At this point in my career, I have worked at a number of organizations, usually technology companies with military contracts. I am convinced that mathematicians strengthen organizations, and sometimes make revolutionary changes, often in small ways that are not celebrated as often as they should.

My ﬁrst job was at the Center for Naval Analysis in Alexandria, Virginia. CNA performs long-range studies for the Navy, and is one of the oldest military Operations Research ﬁrms. I was working for a crusty old radar engineer, who wanted me to perform Monte Carlo analysis of Russian missile raids. This required thousands of runs of the program. One day, I needed to consult with a mathematician on another ﬂoor. I was surprised to ﬁnd that he knew the simulation I was spending my days with. But what really amazed me was when we started discussing speciﬁcs. At that point, he pulled out a big binder containing tables of every possible combination of inputs to the model, and the associated outputs. He had invested the time one week to run all the possibilities and compile them. Having done this, he did not need to run the model for hours a day; instead he had just to pull out the binder and ﬁnd the right row to pull out the results. It impressed me that this approach was much more eﬃcient.

Later in my career, when I was working for another company, we had a large number of engineers working on a new ballistic missile system for the Navy. The schedules were aggressive, and the work multi-faceted and diﬃcult. On one of the projects, it appeared necessary, despite the tight schedules, to spend a year running cases of ﬂight trajectories. However, there was a PhD mathematician working on this, and he argued that since all the factors were known, mathematics could be used to perform a quick study, and come up with all the possible trajectories. He saved the company a year of eﬀort and countless computer runs.

In these cases, Mathematics is not enough. It is important to get the information into the right hands. A junior engineer or mathematician will not be listened to, at least without concerted eﬀort and the right arguments.

I had the opportunity to learn this ﬁrst-hand. I was working on a critical program for the Air Force, and one evening before heading home, I was reading the speciﬁcations (not always easy reading). Before I went too far with this, I came upon something that stopped me in my tracks. Here, in a system where eﬃciency was highly emphasized, was an operation being done 80 times in one set, and then in the next set, the inverse of those operations was being done. This seemed to me something that should be ﬁxed. So I went to my boss and pointed this out. However, I was new, and my boss did not know enough mathematics to understand my claim that *e ^{a}e^{b} = e^{a+b}*. No matter how I argued, she was not going to take my word for it. Her approach, ultimately, was to arrange a panel discussion with some scary senior analysts around the table to make me retract my story. But I did not back down. Looking back on it, the issue was a badly implemented discrete Fourier transform. I left the company soon after. It took about a month before I started getting phone calls asking for my notes. They had come around to agree with me.

The point of all this is, that mathematicians are needed outside of academia. Mathematics is used, and sometimes misused, every day in almost every industry. Mathematicians are needed for their training, but also their insights. I believe that mathematicians are able to ﬁnd efficiencies, and new approaches, that others are blind to. Mathematicians are needed to prevent errors, to analyze complex problems and systems. There is no doubt in my mind that we need more mathematicians in industry.

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