Ramanujan machine
The Ramanujan machine is a specialised software package, developed by a team of scientists at the
According to George Andrews, an expert on the mathematics of Ramanujan, even though some of the results produced by the Ramanujan machine are amazing and difficult to prove, the results produced by the machine are not of the caliber of Ramanujan and so calling the software the Ramanujan machine is slightly outrageous.[5][6] Doron Zeilberger, an Israeli mathematician, has opined that the Ramanujan machine is a harbinger of a new methodology of doing mathematics.[7]
Formulas discovered by the Ramanujan machine
The following are some of the formulas discovered by the Ramanujan machine which have been later proved to be true:[3]
The following are some of the many formulas conjectured by the Ramanujan machine whose truth or falsity has not yet been established:[8]
In the last expression, the numbers 4, 14, 30, 52, . . . are defined by the sequence for and the numbers 8, 72, 288, 800, . . . are generated using the formula for .
External links
- Website of the Ramanujan machine project: The Ramanujan Machine: Using algorithms to discover new mathematics
- Ido Kaminer - The Ramanujan Machine on YouTube
References
- ^ "The Ramanujan Machine". Technion: Israel Institute of Technology. Retrieved 17 August 2021.
- ^ "Ramanujan machine automatically generates conjectures for fundamental constants". phys.org. Science X. Retrieved 17 August 2021.
- ^ S2CID 231805819. Retrieved 17 August 2021.)
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: CS1 maint: multiple names: authors list (link - ^ Kabir Firaque (18 July 2019). "Explained: What is Ramanujan Machine, and why is it named after the Indian mathematician?". The Indian Express. Retrieved 17 August 2021.
- S2CID 231804003. Retrieved 17 August 2021.
- ^ "Math in the Media". The American Mathematical Society. Retrieved 17 August 2021.
- ^ "Opinion 180: The Ramanujan Machine is a Harbinger of Mathematics becoming a Science again (and Fun again!)". Rutgers School of arts and Sciences. Retrieved 17 August 2021.
- ^ "Results". The Ramanujan Machine. Retrieved 17 August 2021.