It is a widely held belief that if you remove a model’s assumption you remove some of it limitations. Some say the more simple the model the better it is. In both cases I believe that these statements are not always true. A simple model with let’s say one thousand assumptions may not be fit for purpose. Why? If a model is true iff all of its assumptions are true and/or robust then in then its results may proved to be unstable. Conversely a model that is so complex, nobody can relate to its results nor connect it to it input may proved to be not fit for purpose.

In my 25+ years as a professional mathematical modeller, I have seen (and some times written) the good, the bad and the ugly models! The Bad is a model too simple to be of use. The ugly way too complicated to be understood and the results to be analysed. A Good mathematical model will have the right amount of transparent and challengeable assumptions, which coupled with an good mathematical approach provides the framework for potential insight into real world problems.

For example, a commercial organisation may use a forecast model to predict market share through time. However a good mathematical model will question the hidden assumption that its competitors will sit back and do nothing while one company take its customers. Added to the further dynamics of a good customer/ bad customer. By definition a “good” customer makes a company profitable while a “bad” customer adds extra costs not profit.

Does a company really want to be number one in the market but the majority of its customer are bad? By extending the gambler’s ruin problem we have a framework of modelling this real world problem. Let’s look at the following figures which shows the predicted market share of six commercial companies and the percentage of good customer. Each company has approximately 50% good customers through time and the ranking of the six companies remain the same.

Now let’s say the lowest performing commercial company in terms of market share wishes to become number one. It may use a simple model that states that its market share will grow independent of what ever its competitors do. Hence, it this was true the respected figures may look like this.

Under these circumstances the future looks bright for the company represented by the Green line. However, there is an underlying assumption that this model prediction is based on; the company’s market share will grow independent of what ever its competitors do. Really? One of the beauties of a good mathematical model is the ability to test the assumptions that underpins it. One strategy the competitors could apply is that they will fight hard to keep its own good customer’s but will persuade its bad customers to leave. What are the implications of this?

Our lowest performing company may become number one but at a cost. It could lose most of its good customers to its competitors making them more profitable.

In conclusion, a model with weak assumptions is a weak model. Nevertheless, a transparent and challengeable assumptions couple with a good mathematical approach, helps with insight into real world problems and will create the right conditions for the model to evolve.

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Now Aston Villa actually did slightly better than the model predicted finishing with 61 as oppose to 58 points. However because of the poor start the model predicted it was near impossible for Aston Villa gaining a play off position let alone automatic promotion. The points need for promotion was actually 80 points seven more than the 10 year average. Nevertheless, the probability of Aston Villa achieving at least 61 points was 35%. So Dr Xia, I give Aston Villa 65 out of 100. All the best for next season.

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“Thank you! Your visit has got to be the best we’ve had in a very, very long time! The students were enthralled and have had some wonderful feedback..they were fulsome in praise, telling their Maths teachers all about it! As a teacher, I was once more learning so much from watching another…we can’t thank you enough..and thanks come from myself, the Maths Dept, and Head of Sixth….and not least our lovely students.”

I will end this blog by quoting one of my twitter friend @LaurenYvonneTX

“Your journey is meant to be shared so that others can be inspired and motivated to reach for the stars”

]]>This year, while talking at a Black History event, The Black Makers, one of the delegates challenged me with the following question:

“Do you agree with me that this society does not have the environment for black scientists to emerge, survive and to thrive?”

With statistics such as:

Black [Physics] academics account for only 0.2% of professors and 0.4% of researchers despite making up 3.3% of the total population.

Source: Campaign for Science and Engineering

The easiest answers are to either to say “yes” and do nothing or say “no, things are improving” and then ignore the issues at hand. However when people and organisations take personal and corporate responsibility to the argument that “science is for everybody”, this is when you do create an environment for black scientists to emerge, survive and to thrive.

Being motivated to succeed from an early age

When I was 15, my school teacher told me I could be a boxer, but never a mathematician. On hearing this, my parents took responsibility by saying to me, “You don’t need anybody’s permission to be a great mathematician!” I embraced what my parents said to me and pursued a successful career as a professional mathematical modeller.

