Around 1820, when he was still studying in Vienna, Bolyai began to follow the same path that his father had taken in trying to replace Euclid 's parallel axiom with another axiom which could be deduced from the others.
Sa paligid ng 1820, kapag siya ay pa rin pag-aaral sa Vienna, Bolyai ay nagsimulang sundan ang parehong landas na kanyang ama ay kinuha sa trying sa palitan Euclid 's kahanay axiom sa ibang axiom na kung saan ay maaaring deduced mula sa iba.