He received his degree in economics from the Corvinus University of Budapest in 2005, where he was also a member of the College for Advanced Studies in Social Theory for 7 years.

[4] In 2013, Tordai left LMP and became a member of the presidium of the newly formed Dialogue for Hungary, where he served as spokesperson between 2015 and 2018.

After placing inscriptions on the door of Prime Minister Viktor Orbán's office in 2017, László Kövér, the Speaker of the National Assembly, banned him from the Parliament "eternally".

[9] Speaker László Kövér fined Tordai more than 8.2 million HUF in March 2021 for violating the house rules.

[11] Subsequently, Tordai defeated Fidesz candidate Csaba Gór, obtaining the parliamentary seat.

[14] Tordai left Dialogue on 9 June 2024, the day of the 2024 European Parliament election right after voting is closed, because he disagreed with the formation of the DK–MSZP–Dialogue Alliance.