He examined multi-valued functions as single valued over a special Riemann surface and solved general inversion problems which had been solved for elliptic integrals by Abel and Jacobi . However Riemann was not the only mathematician working on such ideas. Klein writes in:
Siya napagmasdan multi-mahal function bilang nag-iisang itinatangi sa loob ng isang espesyal na Riemann ibabaw at malulutas pangkalahatang pagbabaligtad ng problema kung saan had been malulutas para sa tambilugin integrals by Abel at Jacobi. Subalit Riemann ay hindi lamang ang dalubbilang nagtatrabaho sa naturang mga ideya. Klein magsusulat sa: