Math in AI/Data Science is not really math, but a shortened version of English paragraph.
In science, researchers often ask 'plz speak in plain English', a presentation that math is just to explain science in more scientific way.

I liked math until high school, but it became an abomination during my college days. I had no choice but to make records of math courses on my transcript as it was one of the key factors for PhD admission, but even after years of graduate study and research, I still don't think I like math. I liked it when it was solving a riddle.

The questions in high school textbooks and exams are mostly about finding out who did what. But the very first math course in college forces you to prove a theorem, like 0+0=0. Wait, 0+0=0? Isn't it obvious? Why do you need a proof for this? I just didn't eat any apple, so did my sister. So, nobody ate any apple. Why do you need lines of mathematical proof for this simple concept?

Then, while teaching AI/Data Science, I often claim that math equations in the textbook are just short version of long but plain English. I tell them "Don't be afraid of math. It is just a language." Students are usually puzzled, and given a bunch of 0+0=0 like proof in the basic math textbooks for first year college courses, I get to grasp why my students showed no consent to the statement (initially). So, let me illustrate my detailed back-up.

Math is just a language, but only in a certain context

Before I begin arguing math is a language, I would like to make a clear statement that math is not really a language as in academic defintion of language. The structure of math theorem and corollary, for example, is not a replacement of paragraph with a leading statement and supporting examples. There might be some similarity, given that both are used to build logical thinking, but again, I am not comparing math and language in 1-to-1 sense.

I still claim that math is a language, but in a certain context. My topic of study, along with many other closely related disciplines, usually create notes and papers with math jargons. Mathematicians maybe baffled by me claiming that data science relies on math jargons, but almost all STEM majors have stacks of textbooks mostly covered with math equations. The difference between math and non-math STEM majors is that the math equations in non-math textbooks have different meaning. For data science, if you find y=f(a,b,c), it means a, b, and c are the explanatory variables to y by a non-linear regressional form of f. In math, I guess you just read it "y is a function of a, b, and c."

My data science lecture notes usually are 10-15 pages for a 3-hour-long class. It might look too short for many of you, but in fact I need more time to cover the 15-pager notes. Why? For each page, I condense many key concepts in a few math equations. Just like above statement "a, b, and c are the explanatory variables to y by a non-linear regressional form of f", I read the equations in 'plain English'. In addition to that, I give lots of real life examples of the equation so that students can fully understand what it really means. Small variations of the equations also need hours to explain.

Let me bring up one example. Adam, Bailey, and Charlie have worked together to do a group assignment, but it is unsure if they split the job equally. Say, you know exactly how the work was divided. How can you shorten the long paragraph?

y=f(a,b,c) has all that is needed. Depending on how they divided the work, the function f is determined. If y is not a 0~100 scale grade but a 0/1 grade, then the function f has to reflect the transformation. In machine learning (or any similar computational statistics), we require logistic/probit regressions.

In their assignment, I usually skip math equation and give a long story about Adam, Bailey, and Charlie. As an example, Charlie said he's going to put together Adam's and Bailey's research at night, because he's got a date with his girlfriend in the afternoon. At 11pm, while Charlie was combining Adam's and Bailey's works, he found that Bailey almost did nothing. He had to do it by himself until 3am, and re-structured everything until 6am. We all know that Charlie did a lot more work than Bailey. Then, let's build it in a formal fashion, like we scientists do. How much weight would you give it to b and c, compared to a? How would you change the functional form, if Dana, Charlie's girlfriend, helped his assignment at night? What if she takes the same class by another teacher and she has already done the same assignment with her classmates?

If one knows all possibilities, y=f(a,b,c) is a simple and short replacement of above 4 paragraphes, or even more variations to come. This is why I call math is just a language. I am just a lazy guy looking for the most efficient way of delivering my message, so I strictly prefer to type y=f(a,b,c) instead of 4 paragraphes.

Math is a univeral language, again only in a certain context

Teaching data science is fun, because it is like my high school math. Instead of constructing boring proof for seemingly an obvious theorem, I try to see hidden structures of data set and re-design model according to the given problem. The diversion from real math is due to the fact that I use math as a tool, not as a mean. For mathematicians, my way of using math might be an insult, but I often say to my students that we do not major math but data science.

