Tuesday 13 October
Is there a secret formula for getting rich? For making something a viral hit? For deciding how long to stick with your current Netflix series, job, or even relationship?
In this talk, mathematician David Sumpter showed how a small set of formulas can provide the answers to questions ranging from the trivial to the profound.
David Sumpter is Professor of Applied Mathematics at the University of Uppsala, Sweden. Originally from London, but growing up in Scotland, he completed his doctorate in Mathematics at Manchester, and held a Royal Society Fellowship at Oxford before heading to Sweden. His scientific research covers everything from the inner workings of fish schools and ant colonies, the analysis the passing networks of football teams, segregation in society to machine learning and artificial intelligence. He has written for, amongst others, The Economist, The Telegraph, Current Biology, Nordic Bet Blog, The Conversation, Mathematics Today and FourFourTwo magazine. He was awarded the IMA’s Catherine Richards prize for communicating mathematics to a wider audience.
The following are notes from the on-line lecture. Even though I could stop the video and go back over things there are likely to be mistakes because I haven’t heard things correctly or not understood them. I hope Professor Sumpter and my readers will forgive any mistakes and let me know what I got wrong.
The first part is about equations that are used in all parts of society and how we can use them too, the equations that applied mathematicians use.
Is there a secret society that controls the world, and could it be run by mathematicians?
The professor asked if the symbol below was recognised. It is a symbol of the illuminati.
The Illuminati (plural of Latin illuminatus, ‘enlightened’) is a name given to several groups, both real and fictitious.
Historically, the name usually refers to the Bavarian Illuminati, an Enlightenment-era secret society founded on 1 May 1776 in Bavaria, today part of Germany. The society’s goals were to oppose superstition, obscurantism, religious influence over public life, and abuses of state power. “The order of the day,” they wrote in their general statutes, “is to put an end to the machinations of the purveyors of injustice, to control them without dominating them.
There isn’t such a society now, although some people (including one of my ex-students) still think it exists and that it consists of a small group of people who control everything e.g. politics, finance etc. in the world.
A fictional example of this secret society occurs in a book called “The Da Vinci Code”
The Da Vinci Code is a 2003 mystery thriller novel by Dan Brown. It follows “symbologist” Robert Langdon and cryptologist Sophie Neveu after a murder in the Louvre Museum in Paris and causes them to become involved in a battle between the Priory of Sion and Opus Dei over the possibility of Jesus Christ and Mary Magdalene having had a child together.
Professor Sumpter said he found the first 100 pages interesting only, but he was interested that there was a secret society called the Priory of Sion who controlled the world in part by using the number Φ, and used it as a code to talk to each other in order to control the world.
Fibonacci numbers are strongly related to the golden ratio
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.
Ratio of neighbouring Fibonacci numbers and the golden ratio tend to Φ
The professor thinks that Dan Brown did go a bit mad but could there be a mathematical code behind everything we do? He didn’t say he thought this was true but he did use this idea as a background to his talk to illustrate how he thinks about mathematics.
In 2018, before the World Cup, Professor Sumpter was approached by two young men, Jan and Marius, who were looking for mathematical secrets. They are professional gamblers who wanted to know if the Professor could help them use mathematics in gambling
The three of them worked together on a betting model, to find bias in the odds which would help them make money.
It took a day to produce the model which would automatically place bets on the matches.
How the mathematics of gambling work.
First ask “Is this a good bet?”
You are offered odds of 3/2 for England winning against Denmark. This means that a £2 bet will give a £3 profit if England wins and a £2 loss if they lose. If the probability that England wins is 1 in 3 is this a good bet?
You are offered odds of 3/2 for England winning against Denmark. This means that a £2 bet will give a £3 profit if England wins and a £2 loss if they lose. If the probability that England wins is 1 in 2 is this a good bet?
1/3 is less than 2/5. 1/2 is more than 2/5
Mathematics is seldom about numbers – but moving towards letters. Proper mathematicians want to get rid of all the numbers.
Is it a fair bet?
A fair bet is when the expected profit is zero for both the gambler and the bookmaker is zero
If the probability that England wins is p then the expected profit is
In this case, the expected profit is zero when
Or when p = 2/5 this is a fair bet
In general, if the odds are x for the favourite winning then for a £1 bet the expected profit
The expected profit is zero (a fair bet) when
Marius and Jan wanted to find an unfair bet that would be to their advantage. They need data. They’ve already got the equations and the model.
