I use the web as a source for learning - see Using The Web To Learn - about a wide range of subjects: making sourdough bread; writing software to analyse a shopping basket; or understanding why football teams are no longer using the 4-4-2 formation. However, there is one area that needs to be improved: access to relevant information based on my level of knowledge about a subject.

Let me give you an example. I have reached an age when medical breakthroughs are becoming more important. Recently a breakthrough was announced in the fight against the terrible disease Alzheimer’s. I was curious about the science behind the breakthrough, in particular the analysis of the data to support the claim, and a quick search found a copy of the paper.

The paper was full of terminology that I didn’t understand. More searches helped to clarify the different proteins, scanning techniques, assessment of Alzheimer’s etc. that give an overview of the research. However, I was still interested in the statistical analysis which was used to support the claim that the test is 87% accurate. This is when the problems started. Further searches started to produce a mish-mash of information: poor quality videos, badly written overheads for a lecture, chapters from draft books, chapters from books no longer available, lecture notes, different mathematical notation etc. After many coffee drenched hours I eventually found the correct level of information that helped me to understand the breakthrough. However, instead of trawling through piles of confusing information it would have been better if my search brought back the information at a level that I could understand in enough time to drink one cup of coffee !

This is my challenge to the search engine companies - when searching on a particular subject I need the information to be at a level that I can understand. So search engine companies - sharpen up your algorithms, speed up your computers and lets see what you can really do !

On a good day I can answer two of the questions that come up during the BBC's programme University Challenge: the quiz where university students answer questions on a wide range of subjects. Using my smart phone I can answer more - it depends on how fast and accurate I can type !. Answering questions using the web is a powerful thing. But what if I want to learn more about a subject ?

I often come across a subject when reading about a hobby, developing a new skill or sparked by curiosity, where I need to find out more. But the subject can be like a brick wall built of strange words and unfamiliar concepts. I am stuck ! For me there is only one approach and that is self-learning, in other words, working through the subject by myself. The following is the way that I use the web to help me learn.

I start by identifying the people who are working on the subject and search for what they have written, for example blogs, papers, public presentations, books, videos on YouTube etc. I also search out any commentators, or critics, on the subject. This initial phase is like detective work - pulling together scraps of information about the subject and assembling them into some sort of overview.

Let me give an example. Tim Harford wrote an interesting article for the FT Weekend Magazine on how we get it wrong when imagining the effects of new technology on the future of everyday life. In the article he mentioned an interesting idea proposed by the economists Daron Acemogula and David Autor where we should view work in bite-size chunks - tasks rather jobs. Basically they think that “routine, codifiable tasks” can be automated while purely human skills such as problem solving and creativity can not. Searches produced papers by the two economists with titles such as: Skills, Tasks and Technologies: Implications for Employment and Earnings, Polanyi’s Paradox and the Shape of Employment Growth, and The “task approach” to labor markets: an overview ). I found Tim’s email address on the web and contacted him for advice on the best papers and he kindly suggested Why Are There Still So Many Jobs? The History and Future of Workplace Automation ).

The next stage is to immerse myself in all of the information that I have gathered which feels like drowning. But after surfacing for a few coffees I find that some of the new terminology makes sense and the subject starts to take shape.

Eventually I reach point where I feel confident enough to test my understanding of the new subject. This is done by working through some examples, or tutorials, and then using my new knowledge on a problem. This can be done more easily in some areas than others, for example using open source software I can test my understanding of new concepts in computer technology. For other subjects then I can only read about it e.g. surgery.

Continuing with my example, the subject falls under the heading economics. Therefore applying what I have learned I can draw any sensible conclusions about changes in business ? For example what is driving the increase in call centres ? Part of the job of a salesperson was to make regular calls to customers to try and drum up new business or chase repeat orders; this was usually when selling to a business and is still practiced today. However, call centres take the “task” of calling customers to retail customers and probably reduce the cost per call due to centralisation of the task. Not a rigorous conclusion but the start of a few interesting thoughts.

What I have described above is the first step. To gain a greater level of expertise in a subject can take many years: there is a debate raging on the web that suggests that around 10000
hours is required to gain a high level of expertise in a subject which is a long time but exploring a new subject is the fun of learning.

Next time I sit down to watch University Challenge I hope too have gained more knowledge from my self-learning so that I can answer more than my usual couple of questions - if not I can always access the web !

