[Tech Talk] In the AI Era, Is Math Important or Useless?

Mathematics Supported by Computers for Decades
Evolving Beyond Simple Calculators to 'Partners'
Should We Trust AI-Generated Mathematical Proofs?

The advancement of artificial intelligence (AI) is said to replace many jobs. However, there is one academic field that is particularly controversial: mathematics. Some argue that to prepare for the AI era, math education should be strengthened. On the other hand, there are bleak predictions that AI could completely replace math majors. What is the truth? Is human mathematical knowledge becoming increasingly important, or is it destined to be replaced someday?

"In the AI era, math is more important" vs "Math will become useless"

A high school student solving a math problem in a mock exam. The photo is not related to any specific expression in the article. [Image source=Yonhap News]

Recently, prominent figures in the U.S. tech and education sectors have launched an online petition urging the government to strengthen public math education. Notable signatories include Sam Altman, CEO of OpenAI, and Elon Musk, founder of Tesla. They argue that "the core of AI lies in key mathematical concepts such as algebra, calculus, and probability," and that "the next generation must build a rigorous mathematical foundation to participate in AI technology development."

Meanwhile, there is an opposing view. There is concern that much of mathematical research will be 'automated' due to AI, potentially shaking the position of pure mathematics. This concern should not be taken lightly. In January, Google DeepMind unveiled 'AlphaGeometry,' an AI that solves math problems independently. It demonstrated high mathematical reasoning ability by solving 25 out of 30 problems from the International Mathematical Olympiad.

Mathematicians and computers have been 'one team' for decades, but...

The Four Color Theorem, which proves the proposition that "any map can be colored with four colors so that no two adjacent regions share the same color."

This problem, proven in 1976, was solved by introducing two computers to perform the vast amount of calculations that could not be handled by human hands.

It is the first case where humanity used the power of computers to solve a mathematical problem and marks the introduction of the "assistant prover." [Image source=Internet Archive]

In fact, mathematicians have collaborated with computers for a long time. Modern mathematical proofs are incredibly complex and extensive. Sometimes, the proof process for seemingly simple problems can span hundreds or thousands of pages. It is impossible for humans to verify all of this manually. Since around the 1970s, the mathematics community has developed computational tools to automate theoretical proofs, known as 'proof assistant' software.

At that time, mathematicians were not overly worried about a 'future replaced by machines.' Computers were useful for checking vast proof data or performing massive calculations at once, but they lacked the logical reasoning ability central to problem-solving. In the past, no matter how smart, computers were merely convenient calculators.

However, with the advent of AI-powered proof assistants, many mathematicians are reportedly changing their minds. The latest AI learns patterns independently through accumulated problem-solving data from the past and sometimes exhibits creativity surpassing humans. While past proof assistants were simple automated calculators, now they are increasingly becoming 'colleagues' exchanging ideas with mathematicians.

What if the balance between humans and machines tips toward the latter?

In other words, the contribution of theoretical mathematicians and proof assistants to mathematical research is gradually becoming 'equal.' What if AI-powered proof assistants become even more advanced? What if the balance between human mathematicians and computer mathematicians tips sharply toward the latter?

Supercomputer [Image source=YouTube]

Modern mathematics is too specialized for ordinary people like us to access, but it remains a core ingredient in industrial and scientific development. Advanced mathematics permeates numerous fields such as chemistry, physics, astronomy, mechanical engineering, heat treatment, and computer engineering. Therefore, if machines come to conduct pure mathematics research instead of humans, the proportion of humans in overall scientific and technological advancement will inevitably decline sharply.

Some mathematicians argue that we must discuss the impact AI will have on humanity’s mathematics even now. Jordi Williamson, a mathematician at the University of Sydney in Australia, recently warned through The New York Times, "Considering the impact AI will have on us over the next five years, mathematicians are not discussing deep learning sufficiently at present."

If AI solves math problems, should we 'trust' it?

However, what mathematicians truly worry about is not simply job prospects. The core issue is whether humans should accept proofs produced by AI as they are if the day comes when AI conducts mathematical research instead of humans.

Regarding this, we will excerpt the conclusion from the 2021 essay published at Cambridge University titled "Will AI Make Mathematicians Obsolete?"

"Mathematical theories solved by AI-embedded proof assistants can be applied today in aircraft control, nuclear warhead development, and stock exchange operations. So what if there is a bug in the proof assistant? Will an artificial general intelligence proof assistant enrich our lives? Or will it completely replace all of us? Now is the time more than ever to consider the ethical and empirical dilemmas of scientific advancement."