The data came from previous World cup matches and Euro matches. Jan downloaded it
Now they have frequencies of wins from bookmakers and odds and they could compare the data with the theoretical curve
Outcome of matches (data)
Compare the data with the theoretical curve
Bookmakers overestimate and underestimate odds at two points
This is when Jan and Marius could see they had an edge. When odds are very short its actually worth backing the favourite, called a long shot bias.
People often bet on the long favourite because if they win, they win a lot of money. You can make a profit by backing the favourite, it will be small, but this is better than nothing.
The equation was complicated and the line through the data didn’t match the data perfectly. Is it possible to improve the situation so the curve goes through the data? Yes, by stretching the curve a bit. To do that add alpha and beta to the equation.
Equation 1: The betting equation
P(favourite wins) =
Alpha and beta are parameters which ‘stretch’ the theoretical curve to be closer to the data.
If alpha and beta equal 1 the equation is as before but if they have any other value the curve is stretched in various different ways.
Logistic regressions were used in order to stretch the curve so it matches the data points better
Adjust the equation to better match the outcomes
This result is what Marius and Jan were after. The equation that could make money on the World Cup if the 2018 World Cup followed a similar pattern.
The table above showed for the England- Uruguay match there was a slight edge over the book maker. Hopefully enough to make some money.
The algorithm was set up and the World Cup model made £200 from £1440 of bets (some luck was involved). This was a bit more than the model predicted
Technically a lot more bets were needed to see if the model was working,
During 19 Jan and Marius used the method again and made quite a bit of money.
€838000 from over a hundred thousand €100 bets. Less than 1% profit per bet (very little luck involved).
They then went travelling.
The model finds very small biases in particular matches. Germans are over pessimistic and Brazilians are over optimistic about their teams. This sort of knowledge allowed Jan and Marius to make money betting. Other information that could be built in to the model included whether it was a home match advantage.
The model involved no footballing knowledge … just an understanding of probabilities.
It’s not about knowing the forms of the team. It’s about finding biases in the odds – purely a statistical model.
Who else is doing this?
The Happy Valley Racecourse is one of the two racecourses for horse racing and is a tourist attraction in Hong Kong. It is located in Happy Valley on Hong Kong Island, surrounded by Wong Nai Chung Road and Morrison Hill Road. The capacity of the venue is 55,000
The gambler who cracked the Horse-Racing code
William Benter (born 1957) is an American and Hong Kong professional gambler and philanthropist who focuses on horse betting. Benter earned nearly $1 billion through the development of one of the most successful analysis computer software programs in the horse racing market.
Benter published a scientific paper explaining how he was going to make all this money.
He has also given a talk about the maths behind his win
Benter even published the equation and he showed how the equation worked over five years of data.
He explained how the odds were collected. He didn’t keep his methods a secret and published mathematical journals.
Mathematicians and scientists are obsessed with citations. Benter’s article on racing was cited less than one hundred times, not a big impact, but it is there for anyone to use and exploit.
Why most conspiracy theories are not true
One of the reasons we know conspiracies theories are wrong is because it only takes one person to break it down. It is different for mathematics
Ten = the society of mathematicians
The ten equations are hidden in plain sight and Professor Sumpter decided to decode them in order to explain how they explain the world and your life
The ten equations include:
The betting equation
The skill equation
The market equation
The influencer equation
The reward equation
The confidence equation
The advertising equation
The judgement equation
The learning equation
Many of these equations can be found in scientific articles – however effort is required to understand them.
People’s mode; of the world tends to be “if I work hard enough, I will come up with a big idea that will make me rich and successful”.
A lightbulb moment
Life is not like that. Most of the time ideas don’t work.
So, you should have lots of ideas at once, and hopefully one of them works. You don’t necessarily have to act on them all at once, but have some ready to go if an idea has failed.
This is the best approach to having ideas. Think about the different things you do in life. As I write this, I am watching BBC news and eating breakfast.
If you try lots and lots of things then one of them will eventually work out. This is a better approach than focusing on just one thing.
