Threefold advice: making the jump from geometric group theorist to computer vision specialist

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by Lucas Sabalka

I began my mathematical career as a research mathematician, but now I work in industry even though my degree is not in an applied area. With so few academic jobs available recently, transitioning to industry is becoming more common for mathematics PhDs. So to help any mathematicians thinking about that transition, let me tell you how I got where I am.

I had always planned on being a professor as I pursued my PhD. That’s what I became: after two postdocs and a decent rate of publication, I got a tenure-track position at a research university. A career in academia has significant pluses, including the promise of tenure and thinking about interesting problems all day. However, through the course of these positions, I gradually realized the impact of two important minuses of a career in academia. One is that, with academic jobs so few and far between, you typically do not get to choose where you live. My wife and I are from Nebraska, and wanted to end up close to family and friends. The second is that research is driven by self-motivation. That’s good for someone like me who is highly self-motivated, but it can also add undue stress: I was easily on-track for tenure, but found myself pushing hard to make a name for myself with little recognition.

The experience that changed my career path from academia to industry was a consultantship. A co-author and good friend of mine, Dr. Josh Brown-Kramer, was working as an applied mathematician at a start-up tech company in my home town called Ocuvera. I have an undergraduate degree in math, computer science, and history, and together with Josh, I had competed in and won a few programming contests back in the day. I had done very little programming in the intervening years, but I had enough knowledge to pick up coding quickly. Josh put in a good word for me, and got me a full-time consulting position one summer. That position turned out to be a good opportunity for the company to see that I was a good fit culturally and could contribute positively to their products, as well as a good opportunity for me to see what working in industry was like. A few months after my consultantship ended, the company extended me a full-time offer. It was a difficult decision to make, but the draw of moving back home and (what was for me) the lower stress of working in industry led my decision. I took the plunge and switched careers: from “mathematician” to “applied mathematician”.

That transition was anxiety-inducing. I had prepared for many years to be in academia. It had the promise of tenure, and it was familiar. Industry was scary: what if my company folded? How would I handle the different stresses? In retrospect, I should have had more confidence in myself. I now trust that I will be able to find another job if my current job were to disappear. The stressors are different, but overall my stress levels have decreased. I have more time for hobbies, including advocacy and volunteerism (I speak with elected officials and thought leaders about climate change and the transition to a clean energy economy).

My job is Computer Vision Specialist. I develop algorithms for computers, equipped with 3-dimensional cameras, to automatically monitor patients in hospital settings. If the algorithms detect risky behavior from the patient that could increase their risk of falling, they automatically alert hospital personnel to determine an appropriate course of action. Falls cost hospitals and patients billions of dollars per year and can result in death. Helping reduce fall risk and introducing automated monitoring should reduce health care costs as well as improve patient outcomes and save lives. It is rewarding to feel like this project could help improve people’s lives.

My dissertation was in geometric group theory, a topic at the intersection of algebra and topology. While my job does not call for geometric group theory or really any graduate-level mathematics, I do use undergraduate-level mathematics concepts extensively, including statistics, probability, calculus, Euclidean geometry, various computer science algorithms, and linear algebra. We use machine-learned algorithms and we also write computer vision algorithms by hand. Consider, for example, taking an array of points in 3-space representing a single camera frame from a video stream of a hospital room, and trying to identify exactly those points that represent a bed. What properties of a bed are important, and how do you quantify that in a way a computer could evaluate? Once you know where the bed is, which points in 3-space represent the patient, and which the nurse? How will you deal with noisy or missing data? I may not be using the tools of my specialization, but I am using the problem-solving skills that I developed while pursuing my degree. My degree is not applied, but having a PhD in mathematics in any subject shows that you’re good at problem solving.

My advice to mathematics PhD students considering industry for work is threefold. First, remember that your degree will mean you are a very good problem solver, and have confidence that there are companies that value your skills. Second, it’s a good idea to get some classes under your belt that could help you in your desired fields: computer programming, statistics, probability, finance, or any classes that could apply in industry. These classes aren’t necessary, but can distinguish you from other candidates and help prepare you for the transition. Third, if possible, I recommend finding an internship in the field you’re looking at. This will give you valuable experience, help you know what to expect, show you whether you’d like that industry job, and will help you on the job market. Even if you don’t take other classes or have an internship, companies provide new employees training for their new roles.

