Srinivasa Ramanujan was not just a prodigal mathematician. He was the master in finding patterns. As you already know, the fascinating story behind the Ramanujan number- 1729- Ramanujan quickly identified (even while he was sick) that 1729 is the smallest number that can be expressed as a sum of two different cubes – not once, but twice.
The Ramanujan Machine developed by a group of scientists at Technion: Israeli Institute of Technology is an Artificial Intelligence machine capable of finding new formulas as conjectures. Some of these formulas have exciting patterns. Many conjectures made by the Ramanujan Machine have been proven true. Some are yet to be studied in detail.
IAS aspirants can read about the life and contributions of Srinivasa Ramanujan (1887-1920) at the linked article.
His biography and achievements prove a lot about him and his struggles to contribute to the field of this subject. All this is also an essential part of the syllabus for aspirants preparing for the upcoming IAS Exam.
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Important Facts about Ramanujan Machine (UPSC)
Before talking about the Ramanujan Machine, it is necessary to explain what a mathematical constant is. A mathematical constant is any definable, unchanging number often denoted with a symbol. It is constant because its value remains unchanged. Some mathematical constants are Pi, Euler’s number, Imaginary Unit etc.
Now, what the Ramanujan Machine does is that it tries to come up with conjectures related to equations containing continued fractions. For example, look at this equation-
Image: https://cdn1.byjus.com/wp-content/uploads/2022/02/Ramanujan-Machine.png
Here we have a formula that contains the mathematical constant Pi. And, on the right-hand side, we have a continued fraction. But the continued fraction is not just a, let’s say, boring fraction; there is a pattern to it.
The machine uses Meet in The Middle and Gradient Descent algorithms to develop these conjectures. The Man In The Middle algorithm comes up with the continued fractions. The entire project is open-sourced and is freely available on Github.
The facts, achievements and contributions presented by Srinivasa Ramanujan have not just been acknowledged within India, but also globally by leading mathematicians. Aspirants can also learn about other Indian mathematicians and their contributions, by visiting the linked article.
Why Is the Project Named ‘Ramanujan Machine’?
The scientists at Technion named the project after the famous Indian mathematician Srinivas Ramanujan. He was famous for coming up with solutions to complex mathematical problems just with the help of his intuition. For example, in one of his letters to Hardy, Ramanujan proposed-
1 + 2 + 3 + 4 + … = -1/12 (also known as Ramanujan Summation)
This might seem weird at first, but it was later proven true. Such was the intuitive power of Ramanujan.
It was, therefore, natural for the researchers at Technion to name their machine that does similar work after Srinivas Ramanujan.
Also, read about December 22 – National Mathematics Day
Criticism of the Ramanujan Machine
While the Ramanujan Machine is a highly appreciable effort, several mathematics experts have dismissed the machine as pure hype. A mathematics professor at the University of Chicago summarily rejected the ‘novelty’ of the conjectures and pointed out that those conjectures are just specializations of Gauss’ theories on continued fractions. Another claimed that the system is fed with similar continued fractions, and it only represented those fractions in the form of Euler’s equations.
The fact that the research paper has been published in Nature indicates that the machine has achieved considerable attention proves that it has substance. Furthermore, we must remember that it is primarily the students who have built the system, which is a thing to clap.
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Frequently Asked Questions on the Ramanujan Machine
What is a Ramanujan Machine?
The Ramanujan Machine is an AI and ML-based computer program that comes up with conjectures related to continued fractions and Mathematical Constant. These conjectures are in the form of equations having interesting patterns. The machine was named after the Indian mathematician Srinivas Ramanujan. The scientists and students developed it at Technion: Israeli Institute of Technology.
What is a conjecture?
In mathematics, when mathematicians propose a theory, equation or similar aspects without knowing whether it is correct, that theory or equation is called a conjecture. The equations given by the Ramanujan Machine are conjectures because there is no prior research on these equations. Hence, one cannot prove their integrity right away.
Who is Srinivas Ramanujan?
Srinivas Ramanujan is a famed Indian Mathematician who took birth in 1887. He is well known for his research on number theory, continued fraction, Zeta function and partition function- without having any formal education in pure mathematics. With Godrey Harvey’s help, Ramanujan gained international attention and secured a seat in the Royal Society of London. His theorems continue to evoke appreciation from mathematicians across the world.
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