The machine can find shortcuts in the tank

One of computer science's most beautiful ideas has just been surpassed -- not by a human, but by a machine. It says more about the future of thinking than about the future of technology.

I learned algorithmic thinking from Edsger W. Dijkstra. He was not a sentimental man. He believed that the goal of computer science was clarity, not speed. His algorithm for finding shortest path in a network stood as one of the most precise expressions for such clarity. For this and other work, he received the Turing Prize—computer science's answer to the Nobel Prize. Now, seventy years later, a new algorithm has enhanced his life's work. And it wasn't made by a human.

What an algorithm really is

An algorithm is a recipe for how to solve a problem — step by step. Not a program per se, but the logic behind it. Alan Turing described in the 1930s how such a recipe could be carried out by a machine, regardless of whether it was numbers, text or images.

The entire history of computer science since then has been about making these recipes more efficient.

When Complexity Becomes Concrete

Complexity measures how many steps such a recipe needs. A picture: You're about to find your way home in a city of one million streets. If you have to check all roads one by one, it will take infinite time. A good algorithm finds shortcuts -- using the structure of the city, not the strength of the muscles. But as the city grows, the problem grows faster than we intuitively understand. Twice as many streets can charge a hundred times as much bill.

This is why everything from traffic management and energy grids to language models meets limits: Complexity eats up advances in computing power.

When Dijkstra was beaten

Edsger Wybe Dijkstra (1930—2002) was a Dutch mathematician, programmer and engineer. He received the Turing Prize in 1972.

Dijkstra's method dramatically reduced this problem. Instead of exploring all avenues, he examined them in an orderly order—always the shortest first. That was the logic shortcut.

In 2025, researchers at Tsinghua University in China found a new way to do this. They managed to remove part of the mathematical sorting that has been inevitable for seventy years. The new method reduces complexity from O (m log n) to O (m log^ (2/3) n) -- a dry expression, but in practice it means large calculations can go up to 40 percent faster.

This sounds like a marginal gain, but it breaks a boundary we thought was fixed. It's like finding out that you can build a bridge without using all the supports -- because the geometry turns out to be more forgiving than we thought.

When elegant thoughts are replaced by raw machine power

The most interesting thing is how it happened. Dijkstra found his solution with pen and paper. The new algorithm was found through systematic machine exploration: Millions of possible variants were tried and discarded until the patterns began to make sense.

Human insight was replaced by machine persistence. And with it, the difference between the elegant solution and the brutal one is blurred. Where Dijkstra sought beauty, the machine finds strength.

A new level of understanding

This is about more than math. We are in the process of moving the boundary of what it means to understand. When machines find better solutions than we do, but without being able to explain why, it challenges the very idea of knowledge. Perhaps it is no longer we who should fully understand the algorithms, but those who help us understand the world in new ways.

Dijkstra said programming is the most precise expression of thought there is. Turing showed that such thought can be formalized. Now it is the very formality that learns to think.

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