If you are faced with a career change and decide to leave academia, remember: a PhD shows you are a good learner and you have the problem-solving skills necessary to succeed in industry!

Contact: sabalka@gmail.com

A random walk toward a net positive

by Derek Kane, Deka Research and Development  dgkane64@gmail.com

Today, I am investigating whether magnetic resonance imaging can evaluate cell viability as we attempt to grow replacement organs: hearts, lungs, kidneys, etc., for patients who need transplants. I believe the child I was at five would approve. Of course, I also have a two hour meeting this afternoon to read C++ code to ensure that it not only performs its intended task, but also conforms to DEKA’s formatting standards. Even the coolest job, and I have a very cool job, includes drudgery and paperwork.

Avoiding boredom was my earliest career goal. My undergraduate degree was mechanical engineering, and my brother got me a job with him at Itek Optical Systems. Itek made cameras and telescopes, largely for the Department of Defense. The engineering challenges were fascinating, but the analysis and algorithm aspects of the work excited me much more than traditional mechanical engineering. However, my lack of deep mathematical training limited the analyses and algorithm development I could handle. At this job, I also noticed two career paths: one group of older engineers became middle managers whose work looked unbearably dull and who seemed very vulnerable to layoffs. A smaller group of engineers, including my boss, served as technical experts. When a new and innovative solution was required, or when a program stalled because a physical or computational challenge could not be overcome, these experts were consulted. I wanted this job.

I decided I also wanted to attend graduate school in mathematics. The deeper understanding of mathematics would enable me to comprehend and address a wider range of analytic and algorithmic problems. Additionally, a PhD provides gravitas when working with other engineers in industry. An engineer with a bachelor’s degree must have a large volume of high quality and high visibility work, before their opinions are considered seriously outside of the company where they work. While there are a great many fools who have doctorates, when you are sitting around a table with several PhDs, it is handy to have your own so you are part of the club.

To prepare for graduate school, I took one or two undergraduate math classes every semester for two and a half years while working. In the process, I discovered that math was beautiful as well as useful. The University of Michigan accepted me into their graduate program, and I studied algebraic group theory, intending to become a professor after graduation. Graduate school also proved an ideal environment to enjoy my two small children. However, as I approached my defense the academic job market was drying up. I could look forward to a series of one or two year positions before finding a tenure-track job. With two children, this prospect was unattractive, so I decided to return to industry.

My previous experience with optics enabled me to join a laser-based project at Lockheed Martin. This project offered the opportunity to work with inertial systems, and this experience made me attractive to Deka Research & Development. Deka was developing the iBot (an inertially stabilized wheelchair capable of traversing rough terrain, curbs and stairs) and the Segway (an inertially stabilized, two-wheel vehicle).

Dean Kamen, the founder of Deka, feels that we should only be working on jobs that are hard and that positively affect many people. The range of work I get to join is varied and exciting: mobility for people who can’t walk, prosthetics for people who have lost arms, clean water for people who will never get utilities from their governments, hearing improvement, safe delivery of drugs, improved dialysis for people with kidney failure, several projects I cannot talk about, and most recently growing new organs for people in need of transplants.

The range of disciplines this allows me to sample is equally wide ranging: thermodynamics, electro-magnetics, computer modeling of liquids, exotic signal processing, statistics, optics, big data analysis, synthetic biology, human-machine interfaces, colloidal flows, causality, complexity, numerical solution of differential equations, etc. Mathematical training allows me to move from discipline to discipline, because at its core, each of these topics depends upon a quantitative approach to understanding data, modeling relationships, and predicting outcomes. Grad school supplemented this flexibility by demonstrating that hard work and research can overcome difficult technical problems. You should leave grad school feeling that if another human has managed to solve a problem and write it down, then you can read their work and understand it.

Today, it is almost twenty-one years since I defended my thesis. I anticipate another twenty-one years of professional life, although I am aiming for at least forty more years. At the beginning of my career, my primary concerns were staying employed and working on exciting projects. Now, I am becoming concerned with why I do the work I do, and whether this work is a net good for the world.

