After completing his Ph.D. in mathematics from the University of Florida, William Severa moved to the southwest to join Sandia National Laboratories as a full time researcher in the data-driven and neural computing department.
Pictured above: Sandia’s Z machine is the world’s most powerful and efficient laboratory radiation source.
1. It isn’t all cloak and dagger.
Yes, Sandia National Laboratories certainly works with sensitive and classified information—though what I learned is there’s a sizeable chunk of national labs’ work that is entirely unclassified and in-the-open. As a researcher, I continue to publish my work, and I can still discuss my research at conferences or meetings. More than that, there’s plenty of internal support to determine just what is sensitive and what isn’t, so you always know what you can or cannot say.
2. I still get to research cool ideas.
One of my worries about leaving academics was potentially losing research freedom. However, it turns out I’m afforded quite a bit of flexibility here. We are encouraged to pursue grants from a number of external funding agencies, and the Department of Energy has its own congressionally-authorized internal research funding called Lab Directed Research and Development (LDRD). These projects range in duration and scale, and the process provides a great mechanism to propose my own research ideas. LDRD projects are focused on high-risk, high-reward research, so they’re always up for the next great idea.
3. It’s an engaging interdisciplinary effort.
Every day I go to work with an incredibly diverse team. Since departments are centered on topics rather than degrees, we have a truly interdisciplinary effort. My co-workers’ backgrounds range from psychology and neuroscience to climate engineering and computer science (and mathematics!). Together we each use our expertise to contribute to a unified solution.
4. ‘Go ahead; Stretch out and try new things.’
I’m the type of person who is always excited to learn new things or apply what I know to new problems. However, as a pure mathematician leaving graduate school, I found it difficult to expand from my core expertise. At a national lab, I am constantly encouraged to approach new challenges. Some are close to my expertise, and some are a little farther. Either way this freedom lets me push my work into different and exciting directions.
5. They give us our breathing room.
Project timelines are on the order of years, not months. As such, we have the time to do basic research, not just push out a product. The exact schedule is, of course, dependent on the program. In my experience, the schedules have always been accommodating.
Sandia National Laboratories is a multi-mission laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000.
“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.
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.
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.
Photos – clockwise from upper left:
1) My official federal portrait
2) Flight simulator at NASA Ames Research Center, Moffett Field, CA
3) Working at NASA Ames Research Center, Moffett Field, CA
4) Tour in Speaker of the House office at the U.S. Capitol
5) Senate baths at the U.S. Capitol.
6) With Nichelle Nichols, who played Lieutenant Uhura in “Star Trek” at a poster session at NASA Ames Research Center, Moffett Field, CA
Until a few years ago, I was a “wayward” mathematician. I thought all I could do was teach and I wanted out. While teaching is noble and one of the highest callings, I wanted to do something other than my tenure-track position.
Now don’t get me wrong, I knew mathematicians did more than teach. But personally, I had not done a lot of applied mathematical work. Nothing wrong with it, I just hadn’t. (My area of research was a branch of Combinatorics called Matroid Theory.) However, when I started looking I found all kinds of employment opportunities.
When I finished my PhD, there didn’t seem to be a shortage of academic jobs. You might not get a position at Research I institution, but you could find a tenure-track position at a pretty decent institution and be happy. I still see colleges and universities hiring for these positions, but when comparing the number of open positions to the number of Ph.D. graduates annually…there are not enough academic jobs. So what to do? I recommend considering jobs outside academia.
All too often in the MATH community, because of its traditions, a common sentiment is one that unless you are tenure-track faculty, you’re not a good mathematician. It took time…but I got over that nonsense. I wanted to do something different with my mathematics. I went BIG.
Personally, I have always been civic-minded. I’ve always been active in my community – volunteering and helping those in need. Academia allows you this fulfillment to a certain extent. So I ask you this…how important is it that we use mathematics in everyday places in our communities and across society with the critical thinking skills and expert problem solving skills? Or use mathematics and technical abilities to help solve the world’s problems to help ease society’s woes? Or use mathematics to bring forth innovation and technology?
Mathematics is a versatile language. Just like mathematics, critical thinking, problem solving and technical writing are equally as versatile. (Did you realize that you have these skills as a mathematician?)
To transition from academia to government, I broadened my experience beyond the classroom by participating in faculty research opportunities with the federal government. While working with NASA, I studied the relationship between random graphs and Bayesian networks to improve methods for determining and maintaining systems health in autonomous avionics. While working with the U.S. Navy, I worked with a team to examine statistical measures of uncertainty to create techniques for use with data integrity problems.
I also took graduate courses in public policy analysis at a local university. Depending on your interests, you may need to do some additional training to expand your own skill set. Further building on my new skills, I applied for and was awarded the AMS Congressional Fellowship. I worked on Capitol Hill as a staffer bringing a scientific perspective to the halls of Congress.
Thankfully, on my path to a non-traditional mathematics career, I encountered people, including fellow mathematicians, who encouraged me to pursue my passion and explore careers where I might use both my analytic skills and my soft skills. It hasn’t been the easiest thing. I have had to navigate uncharted waters and remarket myself for this new world.
I have increased my personal and professional network to include the mathematics community, the broader scientific community and the non-scientific community- the community we are all a part of. This encompasses a world bigger than the classroom, office or campus.
After all of this, the next question might be…what can I do if I’m interested in positions outside of Academia – Business, Industry, Government (BIG)? The BIG Math Network is a great place to learn about opportunities and to network with like-minded individuals, who are also interested mathematical careers in business, government and industry. Explore this BIG website. A good Google search never hurts either.
Finally, I recommend that you Network. Talk to those for doing types of work the interest you. Whether you contact a researcher at a Federal lab or congressional fellow/staffer, most people will be glad to talk to you about their experiences and provide information for similar lines of work. I’m always glad to share my BIG experiences and knowledge with anyone who is interested.
Carla Cotwright-Williams is an IT Fellow/Computer Scientist for the Social Security Administration. Email her at firstname.lastname@example.org.