"What’s one-quarter divided by one-eighth?"

The UK’s 56th prime minister, Liz Truss, routinely peppers staff with math questions at meetings and expects quick answers.

Truss, whose father is a math professor, husband is an accountant, and once worked as an economist for Shell, is often described as impulsive decision maker with a boosterish approach to policymaking, yet people who work with her describe a person driven by data who is both methodical and unsentimental in her policy choices.

Variously described as un-embarrassable, thick-skinned, positive, blunt, impulsive, ambitious, image-conscious, energetic, quick to laugh at herself, anti-establishment, a contrarian and a workaholic, the mother-of-two is a mass of contradictions.

Truss has risen rapidly through the ranks, elected as an MP in 2010, joining the government in 2012, the cabinet in 2014 and named foreign secretary in 2021.

The 47-year-old has been repeatedly underestimated. Her awkward delivery has been a feature of memes – she is widely known in the UK for a speech in which she shouted "We import two-thirds of our cheese… That is a disgrace!" – but her skillful if unsubtle use of Instagram has burnished her media image, and she has worked hard to bounce back from setbacks and occasional mockery.

While many colleagues shook their heads, her political shapeshifting has been effective. The daughter of left-wing activists who wanted to abolish the monarchy when she was a Liberal Democrat and wanted to stay in the European Union when she was a favorite of David Cameron, now appointed as prime minister by Queen Elizabeth II after winning over the anti-EU, right-wing core of the Conservative Party.

Truss is famed in Westminster for studiously exploring all options, whether they’re in the mainstream or not. She shares predecessor Boris Johnson’s positivity, but is also a workaholic – and often comes up with conclusions that raise eyebrows.

Ideologue or pragmatist?

A question asked repeatedly during her successful campaign to become leader of the Conservative Party was "who is the real Liz Truss."

While her unemotional approach to policy has led to a certain flexibility, her policy solutions do tend to be influenced by an underlying belief in a small state.

"She is quite ideological and has a reasonably clear philosophy around competition, free markets and low taxes," David Laws, a Liberal Democrat who served alongside Truss in the education department, told The Times.

She believes in low taxes and lower public spending, and has done so consistently at least since 2012, when she entered government and co-authored a pamphlet called "Britannia Unchained" with future cabinet colleagues including Kwasi Kwarteng, a close friend set to be her chancellor, which essentially argues for government to be stripped back with the aim of allowing a freer economy to flourish and grow.

Now Truss and Kwarteng have the chance to put their philosophy into action. The policies Truss proposed during her leadership campaign would mean radical changes for the UK, from tax cuts funded by borrowing and a major increase in defense spending to relaxing regulations on business and planning.

Yet the data they inherit adds up to a series of daunting challenges and constraints. Inflation in the UK is rampant, energy bills are at record levels and rising, the health service is in dire straits and the central bank governor has warned of a recession ahead.

Next PM: Four challenges and no honeymoon

Critics question whether Truss' ideas can survive contact with reality, but pragmatism and flexibility look to be on the horizon. 

As a candidate in front of Conservative members, she talked in black and white terms in favor of tax cuts and against "handouts." But faced with surging energy costs that could send millions into fuel poverty if not addressed, she is expected to unveil a huge package of support in the coming days.

Unity or loyalty?

Party political considerations will also test Truss. She will be the fourth Conservative prime minister in just six years, and the party is unlikely to be any less rebellious under her. It holds a strong majority in the House of Commons, but only around one-third of Conservative MPs initially backed the new leader.

Winning candidates typically offer defeated rivals or rivals’ supporters major government jobs to try to heal wounds and unite their party, yet Truss looks set to name a top team of close allies and loyalists from the right-wing of the party. The backbenches are likely to be populated by a significant number of malcontents.

She has also has little room to maneuver on issues like tax cuts and the Northern Ireland protocol, given her strongest supporters are now from the right of the party who take a hardline in both areas.

Truss already has a testy relationship with the EU as a result of her hardline approach to the Northern Ireland protocol and there are few signs of deviation. She is strong backer of Ukraine, a vociferous critic of Russia and has taken a hard rhetorical line on China.

Leading a government that’s already been in power for 12 years is in itself a tough task, and the Conservatives trail the opposition Labour Party consistently in opinion polls, with an election due by 2025. 

The new prime minister is inheriting formidable challenges, constraints that will test her ideology and walking a political tightrope. So who will the real Liz Truss turn out to be?