How hard is it to get tenure in mathematics? My curiousity provoked by this question and Igor's answer, I'd like to know: how many mathematics PhD's who want to get a tenured job as a research mathematician actually get that job?  
As a first approximation, I'd like to know how what percentage of math PhD's who get a research-oriented postdoc wind up as tenured professors in research-oriented jobs (pick a number of years $n \geq 6$, and determine the percentage of math PhD's who went on to research postdocs that had tenured jobs within $n$ years; the more data, the better).
(Of course I'd be happy with data for any particular region---e.g. US or Europe or Japan or Australia, and it'd be great to have it all; but maybe the US is the project to start with)
Added in response to Joel's answer: I haven't been able to extract what I want from the AMS data.  If someone else can do that, great!  But even though I haven't search it exhaustively, I don't think the information I want can be deduced from it.
 A: The American Mathematical Society has loads of data about mathematics doctoral recipients, starting salaries, faculty salaries, etc. I am not sure if the specific question about 6-years-after is answered in that data, but the data on starting salaries covers many years going back.
A: I don't think statistics on this are particularly useful to an person trying to assess the difficulty of pursuing an academic career (which is what I'm assuming is the motivation for this question).
Beyond the statistics, if you examine critically the faculty in any number of math departments, you will realize that it is often rather hard to predict who will or will not get tenure. The criteria is roughly based on some unknown weighting of a person's research record, teaching performance, and ability to work and get along with colleagues (this is often called "service"). Moreover, how each of these factors is measured and judged varies a lot among different departments. The decision is also influenced by many external factors beyond the candidate's control, such as what specialties the department wants to build in, who else got tenure recently, who else will be coming up for tenure, and the department and school's overall view of who they believe they can hire and keep. For this reason even a given department might vary in how it decides on tenure from candidate to candidate and year to year.
My general advice to anyone striving for a tenured position is to develop the strongest possible record in all of the criteria I listed above. A common mistake is to focus on the things that are stressed by the school and department where your current tenure track position is. The reason that this is a mistake is that no matter how strong your record is you can always be denied tenure for reasons that are beyond your control. So you will want to be in the strongest possible position to be hired and given tenure by a different school.
I also cannot emphasize too much how much easier it is to get tenure if in addition to having good enough academic credentials (both teaching and research), you demonstrate that you show that you're someone the existing tenure faculty feel they would like to have as a colleague for the rest of their life.
A: The figure I remember from many (many!) years ago is 20 percent.  Who knows which direction it has changed since, or how accurate it was even then.  But as I recall, this related Ph.D.s awarded in mathematics to the steady-state number of faculty in mathematics departments at research institutions.  (Both in the US?)  Of those getting a Ph.D. in mathematics, only 20 percent would end up in a faculty position at a research institution.  The other 80 percent would end up (perhaps after a temporary stint or two) elsewhere ... 4-year or 2-year colleges, Wall Street, National Security Agency, other industry, etc., or even cab driver or unibomber.
A: Here a weird surname-effect: "A 2006 study by Liran Einav, an assistant professor of economics at Stanford, and Leeat Yariv, an associate professor of economics at CalTech, found that faculty members "with earlier surname initials are significantly more likely to receive tenure at top ten economics departments" in the United States". It should be easy to check the data for mathematics instead of economy. 
Edit: Here a "a powerful dose of self-reflection, and has lessons for young scientists looking to move up the career ladder", as John Hawks calls it on his blog, and here "How to find problems to work on".  
A: I think it would be incredibly hard to get good data because it is actually an international market. So some people find postdocs and permanent positions outside the USA while some positions in the USA are filled by people coming from outside the USA. For instance, here in the UK large number of positions is filled by Germans. 
One way to try to estimate the chance is to look at a good number of departments and see how many postdocs they hire each year and how many tenure track positions they fill. But I doubt if this is going to be very accurate.   
A: By the way, this question would localize very poorly, as the meaning and process of tenure varies tremendously from country to country. For instance, in France until the 1960's, the professors were a small elite and in the most part one had to wait for a very long time to reach that exalted status (called in the day's slang mandarin as a facetious allusion to those guys). Then May 1968 went through, and believe or not, university positions in France are now tenured: if you're hired, you don't have to jump through hoops. 
For the record, it's not as nice as it sounds: it's great for those who do get hired, but if you're on a hiring committee, imagine what it's like to decide who is going to be in your department for potentially a lifetime based on a 15 minutes interview (I wish I was kidding!).
A: In the UK, impossible: tenure was abolished by Margaret Thatcher's government in 1988.
A: Look at the Survey of Doctoral Recipients.  This is a large scale survey of US doctoral recipients.  I'm not sure how much they've avoided sample bias.  They have 29,170 employed mathematicians in their sample, of which 