I left the defense industry seventeen years ago, primarily for the selfish reason that it had become wearing and grating to put up with the intrusiveness of security clearances, and because commercial industry was tackling more interesting technical challenges than defense. It is absolutely true that there are sound moral arguments for working for defense, but I never really thought about the ethical justification of my work. I have been extraordinarily fortunate to land at a company where I am sure that my work is contributing to society.

I am largely comfortable with what I worked on, but I regret not seriously considering the moral implications of my early projects. Young mathematicians have complex lives; they need to support families, establish reputations and orient themselves in a world bursting with opportunities. However, it is also very valuable to develop an understanding of the non-technical world: history, culture and philosophy. This helps us avoid choices that make it hard to sleep as we get older. Older mathematicians have reputations, authority and time to reflect. It is morally incumbent that we provide opportunities for young mathematicians, guide them to interesting work, and protect them from external forces who would inappropriately exploit their talents.

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Academia trained me for a BIG career

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by Peter D. Horn

I am honored to share some career advice with the young and mathematically-inclined. When I fit that description, I felt a lack of diversity in the opinions and advice I was hearing from my mentors. This wasn’t their fault, but mine. Classic case of selection bias, as I only sought advice from my professors.  My first recommendation is to connect with many math folks who have walked a variety of paths to get a sense of what is out there (reading the posts on this blog is a great first step!).

When I was finishing up my math major, I felt there was more math for me to learn, and I went on to get a PhD in low-dimensional topology. As a grad student, I was encouraged to pursue a postdoc. By the time I was deep into my postdoc, I had a tenure-track job in my sights. It wasn’t until my third year into a tenure-track position that I evaluated my career choice and realized I would be happier doing something else.

I reached out to a few friends from grad school who went into government and industry, as well as a couple former academics who transferred to tech and finance jobs.  I did a little research to see what was out there, and found “data science” to be a broad enough field to entertain my intellectual curiosities (e.g. machine learning algorithms) while providing plenty of job security (i.e. strong business demand).  Currently, I am a data scientist at the MITRE Corporation, a non-profit company that does R&D for many federal agencies.  I love working at MITRE because I get to define what type of data scientist I want to be.  In my first year, I worked on research projects involving machine learning and agent-based models to drive policy analysis, and I prototyped a web-based simulation tool to explore workforce strategies for the VA.  It’s great to be at a company where the work is challenging and impactful.

While in the transition to industry, I realized that much of my academic training and some of my hobbies positioned me to be an attractive candidate.  As a math major/PhD candidate/professor, I had accrued a ton of experience teaching myself complex, abstract concepts. Employers seek out job candidates who can demonstrate the ability to pick up new things quickly.  Working in help centers/recitations/lectures, I had accrued a ton of experience explaining deep, technical material to non-technical audiences.  Employers like to hire teachers because they can put you in front of customers or use you to mentor young staff.  As a mathematician, you have surely gained similar experience.  Find a way to brag about your superpowers!

You’re going to need programming skills.  In my journey, I was lucky to have learned to code.  In college, I learned a bit of Java in CS 101.  In grad school, the math department hired me by the hour to maintain their website.  I chose to write up my homework in LaTeX.  Frequently, I would need to do some computations in Mathematica, Maple, Matlab, or Sage.  As a postdoc, I got bored one summer and wrote a couple of card games in Objective-C.  For a research paper, I needed to diagonalize some matrices over a non-commutative base ring, and I wrote the code to do this from scratch in Python.  Before I had even heard of data science, I had ten programming/markup languages under my belt, and I put all of them on my resumé to show employers that I am comfortable writing code.  If you don’t have experience programming, I recommend you pick up Python. It’s a good general purpose language.  Pick a project and use Python to attack it (e.g. implement matrix multiplication from scratch).

The last piece of advice I have is to acquire domain knowledge and to network. The biggest hurdle I had in my journey was learning to communicate with potential employers.  I decided to take online courses in data analytics and machine learning, and these courses taught me what people in industry care about, how they talk, and what tools they use.  I also participated in some coding and data science competitions online.  Since I had a noticable lack of business experience, these competitions were something I could point to as proof that I could do data science.  I would also recommend attending meetups in your area. In my experience, meetup people are very friendly and helpful.

