7 University of Toronto advances changing the world right now.

The André–Oort conjecture – a famous problem in number theory and algebraic geometry – stumped mathematicians for nearly 40 years.

Jacob Tsimerman played a pivotal role in solving it through relentless curiosity, creative thinking and collaboration with researchers around the world. The breakthrough earned the U of T mathematics professor the 2026 Fields Medal at 38 – often described as the "Nobel Prize of mathematics" – and forged unexpected connections across mathematical disciplines.

In solving one great mathematical mystery, Tsimerman and his collaborators gave researchers new tools to pursue many others.

Can memories be rewritten or erased? Senior scientist at the Hospital for Sick Children and U of T professor Sheena Josselyn has spent the past 25 years trying to understand how memory functions and is recognized as one of the most formidable minds in the field.

After founding her lab at SickKids in 2003, she became the first person to identify and delete a single, specific memory – a breakthrough in the field.

Her findings have furthered our understanding of everything from post-traumatic stress disorder to Alzheimer’s, and she hopes that unravelling the brain’s machinery can lay the foundations for new treatments.

Long-haul truck drivers have one of the highest fatality rates of any profession.

Raquel Urtasun is developing physical AI that interacts with the real world, starting with autonomous driving. The technology is designed to navigate a wide range of road conditions while reducing human error – the leading cause of collisions. The U of T professor’s company Waabi is using advanced AI and highly realistic simulation to train and test self-driving systems in millions of scenarios before they hit the road.

She recently raised US$750 million in one of the largest venture capital financings in Canadian history and announced plans to launch a fleet of robotaxis with Uber.

How do you repair a brain after a stroke? Restore sight after retinal damage? Relieve pain without opioids? These are the kinds of problems driving Molly Shoichet's research.

By engineering injectable hydrogels that can deliver drugs, stem cells and other therapies precisely where they're needed, the U of T professor and serial entrepreneur is opening new possibilities for treating stroke, blindness, cancer, spinal cord injury and post-operative pain.

Her innovations are advancing therapies that repair damaged tissue, improve drug delivery and move promising discoveries from the lab to patients who need them, tackling some of medicine's most complex and urgent challenges.

“We are no wiser than the Europeans who saw democracy yield to fascism, Nazism or communism,” renowned historian Timothy Snyder writes in his book On Tyranny. “Our one advantage is that we might learn from their experience.”

In his course, Hitler and Stalin Today, now on YouTube, the U of T professor challenges students to consider the relevance of historic regimes to help them become informed stewards of democratic institutions.

By defining the place this dark historical period occupies in contemporary memory and politics, Snyder empowers students with the knowledge to make a difference in this critical time in history.