Professor Sumpter thinks this approach should be applied to your lovelife. I don’t think my husband would be best pleased. Although it could be appropriate to young single people. Learning from the experiences that will benefit the relationship with the “one” at the end.
A karmic, but mathematical, approach to life. Lots of eggs in lots of different baskets
I should add, that as a teacher, I think just focusing on exams at exam time is actually a good idea.
Netflix applies an algorithm to their viewers.
Netflix, Inc. is an American technology and media services provider and production company headquartered in Los Gatos, California.
They use A/B testing
Example of A/B testing on a website. By randomly serving visitors two versions of a website that differ only in the design of a single button element, the relative efficacy of the two designs can be measured.
A/B testing (also known as bucket testing or split-run testing) is a user experience research methodology. A/B tests consist of a randomized experiment with two variants, A and B. It includes application of statistical hypothesis testing or “two-sample hypothesis testing” as used in the field of statistics. A/B testing is a way to compare two versions of a single variable, typically by testing a subject’s response to variant A against variant B, and determining which of the two variants is more effective.
Netflix shows lots of different pictures of a programme to its viewers and invites them to click on the one they like best. The clicks for each picture are counted and the one that is clicked the most becomes the one used to advertise the programme. This is one way that Netflix keeps its viewers watching.
All types of media companies use this approach in order to keep you engaged. Amazon keeps showing me lots of adverts for earrings.
Why moonshots aren’t about risk taking
If the probability of a billion dollar moonshot is 1 in 100 then what is a fair bet on a moonshot?
Is it? $100,000, $1 million or $10 million
If the probability of a billion dollar moonshot is 1 in 100 then the expected profit is
1000000000 ● 1/100 = 10000000
So, it is worth making for anything under a 10 million dollar investment.
People often start companies that won’t succeed.
The influencer equation
The above image shows part of somebody’s Instagram feed. The idea was to do random jumps. So Instagram holder to somebody called Marcus to Lisa Zimouche to a football player to Kim Kardashian to Beyonce to Alexandria Ocasio-Cortez to Probublica to NY Times to Jane Fonda to ? to Lenny Kravitz to the Jackson 5 to ? to ? to ? to ? to ? to Will Smith to The Rock to Joe Biden to Billy Eilish (who doesn’t follow anyone).
Using the idea of randomly jumping between people give an idea how Google etc. see us
People who have done this hopping find they never get back to themselves
So, who is the biggest influencer?
Looking at the above picture it looks like The Rock and Kim Kardashian are the biggest influencers in that they have 4 followers each. Beyonce has 2, Will Smith has 2 and Joe Biden has just 1.
However, looking at the image and sorting the social network as a mathematical problem with matrices might give a different answer
In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.
Producing matrix A
Joe Biden follows two people, The Rock and Kim Kardashian, which is why 1/2 appears twice in his column and can be seen to link with The Rock and Kim Kardashian. The Rock follows two people, Joe Biden and Kim Kardashian, again 1/2 appears twice in his column. Kim Kardashian, Will Smith and Beyonce all follow three people which is why 1/3 appears three times in their columns.
Now the following bits might be rubbish because I haven’t done matrices for a very long time and I didn’t quite understand the method that follows.
Matrix A needs to be multiplied by a one-unit, single column, vector.
In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices A and B is then denoted simply as AB
Start with Joe Biden, on his own, which gives the following situation
The next stage is to multiply matrix A with the single vector product from above. This corresponds to the two people that Joe Biden followed.
You need to continue by multiplying matrix A with the new single vector product
Continuing the process until multiplying the matrix with the single vector product gives you the same single vector product,
The influencer equation
Is what happened if you just keep hopping from point to point for an infinite amount of time – who will you end up on the most.
Well 18 out of 60 times you will get Kim Kardashian. Slightly ahead of The Rock
What is the point of this?
This is the algorithm used by Google in order to rank (page rank algorithm) people and thinks in order of importance on the internet. The result of this is to give an exaggerated view of society.
Some influencers become very popular and are seen all the time. Google, Instagram and Facebook all use algorithms and enhance search results over and over again.
This also happens on Amazon, when it comes to purchases.
It also happens on the news (Covid-19) and can result in exaggerated stories – a feedback loop occurs.
Coronavirus disease 2019 (COVID-19) is a contagious respiratory and vascular (blood vessel) disease.
