Author: BBC Radio 4

Britons entitled to Irish passports After the Brexit vote in June, so many Britons applied for Irish passports that Ireland?s foreign minister had to ask them to stop ? pointing out that the UK remains, for now, in the EU. If some of the figures that have been quoted are correct, the Irish passport service may find itself completely inundated in future. But does one in four Britons really have Irish heritage? We reveal the dubious history of that number and attempt to estimate the number of Britons who are actually entitled to dual nationality with Ireland.

Do women?s periods sync? It is a commonly held belief that if women spend time together, their bodies start to sync and they will have their periods at the same time. But where does this idea come from? And is it really true? We look at the evidence and wonder ? could it be down to chance?

Numbers in music Marcus du Sautoy takes us on a journey through some of his favourite musical pieces, pointing out the interesting mathematical patterns hidden in the compositions.

Dangerous algorithms Cathy O?Neil, a data scientist and activist, has written a new book, ?Weapons of Math Destruction.? She is concerned about the proliferation of certain kinds of algorithms ? that help make important decisions, but that could be based on unfair statistics with hidden biases. She explains how to look out for them, and what we can do to protect ourselves.

Desk of Good News ? organ donations We look at the trends for organ donations and transplants.

Statistics suggest that officially about half of the countries in the world have abolished Capital Punishment, and a further 52 have stopped its use in practice. But we tell the story behind the numbers and show why the picture is more complicated. We speak to Parvais Jabbar, co-director of the Death Penalty Project.

The ?gender pay gap? This topic has been in the news this week after the Institute for Fiscal Studies published research showing women end up 33% worse off than their male counterparts after they have children. But earlier in the summer, Fraser Nelson wrote in the Telegraph that the pay gap is ?no longer an issue? for women born after 1975. Can both assessments be true? And could the label ?gender pay gap? be hindering our understanding of what really lies behind the numbers?

The cost of a hospital If a politician or commentator wants to underline just how wasteful a piece of expenditure is, a common strategy is to compare it to the number of hospitals you could build instead. Of course, hospitals are positive things ? we all want more, right? But just how much is a hospital? Is it really a useful unit of measurement? We speak to health economist John Appleby.

Corbyn Facts As Labour members begin voting on the party leadership, we investigate some of the claims made on the ?Corbyn Facts? website set up by Jeremy Corbyn?s campaign. Did he really give 122 speeches on the EU referendum during the campaign? Were this year?s local election results as good as Labour?s best performance under Ed Miliband? We look at what the numbers tell us.

Death Penalty abolition Statistics suggest that officially about half of the countries in the world have abolished Capital Punishment, and a further 52 have stopped its use in practice. But we tell the story behind the numbers and show why the picture is more complicated. We speak to Parvais Jabbar, co-director of the Death Penalty Project.

The Holiday Desk of Good News This week we outline a handful of statistics to make everyone feel better about the UK and their holidays.

With high profile attacks in Brussels, Nice and Munich, you might think that 2016 has been a particularly bad year for terrorism in Europe. But what happens when you put the numbers in historical context and compare them with figures for the rest of the world? More Or Less hears from Dr Erin Miller of the Global Terrorism Database and Harvard psychology professor Steven Pinker.

(Image: A man wrapped in a Belgian flag holds a candle as people gather at a makeshift memorial on Place de la Bourse two days after a triple bomb attack hit. Credit: Philippe Huguen/AFP/Getty Images)

Is 2016 an unusually deadly year for terrorism?

In a joint investigation with BBC Newsbeat and BBC Monitoring, we?ve analysed nearly 25,000 news articles to assess whether 2016 so far has been a unusually deadly year for terrorism. It certainly feels like it. But what do the numbers say? We estimate that, between January and July this year, 892 people died in terrorist attacks in Europe ? making it the most deadly first seven months of a year since 1994. But the vast majority of those deaths have been in Turkey. The number for Western Europe is 143, which is lower than many years in the 1970s.

Dying ?at the hands of the police?

This week retired footballer Dalian Atkinson died after being 'tasered' by police. His death has renewed concerns about the number of people who die after coming into contact with the police. Recently it was claimed that one person a week dies ?at the hands of the police? and that ?black people are disproportionately affected.? We take a look at the numbers.