Transitioning out of academia was scary, but it has been one of my best decisions.  At first I was worried I wouldn’t be what employers were looking for, but I learned that many employers want to build companies with people from diverse backgrounds. Don’t worry about trying to fit the mold.  Reach out to friends, former classmates, and friends of friends, and you will find all the support you need.

Study Groups with Industry: Mathematics meets the real world

A study group is a type of workshop which brings together mathematicians and people from industry. The meetings typically last for 5 days, Monday-Friday. On the Monday morning the industry representatives present problems of current interest to an audience of applied mathematicians. Subsequently the mathematicians split into working groups to investigate the suggested topics. On the Friday solutions and results are presented to the industry representative. After the meeting a report is prepared for the company, detailing the progress made and usually with suggestions for further work or experiments. Over the years they have proved to be an excellent way of building bridges between universities and companies as well as providing exciting new topics for mathematicians. Of course there is pressure involved in attempting to understand and solve a problem over a short time frame. This can often produce an exciting and intense atmosphere but, in general, a good time is had by all.

 

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Experiments can often help guide a mathematical investigation (or cause even more confusion)

The original Study Groups with Industry started in Oxford in 1968. The format proved a popular way for initiating interaction between universities and private industry. The interaction often led to further collaboration, student projects and new fields of research. Consequently, study groups were adopted in other countries, starting in Europe to form the European Study Groups with Industry (ESGI) and then spreading throughout the world, regular meetings are currently held in Australia, Canada, India, New Zealand, US, Russia and South Africa. A vast range of topics have been covered in the meetings, including beer and wine bottle labelling, legal sale of rhino horn, spontaneous combustion, mortgaging of cows, building toys, city bike sharing strategies, determining fish freshness, etc. New forms of meeting have also evolved, such as the Mathematics in Medicine or Agri-Food Study Groups.

The popularity of study groups can be attributed to their mutually beneficial effects. For companies there is:

  1. The possibility of a quick solution to their problem, or at least guidance on a way forward.
  2. Mathematicians can help identify and correctly formulate a problem for further study.
  3. Access to state-of-the-art techniques.
  4. Building contacts with top researchers in a given field.

The academics benefit from:

  1. Discovering new problems and research areas with practical applications.
  2. The possibility of further projects and collaboration with industry.
  3. The opportunity for future funding.

An important feature of these meetings is that they can also highlight the talents of students, leading to employment opportunities with the companies. In South Africa, after attending a number of study groups, a group of students took a new direction. Noting the gap in the market for applying mathematics to real world problems they started their own company, Isazi Consulting. Now they return to the meetings this time posing their own problems, and looking for new recruits.

Information on the European Study Groups can be found on the website of the European Consortium for Mathematics in Industry. A good source of information for meetings in Europe and the rest of the world is the Mathematics in Industry Information Service, see

ECMI Study Groups https://ecmiindmath.org/study-groups/

MIIS Website http://www.maths-in-industry.org/

 

Tim Myers

Centre de Recerca Matematica

Barcelona, Spain

Blogpost: Parsa Bakhtary

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It is humbling to address future and current mathematicians, but as a former algebraic geometer myself, I will do my best to share with you my story. I work as a data scientist, which the Harvard Business Review in 2012 dubbed “the sexiest job of the 21st century,” at Facebook, which has been ranked by Glassdoor as one of the best companies for which to work. The path that led me from an eager math student who despised applications to where I am today has been a strange one, but the lessons I learned in my undergraduate and graduate math classes have had a profound impact on my ability to analyze concrete problems in industry.

After earning a B.S. in mathematics at UC Davis, I took a year off in which I decided to pursue a graduate education in the same subject. Seven years later, I finally received my doctorate from Purdue University, having written a thesis in the subject of algebraic geometry, and I was eager to take the path which would lead me towards a professorship somewhere. Unfortunately, I was unable to find a post doc in my home country of the US, so I took a position in Saudi Arabia at King Fahd University of Petroleum & Minerals, teaching calculus to aspiring petroleum engineers and occasionally publishing a paper. After three years there, I missed California and returned unemployed in the summer of 2012.

I quickly realized the job market for math professors wasn’t promising at the time, so I started looking for industry positions that would be suitable for someone with my background. After extensive Googling, I realized “data scientist” sounded like something I could do. I taught myself some Python and SQL, practiced analyzing and visualizing publicly available data sets in R and Excel, then started applying. After six months of unemployment, I caught a break and was offered a position at a startup in Chicago. The rest, as they say, is history.