It happens in all parts of society because of social media, but it comes from very old mathematics,
Oskar Perron (7 May 1880 – 22 February 1975) was a German mathematician
It is even found in old Chinese mathematics
The Nine Chapters on the Mathematical Art is a Chinese mathematics book, composed by several generations of scholars from the 10th–2nd century BCE, its latest stage being from the 2nd century CE. This book is one of the earliest surviving mathematical texts from China, the first being Suan shu shu (202 BCE – 186 BCE) and Zhoubi Suanjing (compiled throughout the Han until the late 2nd century CE). It lays out an approach to mathematics that centres on finding the most general methods of solving problems, which may be contrasted with the approach common to ancient Greek mathematicians, who tended to deduce propositions from an initial set of axioms.
Entries in the book usually take the form of a statement of a problem, followed by the statement of the solution, and an explanation of the procedure that led to the solution. These were commented on by Liu Hui in the 3rd century.
In 2001 Lawrence Page took out a patent on the equation. Google uses it
If you closely at the patent document you will find the influencer equation.
Assuming this iteration converges, it will converge to a steady-state probability
which is a dominant eigenvector of A.
Lawrence Edward Page (born March 26, 1973) is an American computer scientist and Internet entrepreneur. He is best known as one of the co-founders of Google.
Page was the chief executive officer of Google from 1997 until August 2001 then from April 2011 until July 2015 when he moved to become CEO of Alphabet Inc.
Alphabet Inc. is an American multinational conglomerate headquartered in Mountain View, California. It was created through a restructuring of Google on October 2, 2015, and became the parent company of Google and several former Google subsidiaries.
YouTube has its own algorithm.
In 2014/2015 YouTube had a problem because people would watch one or two videos and then just leave (I still do). So, they developed an algorithm which kept people watching.
They did this by using the Learning equation which they put into a neural network to optimise watch time. This increased by 2000%
Artificial neural networks (ANNs), usually simply called neural networks (NNs), are computing systems vaguely inspired by the biological neural networks that constitute animal brains.
An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain.
You can take back control of your life.
Two of Professor Sumpter’s students wanted to understand their Instagram feed. They wanted to know what Instagram was prioritising in what they were being shown. They had read that many influencers in Sweden were complaining because Instagram wasn’t prioritising them as much as before.
The students decided they were only going to open Instagram once a day and make a list of what posts they were shown and the time. Were they from friends and family or from influencers? What type of posts were shown more often to them? Were they from companies?
They came up with the following findings assuming random ordering on their feed.
Friends and relatives were prioritised
Non-sponsored companies they followed were deprioritised
Influencers were unaffected
The students felt the exercise improved their relationship with Instagram
“Instead of scrolling down trying to find something interesting. I stop after I’ve seen posts from friends. I know that further down it is just boring stuff”
Take back control using equations
Use the influencer equation to put your own place in social media in perspective
Use the reward equation to create a more balanced approach to social media
Use the learning equation to better understand how you should approach your goals
Oh, and the Illuminati does not exist
But it does make you think. There are many sides to TEN, to society, with the mathematics of life, whether you are a professional gambler or a secondary school teacher.
There are plenty of maths books aimed at professional development to help us think in a more mathematical way
Certain equations have revolutionised certain companies
FSM has helped teams such as Liverpool to revolutionise their game.
Companies using equations learn things about their businesses, and some make incredible amounts of money
There is a vast inequality when certain people, because they, or the people who work for them, have applied the right equations,
However, there is a positive side as some people are using mathematics to improve society.
Below shows images of some of these people
Top left is Adam Hill
Data Scientist and high-energy astrophysicist. He looked at Cambridge Analytica and investigates the network of financed that span the world
Top right is Nicole Nisbett
Her research tackles the assessment of the UK Parliament’s online public engagement activities and primarily aims to effectively harness citizen input from large unstructured data generated automatically through social media. It is an interdisciplinary and collaborative project with the House of Commons which combines theories of public engagement, social science, and data science to understand what effect online engagement is having on Parliament and the public, and develop ways to maximise its impact. Applications of text mining and social network analysis are a core area of exploration.
Her hope is that MPs will be better at communicating with people outside of Parliament.
Below left is Victoria Spicer, who looked at twitter interactions about and between Ukraine and Russia.
