Is there hope on the horizon for patients with Alzheimer’s?

In a televised press conference on Monday, Donald Trump and health secretary Robert F Kennedy Jr made a series of unproven claims about autism and its links to paracetamol use in pregnant women, and about childhood vaccinations. The comments were immediately refuted by scientists and health agencies around the world, but many expressed concern about the impact of this misinformation being repeated at the highest levels of government. So what does the science really say? Madeleine Finlay speaks to Guardian science editor Ian Sample to factcheck the claims made in the announcement, and find out what decades of scientific research into autism tells us about its causes and why diagnoses are on the rise. Help support our independent journalism at theguardian.com/sciencepod

The murder of political activist Charlie Kirk has prompted fears about rising levels of political violence in the US after a number of high-profile assassinations and attempted assassinations of political figures in recent years. But how connected are these events and do they signal a rise in public support for this kind of violence? To find out Ian Sample speaks to Sean Westwood, an associate professor in political science at Dartmouth College and director of the Polarization Research Lab. He explains how political violence has evolved and why overestimating the support for such acts can be dangerous. Help support our independent journalism at theguardian.com/sciencepod

At a recent ceremony for world leaders in Beijing, a hot mic picked up a surprising exchange between Vladimir Putin and Xi Jinping about the possibility of living to 150. Putin suggested the secret might lie in repeated organ transplants. But is this the new frontier of anti-ageing research or a fringe and unproven theory? To find out, science editor Ian Sample speaks to Russian affairs reporter Pjotr Sauer and to John S Tregoning, professor of vaccine immunology at Imperial College London and author of Live Forever: A Curious Scientist’s Guide to Wellness, Ageing and Death. Help support our independent journalism at theguardian.com/sciencepod

The fertility rate in England and Wales has fallen for the third year in a row – a trend mirrored across the world, with two-thirds of the global population now living in countries with below-replacement-level fertility. In the second episode of a two-part series, Madeleine Finlay speaks to Dean Spears, assistant professor of economics at the University of Texas at Austin, and Dr Jennifer Sciubba, chief executive of the Population Reference Bureau, to ask whether declining birth rates are really something to worry about – and how societies can adapt to a future with fewer children. Watch the new Guardian documentary Between Moon Tides. Help support our independent journalism at theguardian.com/sciencepod

The fertility rate in England and Wales has fallen for the third year in a row. It is a story that is being repeated all over the world, with two thirds of the global population now living in countries with below replacement level fertility. Low fertility rates have become a talking point on the political right, with Elon Musk claiming that population decline is an existential threat to the future of humanity. But for others, the timescales involved are too vast to start worrying about now. So how should we be thinking about population decline? In episode one of a two-part series, Madeleine Finlay speaks to Dean Spears, assistant professor of economics at the University of Texas at Austin, and to Dr Jennifer Sciubba, president and CEO of the Population Reference Bureau, to find out what has happened to global birth rates, and how governments are trying to tackle the fall. Help support our independent journalism at theguardian.com/sciencepod