We have all witnessed the power of artificial intelligence and the use of AI applications in various industries. The use of AI in mathematics has been given tremendous power and potential, never witnessed before. Researchers have been able to make use of AI math to prove and suggest new mathematical theorems. Isn’t this great news for a math solver?
- Machine-learning techniques are being used by a math solver to establish new connections.
- Experimental mathematics was about intuition and creativity, and how it is about AI math as well.
- Experimental mathematics is a highly complex, intuitive, and imaginative process. For those learning high school algebra, this is a big surprise.
Some questions that both math solvers and physicists are struggling with every day are:
- How will the world appear at the quantum scale?
- What shape would the earth take if it were as large as the galaxy?
- What would it be like if we lived in 6D (six dimension)?
In order to find the answers to various grappling questions, a math solver tries to identify patterns by relating complex mathematical objects by forming conjectures (ideas formed without having sufficient or relevant proof or evidence).
The conjectures created can be promoted to theorems if they can be proved.
A math solver makes use of the process of intuition and knowledge for converting conjectures into theorems.
The Alpha-Go software program developed by DeepMind defeated the champion Lee Sedol in a Go match in 2016 is a great example of how a machine can display a human-like intuition. DeepMind’s Alpha Go displayed some spectacular moves, showing human-level intuition.
Mathematician have partnered with AI to make huge breakthroughs in solving math problems
- The collaboration between Google’s AI sister company DeepMind, University of Oxford, and University of Sydney, Australia has proved and suggested various mathematical theorems.
- Computers have been able to generate data for human beings for a long time.
- The task of recognizing different patterns relied heavily on the intuition of math solvers.
- With the latest tools and technologies, a math solver can generate more data than ever before.
- A research paper published in Nature explained how Google’s DeepMind programs can help in intuitive and experimental mathematics.
- The recent machine-learning techniques and AI in mathematics have proved to be useful in the discovery of a new conjecture and theorem in two different fields – representational theory and knot theory.
- The results suggested by AI indicated that machine learning techniques could complement mathematical research, and offer human-like intuitive guidance about a problem.
- The use of AI in mathematics can really deepen the understanding of the mathematics world and the real world for a math solver.
How were the new theorems proved?
- Using machine-learning techniques, the different patterns were identified from the data.
- Math solvers at the University of Oxford identified a connection between the algebraic and geometric variants of knots.
- Using this connection, they were able to put across a completely new theorem in the knot theory.
- The University of Sydney used the connections established by AI to prove an old conjecture that had remained unsolved for almost four decades – Kazhdan-Lusztig polynomials.
- The representations can be considered to be molecules governed by the Kazhdan-Lusztig polynomials which can be compared to atoms that form the molecules.
Professor Andras Juhasz from the University of Oxford, Mathematical institute was the co-author of the research paper.
According to him, a math solver formulated conjectures, and proved these to give theorems. Machine learning techniques guided by AI math intuition helped to uncover and prove conjectures in different fields where large volumes of data is available.
Prof. Geordie Williamson – the co-author, Math professor at the University of Sydney, and Sydney Mathematical Research Institute Director
According to him, AI is an extraordinary tool. This was the first time that the use of AI in mathematics has demonstrated complete usefulness for math solvers.
Prof. Marc Lackeby, from the University of Oxford, Math institute and co-author mentioned that the work done in the University of Oxford and Sydney in collaboration with Google’s DeepMind proved that machine learning techniques can really be useful in solving math problems.
Moving into the future, the use of AI in mathematics and AI processes will only increase, offering new math ideas to AI solvers.