An Early Studies Bildungsroman

When I get asked to introduce myself, there are a few different stories I tell depending on the context and the audience. The one that piques the highest amount of curiosity is the one about my early adolescent education: I started taking advanced university courses in theoretical physics when I was thirteen years old – shortly after I had skipped a grade.

In my day-to-day life as an investor, I meet many (highly) gifted and talented individuals and many are curious about this part of my life as well. As a researcher, I have done some light research on gifted education and talent search.

Taking university courses early was one of the best decisions I made. I think there are many more students out there that would benefit from it, but there are constraints that hinder it. In writing this, I hope my experience can illuminate a path for others hoping to take university courses early.

Please have a very low bar to reaching out to me at janniklschilling (at) gmail.com. I would be particularly interested in hearing from you, if your experience was fundamentally different or you have thoughts on gifted education in other regions or with different institutions.

What happened at age thirteen?

I learned how to code when I was around nine years old. I got into it because I was curious about computers and had done some basic hardware experiments with an Arduino. So, I asked my dad to buy me a book to learn how to code. He got me an introductory book to learn Python.

Over the next two years, I became decent at doing small-ish projects in Python. I learned more programming languages for other applications, like Java for some OOP.

Over time, I came across much more interesting problems. But I realized they were beyond my mathematical ability at the time. So, I started learning advanced math when I was around 12 years old. I think I completed the entire high school math curriculum around six months later.

At this time, I was not aware of the possibility yet that I could take advanced math courses at a local university, the University of Hamburg. One has to go through a somewhat lengthy process, so instead, I watched online lectures on topics that I was interested in.

I had also skipped a grade when I was around that age. In hindsight, this was a crucial experience for me as I finally had an opportunity to prove to myself that I could learn very fast on my own, even outside of formal structures. I think I have always been an autodidact, so these things came fairly natural to me.

Why not earlier? In primary school, I had realized that I finished every task much faster than everyone around me, but I still lacked the meta-cognitive abilities to draw the right conclusion and start looking for the right things to learn online. At the time, I was quite reluctant to learn content that was broadly ahead of the age-appropriate content because I knew I would be even more bored three months or one year later.

However, I was doing some other fun math things with my dad. In second grade – I must have been around eight or nine years old –, I asked my parents to give me a graphical calculator (the Texas Instruments TI-84 Plus C Silver Edition) for my birthday. We wrote some programs on it to calculate the volume of various bodies in our house. For that, we derived the formulas together and afterwards confirmed that they were correct in a formula collection (“The Bronstein Handbook of Mathematics”). Through that, I saw lots of other formulas and got interested in other areas of Maths. For instance, when I was in third grade, I found the “TAN” button on my calculator and asked my dad to explain what that was.

Why not later? I was impatient and had the feeling that I lacked something to take my studies to the next level. I was also quite bored with normal courses in my school. And I knew that I could do much more demanding studies.

Would there be benefits from starting later? Not really. Maybe I would have spent more time socializing with students, but I don’t really feel as if I was missing out.

In hindsight, the biggest benefit of taking university courses so early was not what I learnt itself, but the information it provided me about myself. Most people who learn about my past are surprised that I did not end up as an academic. And I think that is reasonable, as becoming an academic clearly seems to be the default path for most child prodigies. When I was 14, I worked with a research group on Star Formation and Galaxy Simulations. While the work was certainly intellectually interesting, I realized pretty fast that I was not the type for the kind of meticulous work on small projects within a highly specialized area that might never lead to new discoveries. Additionally, the kind of theoretical physics I was most interested in (a subset of General Relativity Theory) was not taught or researched at the University, partly because there is not that much research interest these days.

How did I decide early studies was for me?

I just knew it was right for me. It is not that I was not worried about this decision, but I knew this was basically my only chance to make the next five years in school bearable.

There is a distinct memory that I can point to about when it became clear to me that I could not just sit in school and nod-along with the curriculum. Right after I skipped a grade, I was really into math and wanted to learn more. So I asked my teacher about the things I was interested in – how to solve easy integrals, etc. – and they said that I should not be interested in these questions because I would be bored four years later. That day, I started watching lots of explanatory math videos.

What were my other options and why did I eliminate them?

Looking back, here are some of the options I considered and my thinking about them.

Option space in Germany

Why do most people decide not to do early studies?

For a suitable student, someone with the ability and aptitude, there are three common reasons for why students do not end up taking university courses early:

Not knowing about early studies,
Administrative and logistical constraints,
Permission constraints and social dynamics (parents, teachers, peers).

The biggest constraint seems to be the first – that too few people know about this. If you know someone who would benefit from knowing about early studies, please feel free to share my email and/or this blog. Just one more teacher, parent, or student who counterfactually knows and can experience the same enrichment I did makes this post worth it.

The second and third constraints seem rarer to me, but are more annoying. In the following, I will share what the application process looked like and some general ideas on how to navigate the school system.

When I applied for early studies in 2018, the process I took looked something like this (stylised for brevity):

Get my parent’s approval,
Get my headmaster’s written approval and recommendation,
Get a teacher to write a recommendation letter,
Submit an online application,
Get an appointment with a student advisor for an interview. She asked me questions around physics, how I would handle the workload, what my motivations were etc. I suspect that my interview was particularly long because I was so young. For context: most students that end up doing early studies are around 17 years old.
Approval by the faculty and enrollment in courses.

I think the process itself is generally quite straightforward. Unfortunately, some high schools make it unnecessarily hard and I have heard from one case where the headmaster vetoed this. Building a good relationship with my headmaster through engagement with the school has been helpful for me. For most schools, there is no precedent and this process can feel quite tedious.

