Did AI solve a 30-year-old math problem? Does it really understand?

Imagine this: you have been working on a very difficult math problem for 30 years, day and night. It is so complex that no expert in the world has been able to provide a clear answer. But then, you ask an artificial intelligence (AI), and in just 90 minutes, it solves the problem in a way no one had thought of before. How would that make you feel?

Surprisingly, this actually happened. The protagonist is ‘GPT-5.6 Sol,’ the latest AI model released by OpenAI in July 2026. According to OpenAI’s GPT-5.6 family launch announcement and reports by Forbes, this new model is sending shockwaves through the scientific community by easily transcending the logical limits that previous models could not overcome.

Why is this important?

It is far more important ‘how’ this was achieved than the mere fact that it “solves math problems well.” If AI in the past was at the level of stringing together plausible sentences based on massive amounts of data, GPT-5.6 Sol is showing the potential to generate ‘new knowledge’ by reasoning through complex logical structures, just like a human.

This also has great significance for us as ordinary people. It means that in the future, AI could become a reliable partner in solving challenges facing humanity, such as designing complex molecular structures for new drug development or finding optimal energy efficiency paths to prevent climate change. The scientific capability enhancements of GPT-5.6 Sol are accelerating technological progress that improves our quality of life.

Understanding easily: Finding a path in a foggy mountain

Let’s use an easy analogy for the unfamiliar concept of ‘Convex Optimization.’ This refers to a “mathematical method for finding the minimum value of a function.” Imagine you are in a foggy mountain and need to find the lowest point. The process of moving one step at a time while looking only at the slope under your feet to find the lowest place is similar to this mathematical problem.

For the past 30 years, many mathematicians have pondered the most efficient way to find the path in this process. GPT-5.6 Sol Pro solved the problem by finding a new mathematical ‘Bound’ of ‘1.5/L’ in this complex search process.

In short, the AI creatively combined existing methods to uncover the secret of a ‘map’ that humans could not solve for 30 years. The answer that the previous model, GPT-5.5, could not find even after 20 hours of effort was solved by GPT-5.6 Sol in just 90 minutes in collaboration with a statistics professor. This suggests that the AI is not just memorizing data, but is grasping logical connections on its own.

Current status: How far have we come?

OpenAI is currently providing GPT-5.6 in three tiers: Sol, Terra, and Luna. Among them, the top-tier model, Sol, is equipped with a massive memory space that can process up to 1.05 million tokens (the minimum unit of language that AI recognizes) at once, allowing it to understand much longer contexts and more complex problems.

However, AI is not perfect. While it has achieved amazing results in mathematical puzzles, there are definitely points where human oversight is needed, such as some security tests where it still cannot autonomously build complete hacking tools. In addition, regarding this achievement, the academic community continues to carefully verify whether the AI truly ‘understands’ the meaning or if it just happened to find a new combination. Experts acknowledge this achievement but emphasize that a wider range of academic review is needed.

What will happen in the future?

AI will become an even smarter and more efficient tool in the future. GPT-5.6 Sol is designed to process more complex calculations at a lower cost than previous models. Now, the AI by our side will go beyond a secretary that simply summarizes emails or translates text, and will become a scientific companion that provides answers to countless questions that humanity has not been able to solve.

It is time for us to learn how to distinguish whether the answers provided by AI are ‘new knowledge’ or just a ‘glamorous variation’ of existing knowledge, and how to cooperate with it.

MindTickleBytes’ AI Reporter Perspective

AI is now evolving beyond simple information summarization into a scientific companion that offers new clues to questions humanity has spent decades trying to answer. As the performance of the tool improves, the level of questions asked by the humans using that tool will be the key that determines the future.

References

1. Kimi K3 vs GPT-5.6 Sol: Agentic AI Comparison 2026
2. Сравнение GPT-5.6: бенчмарки и тесты моделей Sol… - «Plaan»

3. [GPT-5.6 Sol: Benchmarks, API Pricing & Review

   Coursiv Blog](https://coursiv.io/blog/chatgpt-5-6-sol)

4. OpenAI выпустила GPT-5.6 и научила ChatGPT выполнять многоэтапные рабочие задачи…
5. OpenAI открывает публичный доступ к GPT-5.6 после задержки…
6. GPT-5.6 Sol vs Terra vs Luna: Which Tier Should You Actually Use?
7. Can GPT-5.6 Solve 30-Year-Old Optimization Problems?
8. OpenAI’s GPT-5 Generates Verified Novel Proof in Convex Optimization
9. How ChatGPT 5 Pro Solved a Decades-Old Math Problem - Geeky Gadgets
10. GPT‑5.6: Frontier intelligence that scales with your ambition
11. OpenAI’s GPT-5.6 Lands With Work Agents And A Desktop Pivot
12. GPT-5.6 Sol reportedly disproves a 30-year-old statistics conjecture
13. Previewing GPT‑5.6 Sol: a next-generation model - OpenAI