I am 28 years old and did my PhD last year at an applied math institute and left. However, I am still in good contact with my old working group and my PhD adviser told me I should come back.
At the moment I am a self-employed programmer. Although I really like my current job, I sometimes wonder if I should give the academic career another try. The main reason why I left was that I did not feel integrated in research society.
To be more precise, most articles I read where between 1950-1960. Most of my focus area are was out of scope from my adviser (he is an expert in numerical optimization, I was doing measure theory and Markov operator theory combined with numerical optimization). I had a lot of fun to modernize old theorems and try to apply them to numeric problems. Although I enjoyed the freedom of doing research on my own, I often was wondering if the results that I found are already known. My advisor was often surprised about my fundamental results, but he could not tell me if they are actual new. In fact, after searching persistent for one of my main theorems, I found it in a booklet from 1960 written with a typewriter - with a much shorter and genial proof. Although most of my other theorems have been peer-reviewed and published in B journals, I am still waiting for someone contacting me: "Hello, your result X in journal Y is known for a long time".
The author of this typewritten book is actually still alive (85 years old), on facebook and on top of that even accepted my friend-request. However, lives in New York and I live in Germany, so I can't easily visit for a short talk. I did send a text message, but never received a reply, I am not sure if it was because they do not want to talk about math anymore or if they just did not receive it, because facebook sometimes hides messages.
I was searching the web for professors doing similar research to what I am interested (by entering some keywords together with university into google). However, when I scanned their recent publications, I had no idea what they are doing.
I think I might missed the opportunity to connect to other working groups. I love teaching and doing research, but I also hate doing isolated research and having no defined task.
Is there any specific way of finding people who do similar research that I am not aware of?