Let's think about medieval European countries when French, German, and Italian were first formed by the process of pidgin and creole. In case you are not familiar with two words, pidgin language is to refer a language spoken by a children by parents without common tongue. Creole language is to refer a common language shared by those children. When parents do not share common tongue, children often learn only part of the two languages and the family creates some sort of a new language for internal communication. This is called pidgin process. If it is shared by a town or a group of towns, and become another language with its own grammar, then it is called creole process.

For data scientists, mathematics is not Latin, but French, German, or Italian, at best. The form is math (like Latin alphabet), but the way we use it is quite different from mathematicians. For major European languages, for some parts, they are almost identical. For data science, computer science, natural science, and even economics, some math forms mean exactly the same. But the way scientists use the math equations in their context is often different from others, just like French is a significant diversion from German (or vice versa).

Well-educated intellectuals in medieval Europe should be able to understand Latin, which must have helped him/her to travel across western Europe without much trouble in communication. At least basic communication would have been possible. STEM students with heavy graduate course training should be able to understand math jargons, which help them to understand other majors' research, at least partially.

Latin was a universal language in medieval Europe, so as math to many science disciplines.

Math in AI/Data Science is just another language spoken only by data scientists

Having said all that, I hope you can now understand that my math is different from mathematician's math. Their math is like Latin spoken by ancient Rome. My math is simply Latin alphabet to write French, German, Italian, and/or English. I just borrowed the alphabet system for my own study.

When we have trouble understanding presentations with heavy math, we often ask the presentor, "Hey, can you please lay it out in plain English?"

The concepts in AI/Data Science can be, and should be able to be, written in plain English. But then 4 paragraphes may not be enough to replace y=f(a,b,c). If you need way more than 4 paragraphes, then what's the more efficient way to deliver your message? This is where you need to create your own language, like creole process. The same process occurs to many other STEM majors. For one, even economics had decades of battle between sociology-based and math-based research methods. In 1980s, sociology line lost the battle, because it was not sharp enough to build the scientific logic. In other words, math jargons were a superior means of communication to 4 paragraphes of plain English in scientific studies of economics. Now one can find sociology style economics only in a few British universities. In other schools, those researchers can find teaching positions in history or sociology major. And, mainstream economists do not see them economists.

The field of AI/Data Science evolves in a similar fashion. For once, people thought software engineers are data scientists in that both jobs require computer programming. I guess now in these days nobody would argue like that. Software engineers are just engineers with programming skills for websites, databases, and hardware monitoring systems. Data Scientists do create computer programs, but it is not about websites or databases. It is about finding hidden patterns in data, building a mathematically robust model with explanatory variables, and predicting user behaviors by model-based pattern analysis.

What's still funny is that when I speak to another data scientists, I expect them to understand y=f(a,b,c), like "Hey, y is a function of a, b, and c". I don't want to lay it out with 4 paragraphes. It's not me alone that many data scientists are just as lazy as I am, and we want our counterparties to understand the shorter version. It may sound snobbish that we build a wall against non-math speakers (depsite the fact that we also are not math majors), but I think this is an evident example that data scientists use math as a form of (creole) language. We just want the same language to be spoken among us, just like Japanese speaking tourists looking for Japanese speaking guide. English speaking guides have little to no value to them.

Math in AI/Data Science can be, should be, and must be translated to 'plain English'

A few years ago, I have created an MBA program for AI/Data Science that shares the same math-based courses with senior year BSc AI/Data Science, but does not require hard math/stat knoweldge. I only ask them to borrow the concept from math heavy lecture notes and apply it to real life examples. It is because I wholeheartedly believe that the simple equation still can be translated to 4 paragraphes. Given that we still have to speak to each other in our own tongue, it should be and must be translated to plain language, if to be used in real life.

As an example, in the course, I teach cases of endogeneity, including measurement error, omitted variable bias, and simultaneity. For BSc students, I make them to derive mathematical forms of bias, but for MBA students, I only ask them to follow the logic that what bias is expected for each endogenous case, and what are closely related life examples in business.

An MBA student tries to explain his company's manufacture line's random error that slows down automated process by measurement error. The error results in attenuation bias that under-estimates mismeasured variable's impact in scale. Had the product line manager knew the link between measurement error and attenuation bias, the loss of automation due to that error must have attracted a lot more attention.

Like an above example, some MBA students in fact show way better performance than students in MSc in AI/Data Science, more heavily mathematical track. They think math track is superior, although many of them cannot match math forms to actual AI/Data Science concepts. They fail not because they do not have pre-training in math, but because they just cannot read f(a,b,c) as work allocation model by Adam, Bailey, and Charlie. They are simply too distracted to math forms.

