[1] In 2003, Mach earned a PhD from the Department of Monetary Theory and Policy of the University of Economics, Prague.

[8] In September 2010, Mach addressed the UK Independence Party (UKIP) annual conference and praised Václav Klaus for his opposition to the Lisbon Treaty.

[10] Mach announced his resignation as a member of the European Parliament on 31 August 2017,[11] stating that he wanted to fully concentrate on the parliamentary election campaign.

[15] In September 2019, Mach was announced as a member of the Tricolour Citizens' Movement, and addressed their party conference in Brno.

[16] He joined Freedom and Direct Democracy in 2023 and became the party's lead candidate in the 2024 European Parliament election,[17] heading a joint list with Trikolóra.