Chapter 1: The Shift in Economic Theory

The integration of mathematics into economics has become a contentious topic. Once characterized by eloquent prose, economic theory has evolved into a complex realm dominated by Greek symbols and intricate equations. In the past, figures like Adam Smith and Karl Marx presented their ideas in a format devoid of mathematical expressions. Their works, The Wealth of Nations and Das Kapital, were lengthy yet completely free of equations.

So, what led to this transition? Why do we now incorporate mathematics into economics when earlier theorists managed without it? It’s essential to understand that economics used to be viewed as a branch of philosophy rather than a scientific discipline. While some may argue that this was a superior approach, I respectfully disagree. Philosophy can be nebulous, and vague theories are difficult to challenge. For economics to attain scientific rigor, theories must be tested against real-world data, and models should yield hypotheses that can be validated.

If you intend to pen an extensive analysis of how the world operates, that's commendable! However, it raises the question: how do we determine which interpretation is correct? If I dissect your arguments and identify claims I deem inaccurate, I could counter with anecdotal evidence and historical context. You, in turn, might present counterarguments, and we could easily become entrenched in a cycle of debate.

This scenario might suffice for public intellectuals or politicians who thrive on discourse, but it falls short if we seek a deeper understanding of economic science. The contemporary framework of economic theory can be categorized into three fundamental components: assumptions, derivation, and interpretations.

Section 1.1: Assumptions in Economic Models

Every economic model is built upon assumptions. While lengthy narratives may obscure these assumptions, mathematical models require transparency. Each assumption must be clearly articulated and, importantly, falsifiable. This means that we should be able to conceive of a statistical test that could potentially disprove each assumption, even if such tests are currently impractical due to resource constraints or data availability.

Chapter 2: Interpretation and Its Challenges

The first video titled "What's up with Mathematics in Economics?" delves into the relationship between mathematics and economic theory, shedding light on why mathematical modeling is crucial for economic analysis.

After deriving a model, economists face the task of interpreting its implications for the economy. It's important to remember that a model is a simplified representation of reality, which necessitates careful interpretation to extract meaningful insights.

However, this step often leads us back into murky waters. While mathematics provides clarity, articulating its implications in everyday language can introduce ambiguity. Economists must navigate this complexity to maintain the integrity of their arguments.

The second video, "Can you HATE MATH & MAJOR in ECONOMICS? | Do you have to be GOOD at MATH? | my honest opinion," reflects on the challenges students face when confronting mathematics in economics and whether proficiency in math is necessary for success in the field.

Despite the value of mathematical models, there is significant pushback against their prevalence in economic science, even from within the field itself. Critics usually present a few common arguments:

1. It's not physics. They argue that human behavior can't be reduced to mathematical equations, given the unpredictable nature of people.
2. Nobody understands anything! The complexity of math makes economics inaccessible to the general public, which some believe is an intentional strategy by economists to maintain control over the narrative.
3. The reality is too complex. Some claim that the intricate dynamics of economies are too convoluted for a model to be effective, advocating for a more intuitive approach instead.
4. You are in love with your math! Critics suggest that some economists may prioritize aesthetic elegance in their models over practical applicability.

While these critiques have merit, they often misinterpret the role of assumptions and derivations. When observed behaviors seem irrational, it may be a reflection of faulty assumptions rather than a rejection of economic modeling altogether.

In conclusion, the evolution of economic theory into a mathematically rigorous discipline represents an essential progression toward scientific accuracy. Although challenges persist, the pursuit of a deeper understanding of economic phenomena through mathematical frameworks is a worthy endeavor.