Breaking the world record, a mysterious student defeated Google's AlphaEvolve's optimal solution to a difficult problem with a margin of only 0.00006442.

A schoolboy, with the help of AI, defeated Google's most advanced technology and set a new world record!

While the farce at the IMO is still being debated, this schoolboy, with the aid of AI, has outperformed Google's most advanced AlphaEvolve, which is used for designing advanced algorithms in solving mathematical problems.

In the "Circle Packing" problem, the schoolboy's algorithm surpassed Google's AlphaEvolve by "0.00006442" and also exceeded the record previously set by FICO Xpress.

It's necessary to first introduce what the Circle Packing problem is and how powerful Google's AlphaEvolve is.

Packing Problems, or filling problems, can be simply understood as "filling another polygon with various polygons as efficiently as possible".

The Circle Packing problem is a specific case where the goal is to place several non - overlapping circles as closely as possible in a given area (such as a square), maximizing the sum of the radii of these circles or maximizing the filled space.

When Google's AlphaEvolve was released, it provided the optimal solution to this problem.

First, this problem can be divided into two categories:

Filling within a unit square

Filling within a rectangle with a perimeter of 4

In the first problem, given a positive integer 𝑛, the task is to pack 𝑛 non - intersecting circles in a unit square to maximize the sum of their radii.

AlphaEvolve found two "new constructions" and provided the optimal solution at that time.

When 𝑛 = 26, the original optimal solution was 2.634, and AlphaEvolve improved it to 2.635; see the figure below (left).

When 𝑛 = 32, the original optimal solution was 2.936, and AlphaEvolve improved it to 2.937; see the figure below (middle).

In the second problem, given a positive integer 𝑛, the task is to pack 𝑛 non - intersecting circles in a rectangle with a perimeter of 4 to maximize the sum of their radii.

AlphaEvolve found a "new construction" for 𝑛 = 21 and improved the original optimal solution from 2.364 to 2.3658; see the figure above (right).

AlphaEvolve improved the known optimal solutions for Circle Packing under different constraints and set a world record at that time.

But this record was soon broken!

A credit card scoring company

Claims to have surpassed AlphaEvolve

Before introducing the new record, let's briefly review Google's AlphaEvolve.

On May 14, Google released a coding agent powered by Gemini. As the name suggests, this new tool can design algorithms on its own to solve problems.

Just like AlphaZero after AlphaGo, which improved its chess - playing ability through "self - play", by the way, DeepMind has always been obsessed with Alpha and reinforcement learning.

This new LLM - based, Gemini - powered tool can write algorithms on its own to solve those "notorious" mathematical problems.

The Python code written by AlphaEvolve can find effective solutions to mathematical problems, and in some cases, these solutions are better than the previously known best solutions.

In other words, AlphaEvolve set new records in some long - standing mathematical problems.

An extended view of the discovery process of AlphaEvolve

AlphaEvolve uses an evolutionary approach to discover new algorithms.

Examples mentioned in the white paper report include an improved matrix multiplication method and a new solution to the circle packing problem.

Subsequently, a company named FICO tried to challenge this record.

FICO (Fair Isaac Corporation) is an American company focusing on data analysis and decision - making management. Its most famous product is the FICO credit score, which is widely used in the credit industry to assess individuals' credit risks.

They wondered what would happen if they submitted the same problem to the FICO Xpress Solver (part of the FICO Xpress optimization suite).

They collaborated with the MODAL research park at the Zuse Institute Berlin (ZIB) to test the new method.

The result showed that their algorithm was better!

On multiple benchmark problems reported by AlphaEvolve, the FICO Xpress Solver produced new optimal solutions, surpassing the records previously set by DeepMind.

FICO studied a version of the Circle Packing problem:

The task is to place circles of any size in a unit square to maximize the sum of their radii.

We now know that AlphaEvolve found a solution with a sum of radii of 2.63586275, which is better than the previous optimal value of 2.634.

The FICO Xpress Solver found an even better solution, with the sum of radii reaching 2.63591551.

On the left is Google's construction, and on the right is FICO's. The arrangement of the circles looks almost the same, with only slight differences in the radii. It's hard to notice with the naked eye, let alone exhaustively search by hand.

For non - unit squares, FICO claims that by modifying only five lines of code from the model of the previous problem, it can tackle the next challenge.

The solution obtained using FICO Xpress, 2.36583237, slightly improved the solution obtained by AlphaEvolve, 2.36583213.

These results can be confirmed by the validator in Google DeepMind's Google Colab notebook. The verification code is as follows:

Google also provided the code for drawing the figure, which is as follows:

Here is the final circular data provided by Google for the n = 26 problem. You can try it if you're interested.

All of the above problems can be classified as global optimization problems.

In global optimization, the goal is not only to find a solution but also to prove that the solution is the optimal one (or to provide a bound on how close the solution is to the optimal one).

The algorithms developed by Google with the support of AlphaEvolve adopt a slightly different approach: they are heuristic algorithms that focus on finding better solutions rather than providing bounds for the solutions.

Most of the problems in the AlphaEvolve report are either unconstrained or only slightly constrained, for example, only by simple variable boundary limits.

This makes them particularly suitable for the automatically trained heuristic search method because the algorithm can freely explore the solution space without dealing with complex constraint interactions or getting stuck in locally infeasible situations.

The real challenge of these problems lies in their highly non - linear and usually non - convex objective functions, which may produce multiple local optimal solutions.

Just like the small dots on Google's AlphaEvolve promotional picture.

However, FICO claims that their technology uses global optimization with non - generative AI technology, which is much more powerful.

It can not only handle such non - linear problems but also effectively deal with highly constrained problems, including problems with integer requirements. The feasible solutions to these problems may be very few, and these solutions may be located in narrow or discontinuous regions of the search space.

The "dragon - slaying" schoolboy

Today, a student named Alex on the X platform claimed that after a month and a half of independent work, his "Tactical Maniac v0.5" defeated Google's AlphaEvolve.

This is a multi - agent algorithm discovery framework. At a high level, the algorithm explores the creative space by iterating on existing solutions.

Alex published his results.

In the case of n = 26, his result was 2.63592717.

He also claimed that he had verified the result using the validator in the Google Colab notebook and drawn the corresponding figure.

For comparison, let's put the previous solutions of AlphaEvolve and FICO together:

Before AlphaEvolve: 2.634

AlphaEvolve: 2.63586275 (+0.00186275)

FICO Xpress: 2.63591551 (+0.00005276)

Alex: 2.63592717 (+0.00001166, +0.00006442 compared to AlphaEvolve)

In terms of construction, Alex's solution is completely different from those of Google and FICO!

This is a brand - new arrangement method.