During admission, there are a bunch of stubborn students with a die-hard claim that MSc or death, and absolutely no MBA. They see MBA a sort of blasphamy. But within a few weeks of study, they begin to understand that hard math is not needed unless they want to write cutting edge scientific dissertations. Most students are looking for industry jobs, and the MBA with lots of data scientific intuition was way more than enough.

The teaching medium, again, is 'plain English'.

With the help of AI translator algorithms, I now can say that the teaching medium is 'plain language'.

Korean GDP growth was 6.4%/y for 50 years until 2022, but down to 2.1%/y in 2020s.
Due to low birthrate down to 0.7, population is expected to 1/2 in 30 years.
Policy fails due to nationwide preference to leftwing agenda.
Few globally competent companies leave the country.

Financial Times, on Apr 22, 2024, reported that South Korean economic miracle is about to be over. The claim is simple. The 50 years of economic growth from 1970 to 2022 with 6.4%/year is replaced by mere 2.1%/year growth in 2020s, and it will be down to 0.6% in the 2030s and 0.1% in 2040s.

For a Korean descendent, it is no secret that the country's economy has never been active since 1997 when Asian financial crisis had a hard hit to all east Asian countries. Based on IMF's economic analysis, South Korea's national GDP had grown over 7% per year until 1997, and with linear projection, it was expected that South Korea will catch up western European major economies in early 2010s by per capita GNI. Even after the painful recovery until 2002, per year growth rate was over 5% for another a decade, way above pessimistic economists' expectation, whose projection was somewhere near Japan's 1990s, the country nearly stopped growing after the burst of property bubble at the end of 1980s.

The 1970s model worked until 1990s

South Korean economic growth is mostly based on 1970s model that the national government provided subsidy highly export driven heavy industires. The country provide upto 20% of national GDP as a form debt insurnace to Korean large manufacturers for their debt-financing from rich countries. The model worked well up until late 1980s. Economic prosperity by extremely favorable global economic conditions coined as '3-Lows (Low Korean won, Low Petro price, Low interest rate)'. The success helped the economy to rely on short-term borrowing from US, Japan, and other major economies until 1997.

Forced to fire-sale multiple businesses at a bargain price, the passion for growth in the country was gone. Large business owners become extremely conservative on new investments. They also turned heads to domestic market, where competitors are small and weak. SMEs have been wiped out by large conglomerates, most of which were incapable of competiting internationally, thus turning to safe domestic battle.

Had time and money, but collective policy failures killed all

Compared to North Korean economic struggle, South Korea has been the symbol of success in capitalism. Over the 50 years, South Korean per capital GNI has grown from US$1,000 to US33,000, while Northern brothers are still struggling with US$1,000 to US$2,000, depending on agricultural production affected by weather conditions. In other words, while North Korea is still in pre-industrialization economy, the South has grown to a major industrial power with lots of cutting edge technological products, including semiconductors by Samsung Electrics and SK Hynix.

The country was able to keep higher than expected growth up until 2020, largely because of China's massive import. China, since the opening of its economy in 1998 by joing WTO(World Trade Organization). China has been the key buyer of South Korean electric appliances, smartphones, semiconductors, and many other tech products, most of which were crucial for its own economic developement.

But experts have raised attention that China's technological catch-up was a growingly imminent threat to Korean's tech superiority. The gap is now mostly gone. Even the US is now raising a bar high against China for 'security purpose'. The fact that the US has been keen on China's national challenge to semiconductor industry now even to chem and bio is an outstanding proof that China is no longer a tech follower to western key economic leaders, not to mention South Korea.

US-China trade war expedited Korea's fall

By a simple Cobb-Douglas model, with capital and labor, it is easy to guess that capital withdrawal from China resulted in massive surplus to the US market, where the economy is suffering from higher than usual inflation. It's the cost that the US market pays. On the other hand, without capital base, the Chinese economy is going to suffer from capital shock like Asian Financial Crisis of 1997. Facilities are there, but money is gone. Until there is any capital influx to fill the gap, be it by IMF and World Bank like 1997 or long-term internal capital building like Great Britain from 1970s to 2000s, we won't be seeing China's economic rise.

