Mathematical ability differs across cultures, with Western academia emphasizing abstraction over procedural speed
AI is automating routine calculations, making conceptual thinking more valuable than ever
Future professionals must focus on logical reasoning and model formulation to stay relevant

After years of teaching here at SIAI, we have witnessed a varying cultural differences in perception of experts in AI/Data Science in the western hemisphere and in Asia. What was pronounced the most was the concept of mathematics necessary in this particular field. Most Asian students blindly thought that calculation capacity and problem solving skills are emphasized in our curriculum, just by reading the phrases like 'The Most Rigorous MBA in the world'.

We don't.

And we finally understand where the confusion comes from. Here is our scientific analysis of the differences.

Education researchers often distinguish between procedural fluency (being able to execute mathematical procedures quickly and accurately) and conceptual understanding (grasping the underlying principles and structures of mathematics). Many studies indicate that East Asian education systems emphasize procedural fluency, while Western systems, particularly in higher education, prioritize conceptual depth.

• Research Backing This View: Studies comparing math education in China, Japan, South Korea, and Western countries (such as the US and UK) consistently show that Asian students outperform in procedural tasks but may struggle with non-standard, open-ended problems requiring deeper conceptual thinking (Ma, 1999; Stigler & Hiebert, 1999).

So, we have formalized 3 types of 'Math Genius', and please note that only the last type is needed at SIAI.

1. Calculator
2. Problem Solver
3. Thinker

Let's go over the dichotomy from our definition of 'Math Genius'.

1.Calculator: Speed and Accuracy as Genius

Mathematical ability is often perceived differently across educational systems. In many East Asian countries, proficiency in mathematics is equated with speed and accuracy in calculations. A student who can quickly solve a quadratic equation or compute complex arithmetic is often considered a math genius. This perception aligns with research by Stigler and Hiebert (1999), which highlights that Asian students tend to excel in procedural fluency due to structured and rigorous mathematical training at an early stage.

However, in higher education, particularly in Western academic institutions, mathematical proficiency is defined differently. The emphasis shifts from speed to logical reasoning, abstract thinking, and the ability to construct mathematical models. Research in mathematics education (Ma, 1999; Li & Collins, 2021) shows that while Asian students tend to perform well in structured mathematical settings, they often face challenges when required to engage in open-ended problem-solving and theoretical abstraction.

2.Problem Solver: Procedural fluency as 'Math Genius'

At the high school level, the focus of mathematics education begins to shift from pure calculation to problem-solving. Advanced mathematics curricula require students to derive solutions from first principles, navigate multi-step logical reasoning, and understand abstract mathematical structures. This transition is critical for success in competitive university entrance exams, as seen in South Korea’s CSAT and similar standardized assessments in other countries.

This is why Asian students excel in competitive math Olympiads, which require both procedural skill and non-standard problem-solving.

As students enter university, particularly in STEM fields, the nature of mathematics evolves further. Research in international mathematics education (Li & Shavelson, 2001) suggests that students who rely primarily on procedural problem-solving may struggle when confronted with theoretical coursework that requires constructing formal proofs and engaging with abstract concepts. This distinction between procedural fluency and conceptual understanding is well-documented in the literature on cognitive development in mathematics (Tall, 2004).

Western academia sees calculation speed as "machine-like" rather than as a sign of intelligence is supported by psychological studies on how different cultures define intelligence.

• Expert Perspective: In Western academia, a "math genius" is often equated with someone who can create new mathematical theories, prove complex theorems, or develop novel models—not just someone who is quick at calculations. This is evident in how Western math competitions, graduate exams, and research expectations focus on deep reasoning rather than speed.
• Historical Context: The Western concept of a mathematical genius is shaped by figures like Gauss, Euler, and Gödel, who were not just quick calculators but pioneers in abstract reasoning.

3.Thinker: The Role of Mathematical Thinking in AI and Data Science Education

In applied fields such as AI and Data Science, mathematical proficiency takes on yet another dimension. While theoretical knowledge remains essential for foundational research, most practical applications of AI do not require deep engagement with mathematical proofs. Instead, students must understand the conditions under which mathematical models apply and be able to critically evaluate their limitations.

Given this reality, the MBA AI/Big Data program at SIAI has been strategically designed to align with industry needs while accommodating different mathematical backgrounds. Rather than focusing on formal proofs, the curriculum emphasizes:

1. Understanding Model Assumptions – Students are trained to recognize the conditions under which different AI models (e.g., neural networks, decision trees) are effective and where they may fail.
2. Applying Mathematics to Business Problems – Instead of proving theorems, the focus is on using mathematical reasoning to optimize decision-making in real-world scenarios.
3. Bridging Procedural Fluency with Conceptual Thinking – While problem-solving remains an essential skill, students are guided to transition towards abstract thinking where necessary, particularly in courses on machine learning interpretability and data-driven strategy.

This approach aligns with the findings of mathematics education researchers (Schoenfeld, 2007), who argue that effective mathematical training must be contextualized within the problems students are expected to solve in their professional careers.