My job at Facebook is unique in its flexibility and often quite challenging, though perhaps not in the same way as algebraic geometry. I have worked on game ranking, platform ecosystem health, comment ranking, celebrity usage patterns on Instagram, and discussion of TV show content on Facebook. I was lucky to be the first data scientist on Facebook Live when it launched, and our team helped grow it into one of the biggest live-streaming platforms in the world. The problems I work to solve can either be very technical, involving complex modeling and simulation, or it can be investigatory, requiring me to search for an explanation of an unusual phenomenon, or it can even be exploratory, such as trying to answer vague questions like “What makes a mobile game fun?”

The analytical training that we mathematicians receive put us at a unique advantage in the field of data science. The rigor we’re accustomed to help us break down a general question into concrete analytical pieces which we can answer with data. It is easy for us to spot errors in thinking, or situations where the evidence doesn’t actually answer the question. After learning some basic statistics and the familiarity with an analytical data manipulation environment (e.g. R or Excel), any mathematician can rapidly become a data scientist. The field of data science is also vast, as one can focus on subfields such as product analytics, visualization, or machine learning.

The biggest misconception people have about data science is that they think we all know how to program and have spent many years writing code. While some familiarity with SQL and analytical software is often desired, we are not programmers. We are, if anything, the voice of evidence at a company. We are there to help shape our colleagues’ understanding and intuition based on the data that we see, and to give actionable recommendations that will improve existing products and help define the appropriate strategies. It’s a fun job, and a great option for all mathematicians interested in industry.

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Opportunity: 33rd Annual Mathematical Problems in Industry (MPI) Workshop

Registration is now open for the 33rd Annual Mathematical Problems in Industry (MPI) Workshop, to be held June 19-23, 2017 at New Jersey Institute of Technology in Newark, NJ. The Department of Mathematical Sciences at NJIT is hosting the meeting, with Linda Cummings and Richard Moore acting as local organizers. Funding is provided by our industrial participants and the National Science Foundation.

The format of MPI 2017 will be familiar to those of you who have attended MPI or a similar week-long study group in the past. On Monday, several industrial participants present their research problems to an assembled group of professors, postdocs and graduate students working in the field of applied mathematics. These presentations are followed by break-out sessions, where teams form to work on the problems throughout the week. The week culminates in presentations delivered Friday to the assembled group of industrial
participants and applied mathematicians. A follow-up report is delivered to each industrial participant in the weeks following MPI. These reports are often modified and submitted for publication in peer-reviewed journals, and many past MPI workshops have produced fruitful long-term collaborations.

To learn more about MPI 2017 and prior workshops, please visit the workshop website:

http://web.njit.edu/~rmoore/MPI2017/

A link on the left menubar will direct you to the online registration form. Spaces and funding are limited, so please register as early as possible. Young researchers and those with prior experience at MPI or the GSMMC (see below) are especially encouraged to apply, as are members of groups traditionally underrepresented in applied mathematics.

Graduate students who have not already done so in a previous year are strongly encouraged to participate in the Graduate Student Mathematical Modeling Camp (GSMMC), held at Rensselaer Polytechnic Institute the week immediately preceding MPI. You will automatically be registered for MPI as a Camp attendee. Please follow the following link to register for the GSMMC:

http://homepages.rpi.edu/~schwed/Workshop/GSMMCamp2017/home.html

Although some of the industrial problems have already been selected, we are still
accepting applications to participate as problem-presenters. Please forward this email to industrial contacts who might be interested in exposing their research problems to a large body of creative problem-solvers with broad expertise in industrial applied math.

Looking forward to seeing you at MPI 2017!

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Blogpost: How mathematics can fight the abuse of big data algorithms

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Reprinted with permission from Alan Richard Champneys, University of Bristol

“Is maths creating an unfair society?” That seems to be the question on many people’s lips. The rise of big data and the use of algorithms by organisations has left many blaming mathematics for modern society’s ills – refusing people cheap insurance, giving false credit ratings, or even deciding who to interview for a job.