The sluggish Chinese economy deadly affected its neighbors. One of the trading partners that were hit hard is South Korea in Asia, Germany in Europe, and Apple in BigTechs. Germany used to be the symbol of economic growth in Europe, at least during European sovereign debt crisis of 2008-2012. Unlike other big tech companies, Apple kept its dependency to China until very recently. The company lost stock values by 40% since the peak in 2022. South Korean story is not that different. The major trading partner zipped its wallet. 15% to 40% of trade surplus, depending on industries, were disappeared. Korean companies were not ready to replace the loss by other sources.

The evident example that South Korea was not ready to China's withdrawal is its dependency to Aqueous urea solution(AUS) for diesel powered trucks. Over 90%, sometimes upto 100%, of AUS consumption in the nation was from Chinese sources, which was stopped twice recently. In Dec 2021 and Sep 2023, lack of AUS pushed Korea's large cargo freight trucks being inoperable. The country's logistic system was nearly shut down. The government tried to replace it for two years from 2021 to 2023, but the country still failed to avoid another AUS crisis in Sep 2023.

For South Korea, China was a mixed blessing. Dependency to China from 1998 upto 2020 helped the economy to keep high enough growth rate to run the country. But heavy dependency now creates detrimental effects to every corner of the country's industrial base. Simply put, Korea has been too dependent to China.

Education, policy, companies, all failed jointly and simultaneously

Fellow professors in major Korean universities do not expect Korea to rebound anytime soon. The economic growth model that worked in 1970s have not been working as early as late 1990s. The government officials have, however, been ignorant of failing system. Back then, under military regime, only successful business men were given government subsidy. The selection process was tough. Failing businesses were forced to close down, before creating any harm to wider economy.

But the introduction of democratic system that brough freedom to business, press, and civil rights groups deprived the government of total control on resource allocation. The country no longer is operated by a single powerful and efficient planner. While recovering from devastating financial crisis in 1997, every agents in the economy learned that the government is no longer a powerful fatherhood and tasted some economic freedom.

Had the freedom been regulated properly, the economy would have been armed by national support in subsidy, human resources, as well as 50 million domestic customer base. Instead, except a few internationally qualified products, most of them turned their heads inward. For lack of English speaking manpower, companies were not able to compete internationally, unless they have hard and unique products. Building a brand from 'copying machine' to 'tech leader' costs years of endeavor that we can only see successes in RAM chips and K-pop singers.

Korea had time to renew its economic policy. But Chinese honeyspot provided too much illusion that Korean companies thought its superiority will stay forever. Koreans have kept its 'copying machine' policy. The government officials were not as keen as 1970s, thus any sugarcoated success in overseas countries helped Korean companies to be in a position of demand to subsidy. The country stopped grow technologically. Industries, academia, and press become entangled to one goal. Massive exaggeration to earn government subsidy. For one, Korean government wasted US$10 billion just for basic programming courses in K-12 that are no longer needed in the era of Generatvie AI. In the meantime, China was not willing to stay culturally, technologically, and intellectually behind its tiny neighbor that they have looked down for the last two millenia.

While Korean education puts less and less emphasis on math/stat/science, Chinese took opposite steps. Now Korea's the most demanded college major is medical doctoral track, while Chinese put Mathematics as the top major. Despite higher competition to medical track with large expected income, some students no longer pursue medical track just because they are afraid of high school mathematics and science.

Aging society with lowest birthrate in the world

Will there be any hope in Korea? Many of us see otherwise. The country is dying, literally. The median age of the country is 49.5 as of year 2024. Generations born in 1980s had nearly 1 million babies in a year, while in 2020s they only have 200,000. The population, particularly in working age, will be shrunken to 1/5 in a few decades later. Due to touch economic conditions, young couples push marriage as late as 30s and 40s. Babies by women after 35 have shown some level of genetic defect that even 1/5 of working population won't be as effective as today.

Together with mis-guided educational policy, the country is expected to have less capable brain as the time goes. International competition will become more severe due to desperate Chinese catch up in technology. Companies have already lost passion for growth.

Economic reforms have been tried, but the unpopular minority seldom wins in elections. Even if it wins, the opposition is too strong to overcome. Officials expect that the country is on a ticking bomb without any immediate means of defusion.

Though I admit that other major economies are suffering from similar growth fatigue, it is at least evident that South Korea is now on the list of 'no-hope'. If you are looking for growth stocks, go and look for other countries.