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In addition to preserving fading knowledge and answering old problems, mathematicians and computer scientists have witnessed various breakthroughs in solving unanswerable questions with the help of artificial intelligence. New progress was made in the field—celebrating connections around distant areas of mathematics—while observing the growth of other disciplines.
Although some discoveries offered compelling answers, others promised avenues of explorations for the future generations.
Here are some mathematical breakthroughs in AI so far!
Differential equations to unlock AI algorithm
Researchers from MIT CSAIL have solved a differential equation between the interaction of two neurons, unlocking a new type of efficient AI algorithm. The modes have characteristics similar to that of liquid neural nets, which are robust in nature. This type of neural network can be used for tasks that involve gaining insight into data over time, as they are adaptable even after training.
Dubbed as the ‘closed-form continuous-time’ (CfC) neural network, the model outperformed the counterparts on tasks, with higher performance and speedups in recognising human activities such as motion sensors, modelling physical dynamics of a robot, and sequential image processing.
Read the whole research here.
Solves long-standing math problems
In a newly published study, researchers from the University of Sydney have used AI to suggest and help prove new mathematical theorems in the complex areas of representation and knot theory. The research mainly demonstrates how a supervised learning model was used to spot an undiscovered relationship between two different types of mathematical knots. This breakthrough has now led to an entirely new theorem.
Led by one of the world’s famous mathematicians Professor Geordie Williamson, the research applied the power of Deep Mind’s AI processes to explore conjectures in the representation theory.
Williamson’s co-authors were from Google-owned DeepMind, the team behind AlphaGo, which was the first ever computer programme to win over a world champion in the game of Go held in 2016.
See how Williamson proved the long standing conjectures here.
Proving 1200 mathematical problems using Google AI system
A new AI theorem-proving programme was unveiled by researchers at the California-based Google’s research centre in Mountain View. The programme majorly used HOL-Light theorem prover—used in Hales’ proof in the Kepler conjecture—proving many basic theorems of mathematics unaided by humans. Moreover, the team has provided the tool in an open-source release to assist other mathematicians and computer scientists in their experiments.
The model was trained on a set of 10,200 theorems in areas of linear algebra and real and complex analysis. However, the team claimed that the approach was broadly applicable.
Read how Google cracked these theorems here.
Solving International Math Olympiad Problems with Meta AI
Mathematical theorems have been long regarded as proving to be a crucial step in building intelligent machines by the scientific community. Undoubtedly, Meta AI has modelled a neural theorem prover which has solved 10 International Math Olympiad (IMO) problems.
Meta claims that the new model is 5x better than any previous AI system. It says, “Our AI model also improves upon the current state of the art by 20 percent on miniF2F, a widely used mathematics benchmark, and by 10 percent on the Metamath benchmark.”
The researchers used the method of ‘HyperTree Proof Search (HTPS)’ which was trained on datasets consisting of successful mathematical proofs. The AI was then trained to learn to generalise new and different kinds of problems.
Read more about the IMO problem solver here.
Unsurprisingly, Meta tops the list for me. Which one’s your favourite?
