The United States and Iran have announced a cease-fire deal that would pause fighting for 60 days. “Ships of the World, start your engines. Let the oil flow!” Trump wrote on social media.

Sacha Barbour Gatt has this breaking news update.

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Monday Headlines:

• New poll has Pauline Hanson as preferred PM
• Trump tells all sides to ‘stand down’ amid peace talks
• Nine-year-old Australian girl killed in Pakistan
• Renewed calls for a Sydney shark cull after Coogee attack
• Socceroos stun in World Cup opener against Turkiye

Deep Dive: A proposed $900 million waste-to-energy plant in Fiji sparked fierce criticism before it was ultimately rejected, with opponents warning the nation risked becoming the "Pacific's ashtray" and accusing Australia of engaging in "waste colonialism".

The project has reignited debate around waste-to-energy technology, which supporters say can reduce landfill and generate electricity, but critics argue risks creating a dependence on burning waste rather than reducing it.

In this episode of The Briefing, Chris Spyrou speaks with environmental researcher Professor Ray Wills about the Fiji proposal, the future of waste-to-energy in Australia, and whether burning rubbish is a necessary part of solving the country's growing waste problem.

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Terence Tao was a child prodigy, and became a mathematics professor in the United States at age 24. In his early 30s he won the Fields Medal, known as 'the Nobel Prize of Mathematics'. Tao is considered one of the greatest living mathematicians, in part because of the breadth of his contributions to the field – from finding new patterns in prime numbers to solving several of the "unsolvable" Erdős problems.

On Monday, the King's Birthday, Tao was awarded Australia's highest civilian honour, the Companion of the Order of Australia.

In this bonus episode of The Briefing, Terence Tao, AC, speaks with Natarsha Belling about the pleasures of solving problems, and how maths makes the world a less scary place.

If you want more Terence Tao, one of the YouTube channels he mentions is 3Blue1Brown, and Tao is featured on an episode.

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