Less than 24 hours after the Greek electorate gave Syriza a mandate to end five years of austerity and begin what will undoubtedly be some of the toughest negotiations in the country’s history, the man tasked with undertaking them seems unreasonably calm. Standing on a rooftop in central Athens overlooking the Acropolis, Yanis Varoufakis confesses: “This is the first night I’ve actually felt calm.” The 53-year-old political economist and game theory professor, who studied in Britain at the universities of Essex and Birmingham, has just been made Greece’s new finance minister.

“The first messages we’re getting from abroad is look positive,” he says, certain that the tide is turning for Greece and Europe – but he doesn’t think it will be an easy process.

On Friday 30 January the Eurogroup president, Jeroen Dijsselbloem, will be visiting Athens and the race to find a solution to Greece’s debt that does not include austerity – described by Varoufakis as “fiscal waterboarding” – will begin.

Syriza missed the opportunity to form a single-party government by just 1 per cent, agreeing a coalition with the populist right-wing Independent Greeks instead. Both parties are anti-austerity and anti-corruption, even if they agree on little else.

Its victory brings with it a number of firsts. At 40, the party’s leader, Alexis Tsipras, is the youngest Greek prime minister in 100 years. He is the first not to be affiliated with the Greek oligarchy, the only one to be openly atheist and, in the wider European context, the first anti-capitalist to lead an EU country. The change in Greece has been remarkable. Syriza’s core promise of “a return to dignity” resonates with voters, even those who do not vote regularly for the left.

In fact, polling showed that voters from across the spectrum moved towards Syriza in the lead-up to the election, pinning their hopes on a ministerial team of inexperienced intellectuals and university professors, rather than professional politicians.

There has been a similar turn across Europe. One by one, European leaders are changing their stance towards Syriza and believe a solution to lift Greece’s burden will be found. In Italy, fearing an insurgency to the left of his Democratic Party, Prime Minister Matteo Renzi is getting ready to align with Tsipras.

The French finance minister, Michel Sapin, indicated he would do the same, days before François Hollande invited Tsipras to meet him. Even the hardline Dutch and Finnish governments believe a solution can be found, and maintain that they will work with Syriza.

The new government aims to include the Ecologist Greens party. At the time of writing, it seemed likely it would be assigned the ministry of environment and climate change, possibly marking an emerging alliance between the radical left and the Green movement in Europe. This has implications for the UK, where the “Green surge” continues.

The most immediate repercussions, however, will be felt in Spain. Pablo Iglesias, the leader of Podemos, is banking on Greece to push support for his anti-austerity platform to an all-time high. He joined Tsipras on stage in Athens on 22 January, addressing a crowd of thousands.

What will determine Syriza’s success and viability is not, however, its success in renegotiating the national debt. It will be its success in tackling inequality in Greece. The party will face great resistance from the handful of wealthy families who dominate domestic politics. But it cannot hope to govern if it does not take a firm position. Winning the election on 25 January was just the start; the work starts now.