In 1927 Menger was invited by Hahn to accept the chair of geometry at the University of Vienna when Reidemeister left for Königsberg. Menger was not sorry to leave Amsterdam since he had become involved in a priority dispute with Brouwer and they were not on the best of terms.
Sa 1927 Menger ay inimbitahan ng Hahn na tanggapin ang silyang tumba-tumba ng geometry sa Unibersidad ng Vienna kapag Reidemeister kaliwa para sa Königsberg. Menger ay hindi sorry na umalis sa Amsterdam dahil siya ay maging kasangkot sa isang alitan ng prayoridad sa Brouwer at sila ay hindi sa pinakamahusay na ng mga terms.