Olympic predictions

As the Games in Rio draw to an end, we look back at the medal predictions we made before they started. Which countries have performed as expected? And which failed to meet our expectations?

The cost of a wedding gift

Can economics tell us how much to spend on a wedding gift? Our reporter Jordan is in a tight spot. He?s heading to an old friend?s wedding and needs to figure out how little he can get away with spending on a gift. Luckily, economist Maria Kozlovskaya is on hand to explain her findings on our ?internal exchange rate? for gift giving. Can she preserve Jordan?s friendship while protecting his wallet?

World Records are being set at a much faster rate in swimming than in other sports. At the Rio Olympics, British swimmer Adam Peaty managed to break the men's 100m breaststroke world record twice in two days. Tim Harford speaks to swimming coach, Rick Madge, about the reasons swimmers keep getting better results in the pool.

Also, science writer Christie Aschwanden makes the case for the virtues of the 5,000 metre race. She says that in recent times it has become very popular for people to train to run a marathon. But when you look at the numbers, is the 5K a better distance?

Presenter: Tim Harford Producer: Charlotte McDonald

It has been reported that Prime Minister Theresa May is planning on lifting the ban on creating new grammar schools. Chris Cook, Policy Editor for Newsnight, has been looking at the evidence for whether these selective schools improve exam performance or social mobility.

Swimming World Records New world records are being set in swimming at a much faster rate than other sports ? but why? Tim Harford speaks to swim coach and blogger, Rick Madge about the reason swimmers keep getting better results in the pool. Why do other sports, like athletics, not seem to have the same continual improvements in results?

Teenage girls aren?t so bad after all This week?s Desk of Good News challenges the concept that teenage girls and young women are badly behaved. It features statistics on falling teenage pregnancy rates, drinking figures and improving educational success.

The rise of TV Was the Queen's Coronation the event that sparked the biggest rise in TV sales ever? We take a look at the rise of television in the UK.

Lottery wins Adam Kucharski, author of The Perfect Bet, looks at the maths behind playing the lottery or gambling.

Presenter: Tim Harford Producer: Charlotte McDonald

How can we use statistics to predict how many medals each nation will win? We speak to Dr Julia Bredtmann, an economist at the RWI Leibniz Institute for Economic Research. She has come up with a model to predict how many medals each country will win, along with her colleagues, Sebastian Otten, also from the Leibniz Institute, and Carsten Crede of the University of East Anglia.

Some countries like the US and China have a large population and GDP, but a number of countries do very well for their size and wealth. Julia explains the different factors you have to consider to predict Olympic success.

The Government says that since the introduction of the 5p fee for single use plastic bags their use has plummeted. We take a look at the numbers.

Olympic Medals at Rio 2016 The Olympic Games are with us again. So how can we use statistics to predict how many medals each nation will win? We speak to Dr Julia Bredtmann, an economist at the Leibniz Institute for Economic Research.

Income inequality Politicians and commentators often claim that the rich are getting richer while the poor are getting poorer. But what do the numbers actually tell us about income inequality in the UK? Tim Harford interviews Jonathan Cribb of the Institute for Fiscal Studies, the co- author of a comprehensive analysis of Living Standards, Income Inequality and Poverty in the UK.

Desk of Good News ? Maternal mortality rates The number of women dying in childbirth is falling around the world. In 1990, maternal mortality rates were 385 deaths per 100,000 live births Today there are 216 deaths per 100,000 live births. This means the death rate is down by nearly half.

The Coastline Paradox Why is it so difficult to measure coastlines? The further you zoom into the detail of a coastline, the longer it becomes. This is referred to as ?The Coastline Paradox?. We speak to Mairi Walker, a mathematician at the University of Edinburgh, and Danny Hyam, from The Ordnance Survey - the UK government agency responsible for mapping our coastlines.

How can the techniques of computer science help us in everyday life? We speak to Brian Christian co-author of ?Algorithms to Live by: The Computer Science of Human Decisions?. He argues that the techniques of computer science can help us manage everyday situations in a more logical and efficient manner. So which algorithm can help solve the problem of odd socks? And what is the most efficient way of alphabetising your book collection? Tim Harford investigates.