Below right is Mira Bernstein, She, has been looking at gerrymandering, how politicians split up different areas
Gerrymandering is a practice intended to establish an unfair political advantage for a particular party or group by manipulating district boundaries, which is most commonly used in first-past-the-post electoral systems.
The above link is comedian Adam Hills explaining the Cambridge Analytical scandal
Adam Hills (born 10 July 1970) is an Australian comedian and radio and television presenter. In Australia, he hosted the music quiz show Spicks and Specks from 2005 until 2011 and the talk show Adam Hills Tonight from 2011 until 2013. In Britain he hosts the talk show The Last Leg.
Cambridge Analytica Ltd (CA) was a British political consulting firm that was involved in influencing hundreds of elections globally and that came to prominence through the Facebook–Cambridge Analytica data scandal.
The Facebook–Cambridge Analytica data breach was a data leak whereby millions of Facebook users’ personal data was harvested without consent by Cambridge Analytica, predominantly to be used for political advertising. It is the largest known leak in Facebook history.
Is there a secret society that controls the World?
Yes, there is!
Join today and make a difference.
School children, never say that you won’t use maths when you leave school
Questions and answers
1) Is it possible to include human biases in the equations? Any other ways of tweaking the curve?
There are long shot biases where people don’t want to bet on the favourites. People don’t like betting on draws. Psychological biases are revealed.
When Professor Sumpter came up with the football betting model Marius wanted to know the psychological explanation for a particular pattern. He felt the World Cup odds should be very accurate due to lots of people betting but actually it’s the opposite.
Bookmakers, being experienced, do produce accurate odds but during things like the World Cup, people go a bit mad and bet without thinking too much about the outcomes – this is what gave Jan and Marius the edge.
A different type of model applies if it is just a bog-standard match.
If you just bet draws you are unlikely to make any money although two very good teams playing each other might making betting on a draw a good idea. This doesn’t work for a strong and a weak team playing each other or for two weak teams playing each other. It also unlikely to work for teams outside the premier league.
You have to fit your betting equation to the particular market.
Other factors making an effect include the weather and home advantage. The weather was very important to Benter when he bet on the races in Hong Kong.
2) Jan and Marius had about €50000 to start with and ended up using €120 million which they place on different matches. They had to place concurrent bets as it was an automatic system. They also had to prepared for losing streaks.
3) The betting equation is not the same as a stocks and shares equation.
Black–Scholes equation is one of the ten equations
The Black–Scholes or Black–Scholes–Merton model is a mathematical model for the dynamics of a financial market containing derivative investment instruments. From the partial differential equation in the model, known as the Black–Scholes equation, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of European-style options and shows that the option has a unique price regardless of the risk of the security and its expected return (instead replacing the security’s expected return with the risk-neutral rate). The formula led to a boom in options trading and provided mathematical legitimacy to the activities of the Chicago Board Options Exchange and other options markets around the world. It is widely used, although often with some adjustments, by options market participants.
It is a model of diffusion in financial markets.
4) How could Google patent an equation that was already in the public domain?
They patented the right to use the equation.
A few adjustments had to be made for it to work for internet surfing. Stanford University actually owned the patent and sold it to Google for $350 million worth of shares, now worth 1 billion dollars today.
No other search engines work like Google which is why nobody has challenged their patent and use of the equation.
Facebook has a lot of patents on equations. Three of them appear in Professor Sumpter’s book.
People were able to patent these things easily because they weren’t understood.
Yahoo and Google often threaten to sue each other over patent infringements.
It is the embodiment of the equation that is patented.
5) Are your colleagues gambling addicts? Do they do it for fun or is it just a mathematical thing.
Jan and Marius did enjoy gambling but they are running a company and the proceeds of gambling is the profit of the company. They have employees and they don’t make as much profit as bankers and traders.
Professor Sumpter feels there are far more interesting things to do with mathematics than gambling.
7) Have you been approached by football teams?
Professor Sumpter has talked to most of the top clubs about analysis and he working with a Swedish team – he has very close access to what is going on.
Hammarby IF Fotbollförening, more commonly known as Hammarby Fotboll or Hammarby is a Swedish football club from Stockholm founded in 1915.
A big club like Manchester City has too many people involved who get in the way of each other.