Ralph Bana, credited with many innovations in the travel and leisure industry, was quoted during an interview with the industry magazine Tour & Travel: "I just don't come in and say "ah-hah" ! The answer relates to clearly defining what the problem is, forcing yourself to write it down, researching the alternatives, picking one that will ring the bell and then going out and selling it". This is great advice that could be used by any industry, government, or organisation.

When a problem is written down on a piece of paper the sentences can be analysed in a way that fuzzy concepts, wild ideas, and general waffle can be removed. So how would this work ? Let’s take an example, the National Health Service ( NHS ) in the UK are often criticised about the speed of innovation. This is a complex problem and there maybe many underlying factors but it is often heard that there is a lack of money to help speed up innovation. One attempt at writing out the problem could be:

“The NHS is slow at innovation because it doesn’t have enough money.”

The first thing to observe about the statement is that it identifies a problem: “The NHS is slow at innovation” and a solution: “it doesn’t have enough money”. Digging deeper there are three concepts that are at best unclear: “slow”, “innovation” and “enough”. Starting with “slow” it is unclear how slow is slow - is it a perception or are there some hard facts ? ( a quick web search produces no hard facts about the speed of innovation in the NHS ). Next “innovation”; another search on the web shows that there are many definitions of innovation ( around 1,980,000,000 hits ! ) and therefore scope for many experts and management consultant to debate its definition for many years ahead. Finally “enough” - how much is “enough” ? - twice the current amount, three times the current amount ? Therefore we can conclude that the stated problem, and solution, is loaded with confusion and can only lead to further confusion, and result in wasting time and money.

A better example of analysing a problem when it is written down is:

“One of the highest priorities for the NHS is the reduction of obesity which is estimated to cost £6bn per year”.

The description of the problem is clearly defined and quantified. However, it could be criticised for being at too high a level - too abstract. It could be broken down into factors that are contributing to obesity, for example: education, economic, social context, life style, public health etc. which could be quantified, and then alternative solutions explored.

Ralph Bahna was always looking for competitive advantage, which had to be “neither short-term nor flimsily opportunistic”. The technique of writing the problem out and critically analysing its content is an effective way to clear out muddled thinking. With a clear problem definition then there is a greater chance of finding a successful solution.

A new digital business seems to hit the headlines everyday. The news report suggest that the entrepreneurs had a sudden flash of insight, and after a few coffee fuelled weeks of writing code, a product was launched and truck loads of money rolled in. Reality can be very different.

I recently came across a company called RentHop, an apartment listing service based in New York City, during a predictive modelling competition held on Kaggle. The aim of the competition was to predict the number of inquires a new apartment listing would receive based on the listing’s creation date and other features. To understand the context of the data supplied by the the competition, I gathered as much information on the company that I could find. Themes started to appear during my research that provided a fascinating insight into the hard work and determination that goes into the development of a very successful digital business - there are many lessons for the rest of us.

RentHop was started in 2009 by Lee Lin and Lawrence Zhou following bad experiences with brokers when trying to rent apartments. They initially thought that brokers were not adding any value and therefore the industry was ripe for a radical change - a disruption. After all if books can be bought, taxis ordered and restaurant tables booked with a few clicks why can’t a similar process be in place for renting an apartment ?

The first lesson to emerge from RentHop’s history is to understand the intricacies of the market for your idea - detail is everything ! To understand the detail it is important to experience the market that you are targeting both as a customer and as supplier. In the early days of RentHop they were challenged by the venture firm Y Combinator, who supported them during a summer incubator program, to spend time as brokers so that they could check if their idea was going to work. Lee and Lawrence gained their brokers licence, which required 75 hours of class, and then spent a few successful months as brokers in New York City. They learned the craft of a broker down to the nitty gritty, such as buying six-packs of Coronas for the Superintendents to get in with them so they could get a copy the master set of keys and therefore be the first to get into apartments. During their time as brokers they realised that the most important part of brokering is the relationship developed between the broker and renter. A really good broker makes the process a whole lot less painful for the renter and they realised that a great broker adds value. Therefore RentHop changed direction - pivoted - and worked on adding value to the broker’s activity by increasing the effectiveness of the leads. For example, at the heart of RentHop’s offering is the HopScore which rates the quality of an apartment listing. Listings with higher HopScore appear at the top of the search results where they’ll have more exposure to renters.