Finding career support

The Science Council has been very supportive of me becoming and sustaining my Chartered Scientist status. Nine years ago, a delegate challenged my suitability of chairing a mathematics conference because of the colour of my skin; I asked him to look through his personal copy of Chartered Scientist – The forefront of science. Not only was I quoted in the brochure, I was one of twelve Chartered Scientists profiled. The Science Council had taken responsibility to show that black scientists do belong in the scientific community.

The pinnacle of my career came in 2015 when I became the first black mathematician to be referenced by the Who’s Who since its establishment in 1849. There are only about 30 British mathematicians in the Who’s Who. I achieved this feat through hard work and determination as well as the support of professional organisations such as the Science Council and the Institute of Mathematics and its Application.

Inspiring others to follow

However, my responsibility to create an environment for black scientists to emerge, survive and to thrive has not ceased. I now undertake a number of talks at schools, education and community establishments to talk about my journey. My mission can be summed up by Professor Rosina Mamokgethi Setati-Phakeng, the first black South African female to get a PhD in Mathematical Education:

“Being the first is not something to be proud about, it is a calling to ensure you are not the last.”

Professor Rosina Mamokgethi Setati-Phakeng

]]>The idea of a science forum that would bring together top science students from many countries was most evidently considered after World War Two, when this idea was realized in the form of student exchanges between different schools and communities in the United Kingdom, the Netherlands, Denmark, and Czechoslovakia. In 1959, writing that “out of like interests the strongest interests grow”, one of the LIYSF founders Philip Green initiated a coordinated program housing all participants in one location, the University of London.

In the next decades, the conference expanded across the globe, starting from the United States of America to Eastern Asian countries. The initial goal was to put science into perspective and to encourage those attending to be aware of the needs of the world and what was happening in disciplines other than the one they were studying.

From 1971 to the 21st century, LIYSF has attracted a range of a wide range of notable presidents, including four Nobel Prize laureates, and innumerable distinguished speakers and lecturers.

Top speakers attend each year and have recently included; Professor Fiona Watt, Lord Robert Winston, Professor Sir Roy M. Anderson, Professor Mark McCaughrean, Professor Lesley Yellowlees, Professor Dame Carol Robinson, Professor John Ellis, Professor Sir Christopher Llewellyn Smith and Professor David Phillips.

This year the theme of the 2016 conference was “Great Scientific Discoveries” and I was invited to be one of the eight specialist speaker on the specialist study day.

The idea of the specialist day is that the student body of around 500 students are broken down into smaller groups to consider different themes. The groups will be led by the specialist and begin with a short lecture from the specialist outlining their area of expertise and raise key points. It is then up to the students to spend the remainder of the day to prepare to present this information to the rest of the student body in the afternoon plenary session in the form of a dance/song or drama.

This conference was one of my biggest professional challenges. It is not every day that I present to 500 of the world leading young scientist and the other speakers representing their field were top class. This included a professional science communicator for Discovery channel as well as a scientist from CERN. Nevertheless, the leader of the day Professor Clare Elwell, stated my title was her favourite – Mathematics: The Queen of Science. Of the 500 delegates, 65 choose to come to my one hour lecture and sub-sequential two hours workshop. This was only one behind the most popular session – The Substomic Zoo of Elementary Particles by the CERN scientist Prof Freya Blekman. In my group I had students from Canada, China, New Zealand, France, Malaysia, Poland and India, all were very enthusiastic and I had one hour to prove to them that Mathematics was indeed the Queen of Science. My argument was that not only does mathematics support science, it also leads science especially when it came to the field of mathematical modelling. I focused on the application of my PhD thesis – Extension of the Gambler’s Ruin Problem played over Networks. Firstly, I showed by using the Gambler’s Ruin Problem how we could predict the conditions for a World Economic Crash. Secondly, I discussed the potential of using the Gambler’s Ruin Problem to minimize the potential of Artificial Intelligence Takeover. The talk was well received, the highlight being when all the students shouted WOW when I showed them my main PhD result. For the workshop the student had to put together a 6 minutes presentation based on my talk in the form of a dance/song or drama. My group opted to do a Hip Hop Musical which was very creative and enjoyable to watch. I have never seen my mathematical research translated into this art form.

Overall, I thoroughly enjoyed this day. It was an honour to have the opportunity to inspire the future leading world scientists and showing them that mathematics is indeed the queen of science.

