To look for the significance of algebra is always to look for the significance of quantities, something that is not granted to data except as an ulterior, that is, a causal or empirical observation. Furthermore, quantitative data says nothing about causal rules except by referring to other principles which are not embodied in math, e.g. rules of inference. Although math does have its own rules of inference, these do not have a one-to-one correlation with both data and proof simultaneously. In other words, predicting the number of bison that will populate the Great Plains depends on a rule of inference, that numbers of bison will increase exponentially (for example), that has little to do with the number of bison that currently exist there. And if it doesn't have to do with the current number of bison, then it has little power to predict past or future numbers with any accuracy. Indeed, what actually happened was that bison numbers decreased, which had an inverse correlation with human settlement. This was not algebra, but a form of inference which had nothing directly to do with the quantity of bison. In fact, settlers may have been attracted by the large numbers of bison, not by the small numbers, thus leading to something worse than an inverse relationship: in fact, something that could not be expressed in mathematics. For at the root of it, the psychological impulse was one of being attracted both to bison quantities and also to dead bison hides. And simultaneously, in other respects (the maintenance of the railroad, for example), humans did not want bison at all. And it is hard to predict a stricter quantitative relationship than an inverse relationship, but nonetheless, the result is apparently not algebraic.
In any case, even if algebra could express relationships like bison to settlers, or human intelligence to the degree of experimentation, such relationships are not best expressed in mathematical terms, as the math is inevitably just a starting point to understanding what has actually occurred. In most cases, the data comes off as a vast over-simplification. The data is, at the root of it, not directly contingent upon experience. Data poses the danger of imposing un-realistic thinking over a long period of time that is only second-guessed when it is too late. Indeed, the assumption that data is meaningful is a glaring mistake. And the basic problem is that algebra does not add significant content to the system.
I should really be celebrating, because I finished my last required math class for my philosophy degree (I got an A-). I lasted out! I'm still critical of math!