Google DeepMind’s AlphaGeometry: Without Assistance Solving Olympiad Geometry Problems

AlphaGeometry is an incredible mathematical discovery which works without human assistance. The researchers from Google DeepMind and New York University are the minds behind this amazing discovery. It takes a theorem or a problem as an input and generates output in the form of a solution that is understandable by humans. Theorems actually means why a specific mathematical statement is true by giving logical reasonings.

Proving theorems and solving extremely difficult problems of International Mathematical Olympiad (IMO) has always been a challenge for the researchers of machine learning because these problems require creativity, deep learning and logical thinking. So, solving complex problems without human assistance by any Artificial Intelligence models marks a milestone in the development of automated reasoning. 

The current machine learning approaches faces great challenges when it comes to learning about various new areas of mathematics because it consume extra resources such as time and effort to train. Verifying mathematics problem and translating into machine language takes extra time which is a big challenge in terms of efforts. Also, it is a great struggle to understand and verify geometrical angles and poses due to the nature of geometry and to deal with all these limitations in terms of cost and time, effectively and efficiently.

The researchers presented one solution to all the problem that is AlphaGeometry. It has the ability to prove theorems in plane geometry without depending on human assistance. Rather than human guidance, it is able to create millions of its own proofs and theorems, addressing a diverse range of difficulty level.

AlphaGeometry Example

In the images above a simple example and its diagram is given to the AlphaGeometry. It figures out the example by using a smart deduction engine. This engine works hard and find new information based on what it already knows until it either proves the theorem or can’t find any more new information to use. When the smart deduction engine can’t find a solution, the language model steps in and adds an extra point to the proof. Then, the deduction engine repeats the process. This process keeps going until a solution is finally found

AlphaGeometry adopts Neuro-Symbolic system

AlphaGeometry is a smart machine learning program using neuro-symbolic system that is a combination of two different elements. A neural language model that has extensive knowledge about geometry and symbolic deduction engine that uses the rule for solving really tough problems. It is trained from the scratch using large amount of made-up data. Both of these problems work together to solve super tricky and difficult problems, explore different solution to these problems and navigate through a lot of countless branching paths.  

According to EVAN CHEN, MATH COACH AND OLYMPIAD GOLD MEDALIST “AlphaGeometry’s output is impressive because it’s both verifiable and clean…It uses classical geometry rules with angles and similar triangles just as students do.”

Olympiad level problems were given to AlphaGeometry for evaluation purpose. The model is able to solve 25 from 30 difficult maths problems within given time, which is a very good ratio compared to old methods which was able to solve only 10 problems. Through AlphaGeometry, the success level is getting closer to the gold medalist of International Mathematical Olympiad (IMO).

The best part of AlphaGeometry is that after solving a really tough math problems it explain its solution in such a way that humans can easily understand. When mathematical experts cross checked the solution of International Mathematical Olympiad (IMO) problems from 2000 and 2015. AlphaGeometry showed outstanding performance in all of them. It also solved a more general version of a problem from 2004.

Wrap Up!

AlphaGeometry is an extra ordinary achievement in the world of Mathematics having the ability to solve complex geometrical problems with human guidance and assistance. It also has the ability to provide the reasoning with the solution in a human understandable language.


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