How does a Mathematician think about a business? by Philippe Barbe 14 Apr 2021

Have you ever wondered how others think?

In particular, if they have a skill set very different than your own?

If you want the wrong answer to the question “How does a mathematician think about a business?”, ask Google!

The search engine will give you articles about what math can do for a business person, the importance of mathematics in business, why someone in business should learn some math, and what forms of math ar relevant to business… all legitimate matters, but not answering the specific question… how does a Mathematician think about business?

As a professional Mathematician for 20 years my job was to invent new mathematics, that is, to discover and prove new theorems. I published numerous articles in math journals and wrote books that other Mathematicians read that the vast majority of people on the planet find incomprehensible.

I still write serious mathematical equation occasionally, for it is impossible to stop being drawn by the unknown and guided by the desire to understand what others do not.

Having transitioned from my academic career to the business world 6 years ago, I was recently discussing with a maritime company now diversified into the transportation industry its needs in data science. Beyond seeing trucks on the road this is an industry in which I never worked, have no real knowledge about and no idea of how the business works.

As I was progressing through the discussions, it became evident that I needed to learn something about this industry because although I had the skillset to address the problems, the company was clearly concerned that I didn’t know their business.

I didn’t have much to go on to start my research but as an academic and a Mathematician I’m used to having to search for hard-to-find information. Often, to prove a conjecture and make it a theorem, I need to look around the subject, learn new things quickly, sometimes in depth, sometimes less so, starting with what has already been written on the subject.

First stop: the company’s website where I picked up a keyword phrase “Defense Freight Transportation” which was relevant. With that in hand I uncovered a ruling from the GAO that gave me the history of the company’s contract with the U.S. government but not much on the overall transportation industry.

I kept searching.

With a few hours more searching I found a 3-hour podcast focused on the industry that featured some of the company’s employees. Taking notes as I listened in speed mode I gained excellent information on the challenges that they encounter, which although they didn’t state it explicitly, is that basically, they need more trucking capacity! How did I know? Because in every segment they advertise their company’s desire to work with small trucking companies and ask those companies to call them as the insistently repeat their phone number. That is the deductive part of how Mathematicians think.

I learned that 90% of the trucking business is done by small companies with a fleet of 10 trucks or less. It sounded an interesting curiosity, some sort of general knowledge that could be useful. I didn’t know why, it was just an intuition, perhaps because at one point I was an Economist working on macro-economics

I learned that heavy or oversized shipments are in a different category. One of the podcasts was dedicated to this topic and all the different types of trucks: flat bed, lowboy, gooseneck, etc. I learned that there is a big difference between TL and LTL (full truck load vs. less than truck load) and how they are priced. A little deductive math thinking and the reason is clear: for an LTL, some capacity in the truck remains, and so the route may include other pickup and deliveries, creating routing challenges. I recalled from shipping books across the Atlantic years ago, that freight transportation is priced by weight and distance. The emptier a truck is, the higher the price per weight and distance, since the operating cost of the truck is pretty much constant. Therefore, LTL should be priced higher than TL on a per weight and distance basis.

I also listened to another segment about freight brokers and dispatchers. Another curiosity.

Looking back on my mathematical career, being curious, looking at anything that I did not know, even unrelated to my immediate interest, was a key ingredient in my success. What seemed useless at some point often turned out to be quite useful years later.

There is a strange thing I learned doing math all those years, if I don’t know how to solve a problem, I work hard on it, concentrate enough to think about it constantly, and my brain will process something during the night.

So I slept on the broker and dispatcher.

By then, I had studied the industry for about 10 hours.

The next day, something clicked.

Doing mathematics is very much about finding conceptual patterns. For most people, finding patterns is about looking at numbers such as 0, 2, 4, 6, 8, seeing that these are the even numbers, and continue the sequence. It is about finding things that repeat. This is also the case in doing mathematics professionally, but in a much more conceptual way, and typically, with very few examples.

Shipper, broker, dispatcher, trucker… Shipper, broker, dispatcher, trucker…

Ah ha! I had a clear pattern match in an industry that I know very well… media and advertising.

Advertiser, agency, reps, TV station!

Shipper corresponds to advertiser: they have the money, and want something to be accomplished.

Broker corresponds to agency: they are middle people, who work for the buyer of the service.

Dispatchers and reps work for the seller who sells the capacity.

Trucker correspond to TV stations.

I realized (and will explain in the next article) that the media and trucking industries are in some sense exactly the same.

The Mathematician in me sees the pattern emerging not just because there are 4 entities as there are other industries where I could find 4 entities (farmer, whole sale, retail store, and customer) but because as a Mathematician I can see clearly why these entities are the same manifestation of an abstract pattern. There are many shippers (even if you restrict to B2B, and even if you restrict to a government contract) because there are many sites from which things are shipped, and every site is very much like an independent business; and many trucking companies with 90% of the business done by small carriers.

The other pattern I see is that in both industries contracts need to be negotiated because they are complicated… shipping a heavy/oversize load is like buying a Super Bowl ad.

Eureka… 1 + 1 = 2. Lots of business, lots of customers, lots of negotiations:

you need a lot of middle people! That’s the pattern. With that realization as I dug further into the business I saw more parallels and soon had a list of 15 similarities between the two industries. One thing I have learned over my past 6 years in the business world is that while Mathematicians are fine with 15 variables, business people are not! They want an easy to see and understand structure.

How could I organize my list? I needed to find what these items had in common.

Again, the pattern appears clearly: you follow the business process, from the customer needing to ship something to the carrier delivering the goods. Breakdown that chain. Label each part. Add the supporting functions. Voila! I was then able to create a document showing the amazing similarities between an industry I knew nothing about and one I knew intimately.

So what? What can I do with this knowledge?

On the human side, I can help those in the broadcast media and advertising industry market their skills in the transportation industry thus increasing their employability. And on the business and technical sides,

1. I can now say something meaningful to this company. I now have a deep grasp of some of the problems related to not just strategy and process but also some far more technical ones such as forecasting demand and capacity, pricing, designing systems, and the problem of adoption of these systems by the industry. In a short time my Mathematician’s thinking enable me to have a far deeper knowledge of the industry than if I had not seen the analogy, far deeper than if I had not been able to do so much abstraction.
2. If these industries have the same structure and the same problems, then a solution to these problems should work in both industries. A solution I create for one industry can bring value and revenues to the other without much development cost.
3. There are other industries that have the same structure, for the same reasons, and they are likely in comparable positions in their digital transformation. There is a potential for a solution across multiple industries. Quite a non-obvious one and therefore one that has high return on investment.

How does a Mathematician think about a business?

Like a mathematical problem: study it, learn at the periphery, look around, get examples, abstract, look for conceptual patterns, infer, deduce, imagine, structure.

If you find this way of thinking valuable and can see how it may help your business, feel free to reach out and let’s talk.