We have been here before. Following the banking crisis of 2008, some argued that it was a mathematical formula that felled Wall Street. The theory goes that the same model that was used to price sub-prime mortgages was used for years to price life assurance policies. Once it was established that dying soon after a loved one (yes, of a broken heart) was a statistical probability, a formula was developed to work out what the increased risk levels were.

In the same way that an actuary can tell how likely it is that a loved one will die soon after their partner, a formula was used to predict how likely it was that a person or company would default on a loan. Specifically, it was applied to predicting the risk of two subprime mortgages co-defaulting.

The formula ended up being very wrong. If I default on my mortgage, there is a good chance it is because of a downturn in the economy. So my neighbour, who is in similar socio-economic bracket as me, is pretty likely to default, too. This effect is an order of magnitude stronger than the broken-heart coefficient would predict. So apparently the maths was at fault. Big time.

Did an algorithm gone wrong cause the housing crisis?
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Why didn’t the mathematicians notice? Well, in fact they did, argues Paul Embrechts, a leading financial mathematician who runs the risk lab based at ETH, the Swiss Federal Technical University in Zurich. But few were listening. Embrechts explains it was the blind use of a forumla way outside of its region of validity that was at fault. There was nothing wrong with the formula, it just didn’t apply (as the mathematicians had already shown). Unfortunately, the industry was “stuck in a classic positive feedback loop which no party wanted to walk away from”. Blaming the maths “is akin to blaming Einstein’s E=mc² formula for the destruction wreaked by the atomic bomb”.

Lessons still to learn

There was a lack of appreciation of the difference between risk (something that is priced by the quants – the name the financial services industry gives to mathematicians and data analysts) and uncertainty (what can go very wrong). The Basel Committee on Banking Supervision, in response to the global banking crisis, made it clear that banks must make an explicit assessment of this uncertainty and that different scenarios must be tested.

However, it seems that the banking industry may not yet have learned this lesson, and here I shall change a few details for obvious reasons. I have a friend, with a PhD in mathematics, who recently worked in the City of London, ensuring products sold by a leading financial institution were risk free. He was shocked by what was going on.

Policies are still being sold according to a formula that predicts the company’s profitability. Then a separate team applies simple linear regression (changing a parameter to see how much a value changes by) to “assure” the product against risk. This is to satisfy the requirement of the regulatory authorities.

However, there is little understanding among them of the mathematical theory behind what they are doing and a strong culture in the team to return the answer that all is fine. No possibility is allowed that the fundamentals of the pricing model may have been wrong in the first place, or that risk and uncertainty should be handled in tandem with profitability when the product is constructed.

Critical use of formulae

So the nub of the problem is not that mathematics is to blame, but that in our quantitative world there is often a lack of mathematical understanding among those who are blindly using formulae derived by the experts.

This idea, is in fact the key point of a recent book by Cathy O’Neil, Weapons of Math Destruction. She is not describing the dangers of mathematics per se, but the algorithms used in conjunction with “big data” that are increasingly being used by advertisers, retailers, insurers and various government authorities to make decisions based on what they have profiled about us. She is an advocate for mathematics and for “machine learning” (or artificial intelligence). But what her book seeks to argue against is the use of these algorithms without thought or without feedback.

Don’t blame the maths when the computer says ‘no’.
from http://www.shutterstock.com

The popular TV sketch show series Little Britain had a recurring scene involving a member of the public repeatedly being told by a customer service assistant sat behind a computer screen that “the computer says no”. It is funny, because it is an experience that most of us can identify with.

But the problem is not the computer, nor necessarily the algorithm it is running, but the inability of the person behind the computer to use their common sense. Instead of the computer informing their decision-making process, they are ruled by what it says.

In the mathematical and data modelling classes colleagues and I teach, we encourage students to apply the scientific method to a raft of different problems from across a variety of sectors. Predictions should not just be based on mathematics models and algorithms, but constantly tested against real data. This is an iterative process and lies at the heart of what mathematics is about.

The lesson would seem to be that we need to inculcate more of this kind of thinking in society. As we enter the big data era, rather than mathematics being to blame, it is the lack of mathematical understanding in many key businesses that is at fault. We need more mathematical thinking, not less.

The Conversation

Alan Richard Champneys, Professor of Applied Nonlinear Mathematics, University of Bristol

This article was originally published on The Conversation. Read the original article.