Perhaps the most significant event which turned König's interests firmly towards mathematics happened in 1869 when Königsberger left Greifswald to take up the appointment of a chair of mathematics at Heidelberg. Königsberger had been greatly influenced by Weierstrass 's lectures on elliptic functions and this was the topic which interested him at this time, so he in turn influenced König to also undertake research on elliptic functions.
Marahil ang pinaka-makabuluhang kaganapan na yari sa König interes Matatag sa matematika nangyari sa 1869 kapag Königsberger kaliwa Greifswald upang kunin ang appointment ng isang upuan ng matematika at Heidelberg. Königsberger had been greatly naiimpluwensyahan ng Weierstrass' s lektura sa tambilugin function at ito ay ang mga paksa na interesado siya sa oras na ito, kaya siya sa turn naiimpluwensyahan König na rin magsagawa ng pananaliksik sa tambilugin function.