Manchester City Football Club is an English football club based in Manchester that competes in the Premier League, the top flight of English football. Founded in 1880 as St. Mark’s (West Gorton), it became Ardwick Association Football Club in 1887 and Manchester City in 1894.
8) Can you use maths to win at poker?
Computers are now better at poker than humans. Bluffing plays no part in their game. They play optimal poker.
There is psychology in human poker but computers will not be affected by this.
However, an expert poker player will be better at playing a rubbish player than a computer, and will win more money.
The correlation equation is an advertising equation. Facebook uses it a lot as they want to see what type of person you are in order to decide what adverts to show you (for me it us earrings, hair care and cats however once I turned 50, I started to get adverts for funeral plans and care homes)). Also, if your friend on facebook had bought something you are likely to get the advert).
Nicole Nisbett uses the correlation equation to investigate the interactions between politicians. It allows her to pick out the important stuff.
10) Signal = “is it a good investment to make?”
Noise = a fluctuation
Feedback = We’re all irrational
Financial modelling is about finding these three parameters.
For example, buying headphones
Signal = Sony headphones
Noise = Should it be Japanese?
Feedback = Beats headphones
(Personally, I went for Which magazine’s cheapest Best-Buy)
Financial mathematicians do the calculations about the investments without knowing much about the company they work for. One worked in the area for twenty years and never once tried to work out the underlying value of the company. Just studying the components, how they were correlated and how he could give his company an edge without understanding the company.
11) What is formula used for?
In probability theory and statistics, Bayes’s theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For example, if the risk of developing health problems is known to increase with age, Bayes’s theorem allows the risk to an individual of a known age to be assessed more accurately (by conditioning it on his age) than simply assuming that the individual is typical of the population as a whole.
It is the judgement equation and can be applied to Covid-19 and false positives.
You are in a shaky aeroplane, the worst trip ever. What is the probability you are going to crash and die?
Normally a plane crash is 1 in 10 million. Put the shaky journey data into the Bayes equation and it becomes 1 in 100000 test accuracy (which means you are still unlikely to be in a plane crash).
It is a very subjective and sympathetic equation so if your friend has let you down on one occasion you have a lot of evidence previously when they haven’t. So, you should forgive your friend.
12) Weapons of maths destruction is one of Professor Sumpter’s favourite books. He likes to read Bayes’ original papers.
Thomas Bayes (c. 1701 – 7 April 1761) was an English statistician, philosopher and Presbyterian minister who is known for formulating a specific case of the theorem that bears his name: Bayes’ theorem. Bayes never published what would become his most famous accomplishment; his notes were edited and published after his death.
Other favourite authors include:
12) Confidence equation
Used in gambling but it is also used in determining if racism and sexism has taken place.
For example, sending in CVs with different sounding names to various companies and seeing if everyone had an equal chance of a callback whatever their gender and race. It has been documented that women often have to leave their first name off a CV. One of my ex-students has actually decided to call her daughter, Harry (although this isn’t the name on her birth certificate).
Even in, our so called, equal society women earn 95 cents for every dollar earned by a man.
14) Covid-19 has increased peoples’ interest in maths.
Professor Sumpter is an applied mathematician. He has never had problems with people not being interested in the subject.
I really enjoyed this talk so I hope Professor Sumpter won’t mind me saying that I was a bit sad by it. I have a physics degree and once upon a time I loved learning about the wonderful equations that have explained how the world works. For instance, Newton’s work that allowed us to understand gravity, a bit. Maxwell’s equations that allowed us to understand electricity and magnetism and Einstein’s relativity that began to explain how the Universe works.
The ten equations seemed all about selfish things. How can I get more money, how can my bets win, how can I be liked more?
Perhaps it is my advanced age, but what is the point of influencers. How do we know they actually use the products they are endorsing?
This book is all about the equations that make our world go round. Ten of them, in fact. They are integral to everything from investment banking to betting companies and social media giants. And they can help you to increase your chance of success, guard against financial loss, live more healthily and see through scaremongering. They are known only by mathematicians – until now.
With wit and clarity, mathematician David Sumpter shows that it isn’t the technical details which make these formulas so successful. It is the way they allow mathematicians to view problems from a different angle – a way of seeing the world that anyone can learn.
Empowering and illuminating, The Ten Equations that Rule the World shows how maths really can change your life.