Yesterday, I traded in my old iPhone at the Apple Store and used the credit toward a new iPad and Apple Pencil. Back home, I tried reading PDFs on Good Reader with the Apple Pencil, and it felt great. I’m a strong advocate for e-books and have mostly stopped reading physical books. The reason is simple: e-books are far more portable, especially for someone like me who reads in scattered moments throughout the day—on the subway, during lunch, before bed. But e-books have one obvious downside: taking notes isn’t as convenient, or rather, it just doesn’t feel the same. I’ve always been the type to have lots of thoughts while reading, and I enjoy scribbling and doodling in the margins. Typed annotations never quite capture that feeling. Using the Apple Pencil with PDFs has finally, more or less, satisfied my “bad habit” of scribbling all over my books.
I happened to flip to “Paul Wilmott Introduces Quantitative Finance” by Paul Wilmott, and came across this passage:
Most academic articles in finance have a ‘pure’ mathematical theme. The mathematical rigor in these works is occasionally justified, but more often than not it only succeeds in obscuring the content. When a subject is young, as is mathematical finance (youngish), there is a tendency for technical rigor to feature very prominently in research. This is due to lack of confidence in the methods and results. As the subject ages, researchers will become more cavalier in their attitudes and we will see much more rapid progress.
The gist is that most academic papers in finance are packed with dense mathematics, making them exhausting to read—often leaving readers unsure what the author is even trying to say. Wilmott argues that this happens because when a discipline is still young (like mathematical finance), its papers and research tend to be overloaded with excessively rigorous technical details. This is, in essence, a manifestation of insecurity—a lack of confidence in the methodology and findings.
Let me add my own two cents: compared to disciplines like physics and chemistry, economics is inherently a “rougher” field—difficult to verify with precision, fundamentally more of a humanities subject at its core. And yet, ever since Paul Samuelson introduced a mathematical framework in the mid-twentieth century, the discipline has seemingly transformed into a quasi-mathematical one (at least in how it’s taught in universities). Personally, I think this puts the cart before the horse. The whole point is to explain ideas that are largely intuitive—does wrapping them in a layer of mathematics suddenly make them precise? And shouldn’t the natural order of learning be to first understand the underlying “reasoning,” and then work on the mathematical “dressing”—rather than the other way around?
The same goes for mathematical finance. The concepts behind applying stochastic processes to derivatives aren’t really that hard, yet how many introductory books on the market can a normal person actually read?
Isn’t this exactly the kind of “complexity” that’s manufactured out of “insecurity”?
In my view, a true introductory book should start with intuitive concepts and reasoning, and only then gradually introduce the mathematics. It shouldn’t open with pure mathematical definitions, leaving readers who’ve studied for ages knowing only how to derive formulas while having completely overlooked the reasoning behind them (yes, I’m looking at you—most domestic economics and econometrics textbooks in China). If you trace the history of any discipline, you’ll find that at the very beginning of every field or concept, all people had were vague, intuitive understandings. Rigorous mathematical definitions came much later in a discipline’s development. Shouldn’t the learning process also start from intuitive understanding?
On that note, let me recommend two introductory books on mathematical finance (possibly the only two “truly” introductory books out there 😂):
- “Paul Wilmott Introduces Quantitative Finance” by Paul Wilmott
- “An Introduction to the Mathmatics of Financial Derivatives” by Ali Hirsa