Why This Matters for Asian Students in STEM Fields

Many Asian students who transition to Western universities for undergraduate or graduate studies in STEM fields often experience a sudden drop in their perceived mathematical ability. This is not because they lack intelligence, but because their definition of mathematical proficiency has been shaped differently.

Studies on international students in STEM (Li & Collins, 2021) show that Asian students often find proof-based courses, abstract algebra, and mathematical modeling more challenging compared to their Western peers, precisely because their training has emphasized computational efficiency rather than abstraction

Students who have excelled in rapid problem-solving often struggle with abstract mathematical thinking. They may find courses in theoretical physics, real analysis, or mathematical finance unexpectedly difficult because the emphasis shifts from computation to proof-based reasoning and conceptual applications.

This is particularly critical for aspiring data scientists. In real-world applications of data science and AI, the ability to logically build models, understand theoretical underpinnings, and translate abstract mathematical ideas into real-world applications is far more valuable than simply applying pre-existing formulas.

Case 1

Let's just come to an example. A Korean student at SIAI tried his dissertation on a set of data from shipping company's use of tools like containers, boxes, baskets, and folklifts. Unless the data is only for a few clients of the shipping company, it was expected that there will be a number of one-time clients whose use of tools will unlikely be repeated in out of sample data. The student, despite learning that RNN can only be applied to time series without non-stationary movements, was not able to link the learned math concept to RNN and the data. He suffered from gradient's divergence, and tried to control the parameters of RNN instead of 'cleaning' the data itself.

Case 2

Addtionally, many Asian students are too busy jumping on code lines rather than accessing the problem set's background description. In the introductory math and stat courses (STA501, STA502, STA503), we emphasize a lot about how important the data generating process (DGP) can be, like whether the e-commerce company's daily visitor data being from matured incumbents like Amazon or a start-up looking for next round funding. Like case 1, your application of RNN can be challenged depending on how actively the company is engaged in promotions. Little differences in question's setting is thoroughly designed by professors as the change requires an entirely different set of data scientific tools. Many Asian students struggle to understand why an Instrumental Variable (IV) has to be replaced just because the start-up's series-C funding is postponed, for instance. If the company does not need a short-term boost in website visitors, reference data points should remove exploding ups and downs for next month's projection, isn't it?

Cases like this occur a lot among Asian students whose course grade is high enough for us to trust their mastery in skills. And unfortunately, they end up poor performance at the dissertation stage.

Then, is it really a necessary skill? Isn't just an application of previous project's code lines good enough?

AI may soon replace first two types of 'Math Genius'

The rise of AI tools like ChatGPT and other advanced language models is further shifting the definition of mathematical proficiency. While traditional education has emphasized procedural fluency and structured problem-solving, AI can now perform these tasks instantly. Routine calculations, algebraic manipulations, and even structured problem-solving techniques are increasingly automated, reducing the necessity for individuals to master these skills manually.

As AI continues to evolve, it is likely that calculator-type mathematicians and even structured problem-solvers will find themselves increasingly displaced. These AI systems can solve equations, optimize parameters, and generate step-by-step solutions for a wide range of mathematical problems more efficiently than humans. This transformation raises a fundamental question: What kind of mathematical thinking remains irreplaceable?

One of the key limitations of AI in mathematics is its reliance on pattern matching. Despite their computational power, AI tools do not “understand” mathematics in the same way humans do. They recognize patterns in vast datasets and generate responses based on probabilistic relationships rather than true logical reasoning or deep abstraction. Mathematical creativity, proof construction, and conceptual modeling remain beyond the reach of AI, as these require forming genuinely novel insights rather than simply retrieving and recombining existing information.

For this reason, the focus of mathematical education should shift toward logical reasoning, model formulation, and critical evaluation of AI-generated outputs. While AI can provide solutions, human expertise is required to assess their correctness, interpret results, and apply them meaningfully within different contexts. In fields such as AI and Data Science, those who master abstract thinking and theoretical modeling will remain indispensable, while those who rely solely on procedural problem-solving may find their skills increasingly redundant.

Conclusion: Redefining Mathematical Proficiency for AI and Data Science

As mathematics continues to evolve as a discipline, educational institutions must adapt their teaching methodologies to prepare students for both theoretical and applied domains. Traditional views of mathematical ability—whether based on calculation speed or structured problem-solving—must be expanded to include logical reasoning, conceptual understanding, and model applicability.

For students entering AI and Data Science, the ability to think abstractly is crucial for research, but applied roles require a balance between problem-solving skills and an understanding of mathematical conditions. By designing curricula that acknowledge these distinctions, our institution ensures that graduates are equipped to excel in both academic and industry settings.

By aligning mathematical training with practical applications, educators can bridge the gap between traditional perceptions of math proficiency and the skills required for success in the modern AI-driven economy.

In short, SIAI teaches most unlikely replaceable data science tools in AI.