You have to be Advanced at Basic Math
Note: The views expressed in this article are my views alone and not the views of my employer or anyone else.
Category: Statistics
Author: Swaroop Bhagavatula

You have to be Advanced at Basic Math
Note: The views expressed in this article are my views alone and not the views of my employer or anyone else.
“Quantitative” is a huge buzzword now. With the rise of big data and machine learning, being good with numbers is seen as a gold star on your resume. People in general associate technical skills, particularly math with a sign of intelligence and capability. The movie “The Big Short” had a famous scene with “That’s my Quant” showing how people who were good at Math were basically gods in finance [1]. All of these examples clearly show that being really good at math is seen as a path to a prosperous future.
The other extreme to this is people who argue that math is largely unnecessary in today’s world. They argue that nobody really uses calculus in their real life and most of the math they do anyway is on a computer [2]. Some argue that learning the qualitative skills in the liberal arts are more valuable than the quantitative skills [3].
Like with most things in life, the truth lies somewhere in the middle. Being good at math is important, but marrying that to the Liberal arts is just as important. More importantly, even when it comes to math, most people will not really need to use calculus and differential equations on a daily basis [4]. Instead people use basic math on a regular basis. Basic math includes things like knowing what 15% of 8 Million is or knowing how to multiply 85 x 65 and other basic math tasks but doing them really fast and without a calculator. In other words, you have to be an expert at basic math.
This is something people always conflate. Expertise and advanced skills. Advanced skills in math would be knowing stochastic calculus and Monte-Carlo simulations. Expertise just means mastery along any concept you’ve learnt. You could have learnt stochastic calculus but could be kind of rusty in algebra, which is actually a lot more common than you might think.
There are jobs that do need advanced math skillsets such as finance and machine learning but those jobs are relatively few compared to the entire economy and there are more than enough people to fill those jobs. Most people should invest their time in getting good at basic math or “consultant math”. Some people argue that even if you don’t use advanced math, that you still should learn it. The idea being here that you are “math fluent” and so even if the software is doing the math, you at least know what the software is roughly doing and at least know the direction of the answer and can debug it.
It’s also true that even if you only need the basics, that there is an iterative learning process that happens when you learn more advanced skills. In other words, your understanding of algebra is reinforced when you use it in pre-calculus and that is reinforced when you calculus and so on. The idea being that simply doing the basics is not enough to learn it, you have to apply it in other areas to truly learn the concept. This doesn’t just have to be in other math classes, you can apply those skills in other classes such as physics, computer science and others. Figure 1 shows how most jobs require an intermediate level of basic math in addition, subtraction, etc. Some higher level jobs in finance and engineering require slightly more advanced math and very few require advanced expertise in stochastic calculus. There is no reward to being a beginner at math but there isn’t much of a reward to being good at advanced math.
Figure 1 showing the advanced level of math on the x-axis and the level of expertise on the y-axis. It also shows the jobs that require such skills for the level of expertise and skill level.
The same is also true for Statistics. Data is hot now and everyone is trying to learn statistics to process all of the data that they have and derive insights. The vast majority of this growth in data science jobs will require an advanced expertise in the basics of statistics related to probability and sampling. You will not need to know Bayesian probability.
Figure 2 showing the advanced level of statistics on the x-axis and the level of expertise on the y-axis. It also shows the jobs that require such skills for the level of expertise and skill level.
The flip side to this argument is uncertainty. The new trend now is not to predict trends. People’s new career advice is not to plan for the future [5]. They’re basically saying that we don’t know what the trend of the future is and by pigeonholing yourself into studying just the basics. We didn’t know machine learning existed 10 years ago and we wouldn’t have known what skills would be needed then. Basic math might be what they want today but who knows if that will be true tomorrow.
This doesn’t just apply to Math and Statistics, it applies to all industries, and people should try to develop a broad skillset in college to build off of in the real world. It is also true that being an expert in the basics goes further in those industries too. People in general think that a more advanced skill will always be more in demand.
Figure 3 showing overlap between expectations and caliber
This is partially true, people with more advanced skills are more in demand for all jobs but they are not looking at all jobs. Their caliber has gone up but their expectations have gone up as well. The person who is good at advanced math might qualify for the lower tier math job but now they have an expectation of getting the advanced jobs which are fewer in number. The jobs they do want don’t necessarily want them. They actually might have been better being low caliber and low expectations rather than high caliber and high expectations.
Basic takeaway from all of this is that basics are really important. You have to be able to do a lot of really simple things really well.
Sources:
1. https://www.youtube.com/watch?v=QpsI_Gvn7C8
2. https://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html
3. https://www.bloomberg.com/news/articles/2018-02-06/maybe-stem-isn-t-the-future-after-all-soft-skills-are-coming-on-strong
4. http://www.washingtonpost.com/wp-dyn/content/article/2010/10/22/AR2010102205451.html
5. https://www.cnbc.com/2018/06/27/wharton-professor-adam-grant-do-not-follow-this-common-career-adv.html