Is Mathematical Modelling Inherently Destructive?

I stumbled upon an article summarising Cathy O’Neil's book "Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy", and I thought it is missing a very important point. It feels superficial to me (maybe wrongly so) to talk about ideology in the context of mathematical modelling. But the statement "there is nothing inherently destructive about mathematical modeling" feels deeply inadequate, so I thought I should also make a point. I ended up posting it here.

I myself have had a long journey with Mathematics. I was in one of those Eastern European classes that generate "geniuses" and you read about them in the press. In my class I've had (if I remember correctly) two world medalists in what they call Mathematical Olympiad. I'm unsure of the number, because we had a group of 4-6 people that were competing to get sent there (each nation sends annually a team of 4 from an age range). The most globalised of these people are now a hedge fund manager in New York (Harvard graduate), and two software engineers, one in Boston (MIT graduate), and one in San Francisco (moved over after university). I personally turned out not to be competitive enough to make it even to the extended team of 8, even though I've had moments when I was in. I had to join the equivalent team in Informatics, but still I didn't have the determination to sit and solve tasks so that I can do better than the Russians or the Chinese.

After that, I moved on to study mathematics at university in Germany. Of course there were new things for me there (don't think at school you get to learn Topology, Complex Analysis, General Algebra or other abstract subjects; you are taught to solve the particular kind of problems they give at those olympiads, and get a general good understanding of Mathematics). But it was still much easier for me than for anyone else around. What struck me, was that in Germany you're taught to reduce everything to standard problems, mostly Optimisation. I was able to compare this to textbooks from my country (which were pretty much along the lines of Russian textbooks), from the US and the UK, and nowhere else this was taken to such an extreme. In my mind this was appalling. Not only was I most keen on disciplines like Combinatorics, Stereometry and Graph Theory, which were dumbed down to standard reduction algorithms in Germany, but I felt that they are missing the point of Mathematics.

I'm telling all this to provide the context about a very strong statement that I'm about to make about Mathematics, and Optimisation in particular. To those of you that don't know, Optimisation is the field of Mathematics where given a set of formal conditions, you are supposed to find the optimum solution. The most common (and easy) form is Linear Programming, but it doesn't have to be linear. There are also polynomial, convex and integer, which are also very popular. In fact these have grown into some of the most powerful machine learning techniques, even though, being a real-world problem, machine learning still requires some creativity in problem solving (when I think of it, this is my position, I have a friend that is very successful data scientist and he wouldn't agree to the meaning I put in this, not that he'd claim that his job is not creative, just have very different intentions behind the use of the word). Sorry, I'm getting too distracted.

In fact I'm telling this long story to get to a very simple fact: Optimisation is evil :)

Well, this is not because it didn't feel fun to me. The reason is related, but much deeper: it assumes that all the conditions/constraints are known, and everything else could be ignored. And in the real world this is not the case. Here are a few examples where these assumptions fail humanity and the world:

• Industrial Farming: assuming that yields need to be increased at any cost, results in animal abuse, plant poisoning and desertification of whole countries
• Big Pharma: actually very related to above, but they apply it to people as well. No one understands nature and there are very strong evidence that it doesn't exist in a way subjectable to understanding (think of Relativity and Incompleteness)
• Financial Markets: I don't even know where to start here. Let's say any book title by Nassim Thaleb explains it perfectly
• Politics: who would even think that mathematics is applicable to societies?

Mathematics is an abstract language, always remember this when trying to apply it to something practical. You will always miss something out, and chances are it will be the bigger (actually comparison is already ambiguous in reality) lump of what you're trying to represent. That's why I love applying Maths to games, but it is your own subjective judgement that needs to make the decisions when you try to apply what you've learned in games to reality.