]]>My talk about my mathematics story

This is my story

In America out of population 250 million but out of 46 million African-American it is estimated only approximately 300 have a PhD in mathematics. An American columnist once stated that Black people were intellectually inferior because there has never been a Black Mathematician who has won the Field Medal, the greatest prize in mathematics. My name is Nira Chamberlain, when I was growing up mathematics was my strongest subject but I never had a passion for it but I had a dream that one day I would become some type of super mathematician. However, my career teacher stated I should become a boxer and my classmates would racially tease me if ever I became top of the class. There were no Black Mathematical role models just entertainers and sport stars for me to inspire to. Despite of this I pursued mathematics through GCSE, A level ,degree and finally Masters. I was never the best at what I did but I did enjoyed watching other mathematicians solving the most complex of problems. I had plenty of enthusiasm but I was terrible at exams nor was very confident. Then one day I met the Congress of African-American Mathematicians http://www.caarms.net/home.aspx who challenged me to do a PhD in mathematics. I was inspired and applied to do a PhD but at the interview the University Professor rejected me on the spot calling me naive and technically weak. Defeated and discouraged I went home but my Dad gave me these rousing words

You don’t need anybody’s permission to be a great mathematician

With this, I began to study harder, I lived breathed and eat mathematics. I soon realized that I may not be good in exam conditions but I was very good at solving real life mathematical problems outside academia. I went on to work in France, the Netherlands and Israel doing the mathematics that nobody else could do. 15 years later within 2014 within six months I got my PhD in mathematics, I was awarded by the Science Council as one of the UK top 100 Practising Scientist and in 2015 I became the First Black Mathematician to be referenced by the Who’s Who since its establishment in 1849. There are only 30 mathematicians in the Who’s Who and they tend to be the top mathematical geniuses in the Britain. I am glad I never became a boxer, but I persevered with my dream and became a super mathematician after all!

*No matter what profession you wish to purse, you can be the greatest!*

No one of the things that my Father use to say to me repeatedly until, I believe it was

*You don’t need anybody’s permission to be a great mathematician!*

In my formative years, I didn’t have any mathematical Black heroes or role models to inspire me to head for the heady heights. But what I did have was passion, enthusiasm and an determination to pursue the dream of becoming a mathematician. For this, first and foremost I give glory to God for putting the appropriate non-mathematical role models in my life such as Muhammad Ali.

The Muhammad Ali influence inspiration is evident. In support of Cambridge University outreach project, Plus magazine, I did a Video interview called Five minutes with Dr Chamberlain . Here I discuss how solving mathematical problems can be like fighting an invisible boxer! Thinking about it, it sounds like rope the dope.

In your honour your name Mr Ali, I hope continue to Float like butterfly and Sting like a Mathematician!

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I was invited to the film premier of “The Man Who Knew Infinity” based on the true life story of Srinivasa Ramanujan. Ramanujan, born in Madras India 22nd December 1887, was arguably, one of the greatest mathematicians to come out of the 20th Century.

I familiarised myself with a number of texts, prior to watching the film. I anticipated that film makers would possibly, not portray him in his true likeness. However, I was pleasantly surprised, with the adaptation of the story by Warner Brothers. The film begins in earnest in 1913, with Ramanujan sending a letter to Godfrey Hardy, a pure mathematician, stating that he had found a solution to the Prime Number Theorem [1]. Upon recognising that Ramanujan was some one of great potential, Hardy invited Ramanujan to travel from India, to work alongside him at Cambridge University.

Despite religious misgivings, that he would be cursed for crossing the sea, leaving his young wife and family behind; Ramanujan travelled to England in 1914, desperate for his work to be published. The film demonstrates Ramanujan struggles to settle in Cambridge, both culturally and academically. His wellbeing gradually deteriorated as he neglected his health in a quest to have his work recognized by leading experts. Ramanujan and Hardy clash over their differing mathematical approaches. Ramanujan at the time relied on intuition whilst Hardy insisted that the proof should rule supreme. Ramanujan and Hardy also disagreed over religion, Hardy was an atheist whilst Ramanujan was highly religious. Ramanujan, nevertheless looked to Hardy for emotional support but Hardy was very reserved. The film also revealed that Ramanujan unfortunately suffered racism. A scene that I could relate to as a BAME mathematician, was when one of the Cambridge professors tried to belittle Ramanujan by stating “you don’t belong here” Conversely Ramanujan was able to answer a complex problem posed to him that proved he had as much right as his critics to be at the university. Certainly in my formative years I could remember being told those very words.

