they're willing to accept all the sacrifices that come with post-docs.
A: Another factor is that as the decades have gone by, in many branches of math the amount one has had to learn to get going researchwise has increased markedly. This of course varies a lot from subject to subject, but in many areas it can take quite a while after the PhD to develop the kind of research record that a research university wants to see before they hire you on the tenure-track and take the risks associated with that. This encourages the proliferation of postdocs as well.