Nothing stands still is the next big lesson. Markets are constantly changing: new entrants, new technology, new legislation all provide a turbulent background where your are trying to hold onto your customers and find new ones. In the case of RentHop new entrants into rentals are AirBnb who are changing the rental landscape. Is AirBnB a short term let or are they moving apartments into the hotel business ? The development of mobile technology continues having an impact. It’s inherent value can be exploited, for example brokers arranging meetings with clients while on the move or updating the information about an apartment after a visit and therefore increasing its HopScore while on the move. Also, as RentHop continues to grow it can leverage its property data - its digital assets - and by combining with with public data ( e.g. New York City Rents By Subway Stop 2017 ) to provide a better service and therefore competitive advantage.

One advantage of a digital business is that it can grow very quickly compared to a bricks and mortar type business - easier to scale. However, another lesson is that scaling has to be sensitive to local markets. For example the HopScore had to be changed when covering other cities. In New York City the more people that see an apartment but show no interest, then it can be concluded that it is poor quality, and therefore the HopScore can be dropped. However in other cities there maybe bottom feeder investors looking at the apartment therefore the eleventh showing could be just as important as the first visit.

Behind the click-to-cash headlines for a digital business there are many years of hard work by dedicated entrepreneurs. Analysing the development of companies like RentHop provides valuable lessons for future entrepreneurs.

For more information on RentHop, its history, challenges and many more lessons, see:

You’ve Got The Power With Lee Lin, Founder of RentHop #137 - a fascinating interview which covers why and how RentHop started, the intricacies of rental markets, the impact of new technology and legislation. The post: Why Real Estate Brokers Exist in 2016 And Beyond analysis the future levels of automation of the brokers activities. Finally, Lee describes the similarities between brokers and chess players in the post: Hello from RentHop – and why brokers and chess players are similar

You will be joining a highly dynamic profession with a track record of success that stretches over 4000 years. Mathematicians continue to make major contributions to the development of civilisation, and remain at the centre of creating solutions that affect many aspects of people's lives.


You will be involved with a wide range of clients at all levels in organisations as diverse as education, local and national governments, small to large multinational businesses, policy making bodies and charities. Many of the projects require a pioneering approach to solving complex problems, very often in diverse environments, and may require the development of new mathematical concepts and techniques. Amongst your roles you will be expected to use modelling and simulation techniques to manage and analyse large amounts of data. With your mathematical skills and experience you will be expected to help the clients understand their problems which will enable them to make better decisions.


You will be required to shape and drive projects from the initial discussions with the client through to successful implementation of the solution. Projects can cover: improving the scheduling of transportation to reduce its impact on the environment, linking DNA information to diseases, predicting the spread of viruses through populations, developing algorithms used in computer graphics to explore new ways to visually represent data and open up new forms of entertainment, optimisation of manufacturing process to efficiently produce goods, create new mathematical models for space flight which will be used to explore the universe, model human intelligence that will be applied to improve artificial intelligence, and develop learning algorithms to be used in developing new business models for e-commerce.


  • Develop the objectives of projects, planning the resources and execute the project taking into account risk management, change control and documentation.
  • Successfully manage all of the people involved in the project, including the client, scientists, engineers, regulatory and standards groups, senior management and other functions within an organization.
  • Communicate the excitement in developing and applying mathematics to audiences ranging from schools to the general public. Also, promote the potential use of mathematics to professions not familiar with its capabilities.

Your Background

  • Must enjoy finding patterns in every day situations whether it is in the geometry of a coastline, the flight path of a tennis ball, or the movement of people through a shopping centre.
  • Prepared to sacrifice many hours in answering the question “why?” about the patterns that are observed in the surrounding world, and using the insight derived from the answer, to predict how the patterns will evolve.
  • Courage and determination in developing solutions to mathematical problems, and resilient to skepticism about the role of mathematics in everyday life.

More Details

For more information read about: Pythagoras of Samos, Euclid of Alexandria, Sir Issac Newton, Albert Einstein, René Descartes, Emmy Noether, Richard Feynman, Henri Poincaré, Sophie Germain, Ronald Fisher, Hendrick Bode", Joseph-Lois Lagrange, David Hilbert, Gottfried Leibniz, Carl Gauss, Rudolf Karman, Bernhard Riemann, Edward Witten, John Forbes Nash, Jr., Alan Turing, George Zames, Ada Lovelace, John von Neumann, Andrew Wiles, Évariste Galois, Sofia Kovalevskaya, Maryam Mirzakhani, ...