The quote mostly reflects individual experiences.
In general surveys on satisfaction with supervision and employment of international PhD (and other) students, Germany only scores slightly worse than the international average.
The quote in question is a great example for one of the reasons why we do not allow shopping questions on this site (quoting myself):
No single person can compare the alternatives in life-changing career decisions (such as choosing a field), because everybody only has one life. At best you could statistically evaluate the experiences of people who made a similar decision a decade ago. However, during such a long period of time there will likely be changes that invalidate the comparison.
Specifically, the quoted text mixes some clearly individual experiences (“If you are a foreign student, the professor will do nothing to help you […].”) with ones that could be based on general facts (“20 to 30 [PhD students per professor] is very common.”). This suggests that the author of the quoted text is just stating their experience as general, while lacking any true means of comparison. And since you can go through the experience of doing your (first¹) PhD only once in your life, no single person can.
In general, doing a PhD is a highly individual experience.
The impact of the individual professor or workgroup is much higher than that of the country or even university (in particular in countries like Germany, where there are no such big quality differences between universities).
Therefore, I suggest to focus on assessing your supervisor when deciding for a PhD.
On top, all statistics and experiences you find now are inevitably outdated since they at best apply to people who were in the same situation as you three years ago, but usually it’s rather five to ten years ago.
This particularly applies to pursuing an academic career in Germany after your PhD, it’s hard to predict how the academic job market will look in three to fifteen years, which is the relevant time span for you.
For example, the mentioned twelve-year time limit on fixed-term academic jobs will only apply to you in twelve years².
There are good chances that the law is changed until then.
I am using the following sources:
Mind that none of these resources contains relevant data specific to mathematics.
However, the quote in the question suggests that the alleged problems are a consequence of the German system, culture, etc. Hence they should affect the general statistics.
Conversely, while it is conceivable that mathematics is the big bad outlier here, I see no indications for this and nobody has suggested so so far.
At the top is the professor, who […], can take as many Ph.D. students as he wants. 20 to 30 is very common.
According to BuWiN (Abb. B47 on page 150), the average number of PhD students per professor in mathematics and physical sciences is 6 (at a given time, not over the entire career).
Mind that this number is not limited to mathematics, where the average number of PhD students is lower.
Other groups of fields have similar values, with the main outliers being engineering at 11 and veterinary medicine at 9³.
The study also states (p.149) that only 1100 professors (of 46700, Tab. B8) in all fields have 21 or more PhD students.
If you are a foreign student, the professor will do nothing to help you stay on, network, or find a job in Germany.
he will only push a bunch of favorites who are German
ISB 2018 (p. 37) asked all students (not only PhDs) “How well has your experience prepared you for your career goals?” (final year only). For Germany, 10% answered “not well”, 26% answered “moderately well”, 41% “well”, and 22% “very well”, whereas the international averages are 8%, 25%, 42% and 25%.
Also, in ISB 2018 (p. 37) 71% of all students (not only PhDs) were “satisfied that their course will help them to get a good job”, 71% were “satisfied with making good contacts for the future”, and 62% were “satisfied with the career advice from academic staff”, whereas the international averages were 72%, 73%, and 60%.
If you take a PhD and then try to move to industry you need to have a job that requires a PhD and in practice it will be an immigration officer who decides that
ISB 2016 (p. 52) included the question “What would make you leave your host country after graduation?”.
For Germany, “Work permit restrictions” ranked at 28% (vs. 25% in the international average), “Visa restrictions” at 35% (vs. 27%), and “Employers are not interested in foreign candidates” at 36% (vs. 35%).
Note that this data is not specific to PhD students.
Other Satisfaction Scores
In ISB 2016 (Figures 6 and 11), there is data comparing the satisfaction of “postgraduate students” with the international average for certain items:
- “managing research”: 85.9% (Germany) vs. 89.6% (all)
- “topic selection”: 81.0% vs. 86.7%
- “opportunities to research”: 65.1% vs. 71.5%
- “graduate school”: 93.1% vs 94.2%
ISB 2016 (p. 10) also reports: “Of the 1,835 international PhD students who answered this question, 40% stated they would actively encourage others to apply to a German higher education institution.”
ISB 2018 (p. 40) asked “How likely is it that you would recommend this institution to family or a friend?”, grouping the results into three groups (detractors, passives, and promoters).
Germany scored 25%/42%/32%, while the international average was (20%/42%/38%).
In Sozialerhebung (Fig. 6.15, p. 71), 56% of international PhD students answered “yes, absolutely” and 28% answered “yes” as to whether they would recommend Germany as a place to study.
These scores considerably (measured for all students) considerably improved between 2006 and 2016 (Fig. 6.14, p. 70).
To give some comparison, BuWiN (Tab. B29, p.151) cites two studies (from 2011) of satisfaction of all (not only international) doctoral students in Germany, according to which 55%–65% are satisfied with their supervision and 15%–19% are dissatisfied.
In case you think I am just bitter, here is another link that discusses this
If You’re Considering Graduate School in Germany
This link is mostly about part-time employment in addition to your PhD, which is not very common in Germany, as your PhD position should give you sufficient money (though, admittedly, this is about Munich, which is notoriously expensive).
Also, taxes in Germany are much higher than in the US because of the social security system (health, pension, etc.); in the US, you would have to pay all these things from your salary (or not have them).
If you cannot find a job in the 12 years after your PhD you are barred from applying to academic jobs.
This is not completely true, as it does not apply to several funding programmes for junior professorships and similar.
It should be noted that it is generally considered an asset (or even a condition) for such programmes to have international experience – for which your experience probably already counts, while people who did their PhD in Germany usually do a postdoc abroad to fulfil exactly this.
¹ Doing a second PhD is inevitably a completely different experience since you already know how academia works, etc.
² Technically, it can affect you somewhat earlier, as it also prevents you from entering fixed-term employments that exceed the time limit.
³ This is not about PhDs, but VMDs (doctors of veterinary medicine), which have considerably different requirements in Germany.