How can you show geometrically that 3 < π < 4?

Approximating Pi was a favourite pastime of many ancient mathematicians, none more so than Archimedes. Using his polygon approximation method we can get whole number bounds of 3 and 4 for the universal constant, with only high-school level geometry.

This is the latest question in the I Love Mathematics series where I answer the questions sent in and voted for by YOU. To vote for the next question that you want answered next remember to ‘like’ my Facebook page here.

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Equations Stripped: Normal Distribution

Stripping back the most important equations in maths so that everyone can understand…

The Normal Distribution is one of the most important in the world of probability, modelling everything from height and weight to salaries and number of offspring. It is used by advertisers to better target their products and by pharmaceutical companies to test the success of new drugs. It seems to fit almost any set of data, which is what makes it SO incredibly important…

You can watch all of the Equations Stripped series here.

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BBC News – Maryam Mirzakhani’s Legacy

Live interview on BBC News about the legacy of Iranian Mathematician Maryam Mirzakhani who tragically passed away today (July 15th 2017). She was the first female winner of the Fields Medal – the mathematical equivalent of the Nobel Prize.

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Blueprint Interview

Interview with the University of Oxford’s Blueprint magazine about my mission to popularise maths and my outreach work with the St John’s Inspire Programme. The full interview with Blueprint’s Shaunna Latchman can be found in the online magazine here.

While some avoid arithmetic at all costs, Tom fully immerses himself daily teaching maths to the first and second year undergraduate students at St Hugh’s College. He also arranges activities for St John’s College as the Access and Outreach Associate for Science, Technology, Engineering and Maths (STEM) for the Inspire programme. Another activity is planning and filming content for his own outreach programme – Tom Rocks Maths.

‘It was the subject that felt most natural to me’, explains Tom, who first realised his love for numbers aged seven when his class had been set ten long multiplication questions. He raced through the whole book. However it wasn’t until he received ten A*s in his GCSEs that he began considering an Oxbridge education. ‘Academically there isn’t much of a difference [between Oxford and Cambridge]’ Tom comments, ‘but Oxford felt more like home.’

Later, after completing his PhD in Applied Maths at Cambridge, he was offered an internship with public engagement team, the Naked Scientists. The group strip back science to help make a complicated theory easy to digest. Weekly podcasts are broadcasted through BBC Radio 5 Live and ABC Australia, where audiences reach up to one million listeners a week.

Tom saw an opportunity to bring his appreciation for maths to the masses, but he wanted to do it with a twist. Eager to move away from the stereotypes of maths being a serious subject taught by older men in tweed jackets, he thought ‘what is the best way to make maths less serious? Doing it in my underwear!’ And so, the Naked Mathematician was born.

Since joining St Hugh’s, Tom continues to break down day-to-day activities on his YouTube channel to prove that maths is an integral part of everything we do.


His passion for engagement doesn’t end there. The Inspire programme, part of the Link Colleges initiative, is a series of events, visits, workshops and online contact for pupils in years 9 to 13. Tom works with the non-selective state schools in the London boroughs of Harrow and Ealing.

The Link Colleges programme simplifies communication between UK schools and the University. Every school in the country is linked with an Oxford college, with the hope that this connection will encourage students to explore the possibility of attending university.

‘The aim is to have sustained contact with the same group of students over five years,’ says Tom. ‘There are still students who haven’t thought about university, or maybe it’s not the norm in their family or area to attend university. So, we explain what it is, how it works and the positives and negatives. We want to inform and inspire them.’

Tom is responsible for arranging all STEM events across the year for 60 students in each year group. He calls on the expertise of his colleagues at Oxford as well as encouraging a partnership with the University of Cambridge and several universities in London. ‘The syllabus includes various topics such as the science of food and using maths to improve diet.’

During Tom’s famed Maths vs Sport talk, students are encouraged to participate in an on-stage penalty shootout – but only after learning about the mathematical makeup behind such a pivotal moment in a football game, of course.

Tom believes maths is made more accessible by relating it the world around us. He encourages his students to question things, like why bees make hexagonal shapes in their hives and how many Pikachus it takes to light up a lightbulb.

Whether visiting schools up and down the country to deliver talks, recording the weekly dose of Funbers for BBC radio – fun facts about numbers that we didn’t realise we secretly wanted to know – or in front of his class of students, Tom is certainly making waves in the world of maths.

Oxplore: Could we live on another planet?

Livestream debate with experts from the University of Oxford discussing the BIG question ‘Could we live on another planet?’ Featuring a meteorite from outer space, a holiday on Venus and my fantasy of owning a pet tiger…

Ancient Greek Mathematicians

A new feature from Tom Rocks Maths – a weekly maths puzzle for you all to enjoy! Answers will be posted when the next puzzle is released so remember to check back and get your thinking hats on…

Below are portraits of three famous mathematicians from Ancient Greece. Your task is to give me the name of each of them along with one of their mathematical discoveries… Send your answers in on Facebook, Twitter, Instagram or via the contact form on my website. Good luck!

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Answer to be posted next week along with the next puzzle.