For the interview, I think the best advice is having good grades, a clear plan for how to navigate the school system, and good subject understanding (someone got rejected from doing early studies in Philosophy because they had never read a Kant before).

Logistics

Most of my early studies experience was in 2018 and 2019. I attended University around 2-3 times a week to attend lectures and tutorials. I attended an information seminar in November 2017, applied in January 2018, and started studying in March 2018.

Transport: I took the train from my school to the City of Hamburg which takes around 1hr.
Safety: Germany is quite safe. I rarely felt in any kind of danger. I was mostly taking the same train rides every single time and soon knew what to avoid.
Parental involvement: My parents accompanied me to an information session in the beginning. They made sure that I knew the way and had all the things I needed in the beginning (enough money, my ID card, etc.), but overall they were willing to give me a lot of responsibility.
Failing classes: It does not seem to be super common to fail lots of classes when doing early studies based on my friends’ experiences (n=5).
Balancing high school and early studies: In order to do early studies, my school (including the headmaster and all my teachers) ultimately had to agree to me doing this. After I had the approval from my headmaster, it was much easier to convince my teachers. I was going to school regularly for around two days a week, where I just attended the normal lessons (although I took the 11th grade math lessons when I was in 7th grade). Because I was quite well read, I found school to be really low effort and spent hardly any time on homework each week. For the 3-ish days that I was missing, I had my friends send me the material and looked at what they did. For most subjects, this was sufficient as long as I got a great grade at the exams that I had to attend. Often, I had to do a project as make-up work and to substitute my oral participation. This took a few hours, but thankfully happened only twice a year. As I took advanced courses in the natural sciences, I never had to do any work for any natural science, cs, or math because I knew the material inside-out. With some of my teachers, I also had a gentleman’s agreement that I did not have to participate in their lessons (i.e., just sit in the back and do PSets), unless there was a hard problem that only I could solve.

As a note of caution, these arrangements only worked because I was still getting perfect grades in basically every subject. I would have gotten a lot of pushback if I would have started to get substantially worse grades.

How was the early studies experience different from that of regular university students?

I was a non-degree seeking student. That means that I was not eligible for discounted meals, any scholarships, or even most of the student discounts that regular students can use.

On the flipside, one could fail exams as often as needed (whereas regular students get exmatriculated after a failed third attempt for any given one exam) and could retake exams as a regular student, if one wishes to do so. Obviously, one does not have to take them again if one is satisfied with the results.

Considering the social aspects, there was clearly a difference in interests and life stage between me and most of the other students. However, I think this is more a feature of the German university sorting system and this would not have been substantially different five years later. I socialized with a very limited set of students who were mostly academically successful. Personally, I did not feel that I was missing out on a lot, but I never had a strong desire for parties or similar activities.

In terms of soft skills, I learned a fair amount – like giving academic presentations, some mild teaching, and research – but I suspect I would have learned marginally more as a regular student. I could not be a paid TA/RA because of child labor protection regulation, for instance.

What were the constraints for making this much more effective?

If your benchmark for this is another gifted student in Germany, my school experience was superb. If your benchmark is the best case for child prodigies that is sometimes achieved in other countries, there are lots of low-hanging fruits to make early studies much more effective. If you face any of these constraints, please let me know and I might be able to help.

Financial constraints: As a child, you have limited pocket money that is most likely not sufficient for self-funding this. You kind of need your parents to pay for arising expenses. Textbooks are quite expensive – I think my parents spend around $1k for various textbooks. Because I was a non degree-seeking student, I was not eligible for any scholarships.
Lack of tacit knowledge: For early studies students, there are more obstacles that regular students do not face. There is also much less explicit support and I had to figure out most things on my own. I would have benefited a lot from knowing someone with a lot of tacit knowledge. This knowledge is mainly tacit because there are so few people that are confronted with these problems.
Specific problems that arise here: How much prerequisite knowledge should you know before starting studies? How do you acquire knowledge when you are missing lots of the regular university lectures? How can you convince professors to make exceptions for you because of your constraints? – i.e., not turning up to hand in PSets but sending them via email, etc.
Lack of a community of similarly-minded people: Although I participated in most (?) of the gifted education offerings in Germany, I don’t think I met anyone who had similar levels of talent to me until I was around 17 or 18 years old and went to a fellowship program in the United States. There was a lack of connection between other students that did early studies and most were much older and less talented – because they used the program to test what they would study six months later and not because they were deeply curious and prodigious. In turn, transfer of tacit knowledge, strategizing on how to deal with administrative and bureaucratic constraints, etc. are limited and concentrated on a grade 12 student testing for fit instead of a 13 year old pushing their limits.

Next steps

In closing, I want to emphasize how important and trajectory-changing early studies can be. They were for me. They not only showed me how beautiful theoretical physics is and taught me an awful lot of math. But early studies also helped me figure out that I don’t want to become a theoretical physicist and helped me prove my academic potential to myself.

Acknowledging all of the barriers outlines earlier, and that I was an anomaly, here are some things that I would like to do in the future:

First, I would love to help more young students figure out how they can push their aptitudes and aspirations – both in Germany and elsewhere. If there is anything I could be helpful with, please reach out to me. I know many students that were prodigious and have advice and guidance on how to navigate different education systems and self-study different subjects. I also know some funding opportunities and organizations that support gifted children.

Second, I think it would be valuable to compile more resources on what areas of science prodigies can look at, where they can find great textbooks and lectures, how they can navigate the university system in different countries, etc. This piece is hopefully the first step in this.

Third, I would like to learn more from the experiences of others and build support systems for them – especially those in contexts like Germany where the systems are idiosyncratic. If you’re interested in this too, please reach out.

Thanks to Zi C. (Sam) Huang for helpful contributions and editing.