Claudia Sheinbaum casts her vote during the presidential elections on June 2, 2024, in Mexico City. CRISTOPHER ROGEL BLANQUET/GETTY IMAGES

Claudia Sheinbaum, who will be Mexico's first woman leader in the nation's more than 200 years of independence, captured the presidency by promising continuity.

The 61-year-old former Mexico City mayor and lifelong leftist ran a disciplined campaign capitalizing on her predecessor's popularity before emerging victorious in Sunday's vote, according to an official quick count. But with her victory now in hand, Mexicans will look to see how Sheinbaum, a very different personality from mentor and current President Andrés Manuel López Obrador, will assert herself.

While she hewed close to López Obrador politically and shares many of his ideas about the government's role in addressing inequality, she is viewed as less combative and more data-driven.

Sheinbaum's background is in science. She has a Ph.D. in energy engineering. Her brother is a physicist. In a 2023 interview with The Associated Press, Sheinbaum said, "I believe in science."

Observers say that grounding showed itself in Sheinbaum's actions as mayor during the COVID-19 pandemic, when her city of some 9 million people took a different approach from what López Obrador espoused at the national level.

While the federal government was downplaying the importance of coronavirus testing, Mexico City expanded its testing regimen. Sheinbaum set limits on businesses' hours and capacity when the virus was rapidly spreading, even though López Obrador wanted to avoid any measures that would hurt the economy. And she publicly wore protective masks and urged social distancing while the president was still lunging into crowds.

Mexico's persistently high levels of violence will be one of her most immediate challenges after she takes office Oct. 1. The country has seen a 150% uptick in violence, with 37 candidates assassinated during this election cycle, according to a report by the Mexico City-based consultancy Integralia. As CBS News' Enrique Acevedo reports, the murders were linked to cartels who control much of the drug trade in the United States.

On the campaign trail she said little more than that she would expand the quasi-military National Guard created by López Obrador and continue his strategy of targeting social ills that make so many young Mexicans easy targets for cartel recruitment.

"Let it be clear, it doesn't mean an iron fist, wars or authoritarianism," Sheinbaum said of her approach to tackling criminal gangs, during her final campaign event. "We will promote a strategy of addressing the causes and continue moving toward zero impunity."

Sheinbaum has praised López Obrador profusely and said little that the president hasn't said himself. She blamed neoliberal economic policies for condemning millions to poverty, promised a strong welfare state and praised Mexico's large state-owned oil company, Pemex, while also promising to emphasize clean energy.

"For me, being from the left has to do with that, with guaranteeing the minimum rights to all residents," Sheinbaum told the AP last year.

In contrast to López Obrador, who seemed to relish his highly public battles with other branches of the government and also the news media, Sheinbaum is expected by many observers to be less combative or at least more selective in picking her fights.

"It appears she's going to go in a different direction," said Ivonne Acuña Murillo, a political scientist at Iberoamerican University. "I don't know how much."

As one of the U.S.' most crucial economic partners, leaders in Washington will be watching closely to see which direction Mexico takes — "particularly in terms of Mexican stability and Mexican reliability for the U.S.," said political analyst Carlos Bravo Regidor.

Sheinbaum will also be the first person from a Jewish background to lead the overwhelmingly Catholic country.