Naked mole rats could help stroke victims

Stroke occurs every 2 seconds worldwide and is the second largest cause of death. When a stroke happens, the most important tissues of our body, the brain and heart, are starved of oxygen causing cell damage. To improve therapies for stroke patients we need to understand how the human body copes without oxygen and one researcher at the University of Cambridge thinks he may have found the answer in the form of a small rodent called a naked mole rat. Dr Ewan St John Smith and his colleagues were able to identify a new mechanism used by the naked mole rats to maintain an energy supply to the cells in their body without using oxygen. He told me more about these fascinating creatures…

  • Naked mole rats are the same size as a mouse, are the only cold-blooded mammal that we are currently aware of and they live for over 30 years despite the maths suggesting they should only live between 3-5 years.
  • They live underground in large colonies of up to 300 and so have adapted to be able to function normally in a low-oxygen environment.
  • A low-level oxygen environment, such as that experienced by the brain when a human suffers a stroke, will kill a mouse, but the naked mole rats are able to survive for 20 minutes without experiencing any side effects.
  • The heart rate of the naked mole rats drops to around 20-25% of normal levels during the oxygen deprivation and the question faced by the researchers was where does the energy come from, as it can’t be via the usual method of aerobic respiration with glucose.
  • Their findings suggest that the brain and heart cells of the naked mole rats are able to undergo respiration using fructose in their blood, rather than glucose from their cells, and while this also has a limited supply, it does provide a back-up plan to survive the oxygen depletion.
  • With this new understanding of how nerve cells function, Ewan and his colleagues hope to be able to develop a similar response in human cells to act as a preventative strategy to stop brain damage during a stroke.

You can listen to the full interview with the Naked Scientists here.

Photo credit: Jedimentat44 on Flickr


Funbers 9

We love the number 9 as humans – perhaps due to the 9 months we spend inside our mother’s womb before birth… There are also LOADS of fun maths tricks that you can do with the last single-digit number, with my two favourites explained in the video below.

You can listen to all of the Funbers episodes from BBC Radio Cambridgeshire and BBC Radio Oxford here.

Men and women may feel pain differently

It’s an age-old debate, who feels more pain, men or women? Scientists at McGill University have taken us one step closer to answering this question with a study using mice. Jeff Mogil and his team have discovered that the biological pathway that causes chronic pain is completely different in male and female mice. If the same is found to be true in humans it could lead to gender specific, or ‘his n’ hers’, painkillers in the not too distant future… You can listen to the full interview with the Naked Scientists here.

Jeff – We found that a major biological pathway involved in pain processing that’s been studied for the last 15 years or so by researchers around the world is actually only relevant and valid in male mice. And in fact it appears not to be used at all in female mice who instead appear to be using a completely different biological pathway.

Tom – What did you actually do in these experiments?

Jeff – Well we were studying a common and important symptom of chronic pain called mechanical allodynia. Mechanical allodynia is when a stimulus that should be perceived as touch is actually perceived as pain. 

Tom – Could you give an example of what that would be in a human?

Jeff – Everyone has had mechanical allodynia. If you’ve ever had sunburn – let’s say you’ve sunburnt your back and I came by and sort of gave you a playful slap on your back. Under normal circumstances that wouldn’t be painful, but if you had a sunburnt back you would go through the roof and that in fact is mechanical allodynia. Before injury mice will tolerate about a gram of force applied to their hind paw. After the injury, they will now withdraw form fibres that are 0.1 or maybe 0.2 grams of force. And then we looked at how we could block that mechanical allodynia, by blocking a cell in the spinal cord called microglia. In males what we would see is that the withdrawal thresholds would go right back up to 1 gram, whereas in females they would stay down at 0.1 grams. There has to be another system that is picking up the slack and performing the same function in female mice. In our study, we preliminarily identified another system involving T-cells, which are also immune cells, but a completely different type of immune cell than microglia.

Tom – And you think this potentially could translate to humans?

Jeff – I think our default assumption is always that the biology of pain in mice and humans is likely very similar until proven otherwise. Now of course there are always species differences, but in general biomedicine only works because these species differences are few and far between. 

Tom – So you’ve shown this in mice and this potentially could be the same in humans, but what does this actually mean?

Jeff – There’s a lot of drug development going on – there’s great need for new analgesics because the analgesics that we have available either don’t work very well or have really terrible side effects. So, there’s a huge need for new analgesics in the world, new painkilling drugs and there are lots of people trying to develop them. Many of the compounds that are under development are actually working on this biological circuit that we have now shown only applies to males. That of course is a problem because what that would predict is that the drugs that are going to be developed will work in men, it’s just that we have no reason to believe that they will work in women. The clinical trial is going to come along, which by law are half men and half women and what might happen is that if the drug works in the men but doesn’t work in the women, overall it’s going to look like the drug doesn’t work and that clinical trial is going to fail. The drug will never get on the market, it will never help the half of the population that it could’ve helped and hundreds of millions of dollars will have been wasted and no-one will really know why. The other thing is that while there’s a whole biological circuit that applies to females and not males, then eventually drugs might come out of that which work on women and not men. So, you can think of the idea of blue pills and pink pills for pain. I really believe that one of these years that’s actually going to be reality.

Part of the ‘Throwback Thursday’ series – you can find all of the highlighted interviews here.


In the final Critter of the Week for Marine Month, I introduce the villainous Anglerfish with the help of SeaLife Europe’s Joe Lavery…

  • There are more than 200 species of anglerfish identified and they can range in size from a tiny thumbnail to a small dog.
  • The name Anglerfish comes from the ‘fishing rod’ on their head which is in fact a modified dorsal spine called an illicium that’s used for hunting.
  • They can go for days on end without eating but when the time does come they’re able to eat a fish which is twice their own size.
  • The deep-sea Anglerfish lives more than a mile underwater on the desolate ocean floor, meaning that when a male and female cross paths they don’t hang around.
  • The male angler bites into the female and fuses its mouth to her body, eventually becoming a part of her used only to fertilise her eggs.

You can listen to the full interview for the Naked Scientists here.

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