2/16/25: How to Not Freeze In the Face of Cryptic Math
Arya b -
Reading mathematics-based production models in the “American Economic Review” isn’t exactly a typical activity for a high school senior. But there I was, tearing hairs off my head at some of the most intimidating equations known to mankind. It felt especially discouraging when a solution presented as “obvious” took more than two hours to figure out, an achievement only rendered possible with essential knowledge of multivariable calculus. But why this self-inflicted torture?
Even before the emergence of ChatGPT in 2022, businesses had begun to implement AI, performing tasks from customer service to data scraping. Numerous corporations were elated at the wonders of AI, as it was a way for firms to increase productivity while keeping costs low (ex: less labor costs). As the rise in machine learning implementations continued, many raised questions on how workers would be impacted, and which industries would see a larger level of AI implementation. I became curious as to how AI would affect businesses currently relying on cost-cutting measures, such as offshoring, and what this would mean for the wages and the jobs of overseas workers relying on offshoring firms.
To figure out these effects, I would need to understand the direct economic effects of a machine learning implementation and also study mathematical models involving technological implementations in firms. The former would be the easier task, while the latter would take significant time to digest the monstrous equations in front of me.
Exploring relevant and recent literature reviews from the “Journal of Economic Perspectives” and the “Journal of Economic Literature” taught me that machine learning possesses four direct implications: it will automate entire jobs, it will increase productivity of existing jobs (called task complementarities), it improves productivity of already automated tasks, and it creates new jobs. For the first implication, the likelihood of machine learning to automate a job depends on how much the job involves prediction. For instance, a cab driver with intimate knowledge of the streets can easily be outdone by Uber drivers, as the art of predicting the shortest routes can also be done by Google Maps or other navigation apps. For the second, AI can complement certain workers’ jobs by providing assistance to workers in their jobs and performing tedious tasks for workers so they can focus on tasks they are more productive in, boosting the overall productivity. For the third, certain tasks that may already be automated can be completed even faster with assistance from machine learning models, increasing productivity even more. Lastly, the implementation of AI requires jobs to maintain the algorithm and add improvements, opening up new tasks for workers.
But the most of two weeks were spent on just exploring mathematical models by Nobel laureate Daron Acemoglu that would improve my own mathematical analysis, as his remarkably useful work was not exactly meant for a naive high schooler. In spite of all of that, I was still able to understand some sections and salvage useful information for my own study. How? Reading with a purpose. Each time I read an intimidating line of calculus or linear algebra, I asked myself, “Is this really useful?” I constantly visualized how such information could directly contribute to my model, while making sure to carefully read areas with conceptual rationale to better understand the math. I spent hours on portions that I felt were crucial insights to my own study, while skimming over the sections that were not as relevant. As a result, I found the math less petrifying and salvaged significant material out of each paper (Note: I am not sharing these equations for the sanity of the reader).
Next week, you should stay tuned for some experiential advice, as I myself navigate the art of writing a strong literature review, which has almost universal applications across academia. However, the insanity resumes after, where I will share my harrowing experiences of writing the mathematical model.
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