*

*17,290 are employed at "universities and 4-year colleges."

*860 are employed at "Other educational institutions"

*7,310 are employed at private companies

*1,050 at non-profits

*1,290 by the federal government

*350 by local governments

*1,020 are self-employed


Of those employed at "universities and 4-year colleges"


*

*5,340 graduated less than 10 years before the survey, of whom 880 are tenured,  2,750 are tenure track, 390 not on tenure track, and 1,310 are in positions where tenure is not applicable (it looks like 1,080 of these are postdocs)

*11,950 graduated more than 10 years before the survey, of whom 9,920 are tenured,  520 are tenure track, 730 not on tenure track, and 780 are in positions where tenure is not applicable (again, not sure what that means)


The total number in the sample who got their Ph.D.s more than 10 before the survey was 19,790, so about half of them got tenured positions at universities and four year colleges (of course, that number will go up a lot when you remove people who left academia right after graduating).  
[Edit by GS]:
The survey by the NSF is of "doctoral scientists and engineers": their definition is 
"Doctoral scientists and engineers are defined in this report as individuals less than 76 years of age who have received a doctorate in a science, engineering, or health field from a U.S. academic institution and who resided in the United States or one of its territories on 1 April 2006."
So Yiftach's objection that the market is really international has force here.  And a Ben notes, maybe there's some sample bias (perhaps people who hadn't done so well did not return the survey?) On the other hand, I still think I got some useful information out of the link Ben provides above.  
For instance, of the 33,830 people included in the survey with a math/stats PhD, about 4000 were retired, 330 unemployed, another 330 neither employed nor seeking work, and of the remaining 29000 about 26000 were employed full-time.  The "involutary out-of-field rate" was 4% (lower than the unemployment rate for just about every other type of degree!).  I wonder whether we can safely assume that this gives an upper bound on the unemployment rate for US math/stats PhDs (most will not leave the country without work---or are there enough internationals with visa issues to balance this out?)
Another useful piece of information: the number of math/stats PhDs in the US is not keeping up with population growth.  Of the roughly 29000 employed PhDs in the sample, about 8200 were between the ages of 55 and 64, about 6400 were between 45 and 54, about 8200 were between 35 and 44, and about 3300 were less than 34.
Of the 17,290 math/stats PhDs employed by "universities and 4-year colleges", about 5000 are primarily researchers, while about 10000 are primarily teachers, with another 2000 or so in other capacities (most popularly, "management/sales/administration").  It's hard for me to tell how many of the 5000 in research have tenure---though apparently the number math/stats PhDs with "postdocs" is about 1160 (I'm not sure why this differs with Ben's number above---mine is from table 36), with 660 "mathematical scientists" and 500 "postsecondary teachers" (I don't know what this means... perhaps the mathematical scientists are the ones who are primarily researchers?)
Unfortunately, I still don't know the answer to the question that motivated me (given that you get a postdoc after grad school, what's the probability that you wind up as a tenured research mathematician?)  But my feeling is that this probability is much higher than implied by the grim discussion in Philip Greenspun's article (linked to in Igor's answer to Ben's question, that I linked to above). 