Despite their differences, Ramanujan and Hardy they had one thing in common, their passion for mathematics. Hardy recognized this by agreeing with his closest collaborator, mathematician John Littlewood that “Every positive integer is one of Ramanujan’s personal friends.” Together they developed the theory of partitions [2]. Despite opposition from his colleagues, in 1918 Hardy battled to make Ramanujan both a Fellow of the Royal Society and Trinity College. Still, despite his mathematical achievements, depression and ill health led Ramanujan to attempt suicide; fortunately he was unsuccessful. Eventually a mutual decision was made, that due to health concerns, Ramanujan needed to return to India.

What was truly amazing about Ramanujan, was that he accomplished extraordinary heights in mathematics, during the early 20th century. This was before he came into contact with the British educational system. As stated in the New York Times [3] a genius can arise from anywhere.

The director focused on Ramanujan’s relationship with the highly acclaimed mathematician, Hardy. The film recognised that Ramanujan was a mathematical genius, who was not devoid of deep emotions. Consequently, because of the great sacrifice he made, this unfortunately led to his premature death, at the tender age of 32.

I found the film engaging and a moving experience. Dev Patel (Ramanujan), the leading protagonist, represented the character, as a believable mathematical genius, struggling in an alien environment. I score the film 1729 out of 1729!

Dr Chamberlain with the actor Dev Patel (Ramanujan).

[1] The man who loved only numbers, Paul Hoffman, Fourth Estate 1998

[2] Dr Riemann’s zeros, the search for the $1 million solution to the greatest problem in mathematics, Karl Sabbach, Atlantic Books London 2002

[3] The New York Times Book of Mathematics, Gina Kolata, Sterling New York, 2013

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With the sad passing away of the magician Paul Daniels, a number of news outlet played some of his magic tricks. One of them was – How to make an Elephant disappear in the middle of a field! Now was this magic or mathematics? As a mathematician, I am naturally going to say mathematics. Consider the following figure

What we have is a tent with a roof. The camera is raised above ground level. The sides of the tent is removed periodically, but the roof remain for most of the performance. This means there are some area behind the tent the camera eyesight cannot see.

Now add the elephant. Because, the elephant is positioned outside the triangle with the dash line it is in the camera view, hence the viewers can see the elephant in front of the tent.

The elephant enters the tent, it is in the cameras view up until the sides are brought down. I conjecturize that at some time after this the elephant is taken to the back of the tent like this.

Even when the side of the tent is removed, the elephant is hidden from the cameras view. In effect, to the audience the elephant has disappeared. In the YouTube clip there is some mis direction before the tent is removed but the elephant is no where to be seen. I conjecturize in the misdirection, the elephant has been moved totally out of site, either to the side, behind an artificial natural looking object or even further back. What you don’t see is all angles of the tent at all time. So is this magic or mathematics. If we consider all the angles, this is definitely mathematics.

]]>They seemed doomed for regulations. Now almost every week, the local Radio Station DJ, Radio WM Paul Franks ask the depressed Villa fans – what is the probability of Aston Villa staying up? Now depending on how Aston Villa play in their last game, the answers ranges from 0 to 20%.

However, how did they come up with such a figure? Is a pure emotional response, football experience of previous club in the same situation or just good old gut feel?

Well, as we are talking about probability surely there is a mathematical way of finding the probability.

Now football is a funny old game, the closer we get to the business end of the season the more the form book is thrown out of the window. Let us look at the table as it stands on the 6th March 2016

By using the simplifying assumption (the form book is thrown out of the window) and the mathematical method – The Random Walk, one can calculate the probability of Aston Villa remaining in the Priemiership.

A random walk is a mathematical formalisation of a path that consists of a succession of random steps. For example, the path traced by a molecule as it travels in a liquid or a gas, the search path of a foraging animal, the price of a fluctuating stock and the financial status of a gambler can all be modelled as random walks, although they may not be truly random in reality.

By considering the bottom seven teams, a simulation of each team’s random walk to the end of the season is calculated. To every game to the end of the season, the random event of a win, draw or lost is allocated to the team. This is repeated over and over again to see how many times Aston Villa finishes outside the bottom three. The answer is 0.6%.

Everybody knows Aston Villa chances are slim, but with mathematics we can qualify our feelings.

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