Summary of Key Points
Paul Erdős is considered one of the most productive mathematicians in history, leaving behind a vast body of mathematical research upon his death in 1996. Twenty years later, with the surge in AI technology (such as AlphaGo's victory over Lee Sedol), nearly all AI companies began to study the mathematical problems he had posed—because these seemingly abstract theories turned out to be the fundamental foundations for AI algorithms.
Detailed Explanation
1. Who was Erdős? – A Math Genius with an Unusual Approach
Erdős never had a permanent job or home; he traveled around the world with his suitcase, collaborating with over 500 scholars to publish more than 1,500 papers (which is already an incredible achievement for an average mathematician). He also introduced the concept of the “Erdős number,” which indicates the number of people one has collaborated with directly, and the number of people those individuals have collaborated with in turn. Hundreds of thousands of people around the world have an Erdős number, reflecting a kind of “six-degree-of-separation” within the mathematical community. His research focused on fundamental areas such as graph theory (the study of networks formed by points and lines) and combinatorial mathematics (the study of optimal arrangements). These fields may not have seemed practical at the time, but they have since become invaluable for AI.
2. How Do His Mathematical Problems Relate to AI?
The essence of AI is using algorithms to process data, and Erdős’ research addressed some of the core challenges in this field:
- Graph Theory: When you watch videos on a platform, the recommendations are based on the relationships between you and those videos—this is a type of “network structure” that Erdős studied, which helps AI quickly identify relevant content.
- Combinatorial Optimization: AI models need to find the best solutions from numerous possibilities (for example, optimizing the accuracy of cat recognition algorithms), and Erdős’ combinatorial mathematics can help AI avoid unnecessary steps in this process.
- Stochastic Processes: AI uses probability calculations to predict user behavior; Erdős’ theories provide the tools for making these calculations.
3. Why Did It Suddenly Become Popular in 2016? – The Turning Point from Experimental to Practical AI
AlphaGo’s victory over Lee Sedol marked a shift in AI from a laboratory curiosity to a practical technology. While AI had previously been used for simple tasks, it needed more solid mathematical foundations to handle complex problems like autonomous driving and recommendation systems. It was then discovered that Erdős’ research from decades earlier could solve these new challenges. For instance, autonomous driving requires analyzing the relationships between vehicles, pedestrians, and roads; using Erdős’ graph theory, routes can be planned more efficiently.
4. What Has His Legacy Brought to AI?
Here are two examples of how Erdős’ work has impacted AI:
- Recommendation Systems: Platforms like Taobao and TikTok use Erdős’ graph theory to analyze user interactions with products, making recommendations more accurate.
- AI Model Training: His combinatorial optimization theories have reduced the time required to train AI models by half, significantly lowering costs. For example, what used to take 10 days can now be done in 5 days.
- Interdisciplinary Collaboration: Erdős’s lifelong collaborations with experts from various fields have shown that progress in AI requires collaboration between mathematics, computer science, and engineering.
5. The Lesson of Fundamental Research
Erdős’ story highlights the value of fundamental research: Many studies may seem useless at the time but can change the world decades later. Just as AI relies on his mathematical work today, future advancements in quantum computing and biotechnology could also depend on seemingly abstract foundational research. Therefore, we should not focus solely on short-term practical applications; long-term basic science is the root of technological revolutions.
In simple terms, Erdős was like a “mathematical treasure hunter.” The insights he gained decades ago have become invaluable assets for AI companies because AI requires a solid mathematical foundation to function effectively.