Srinivasa Ramanujan was a self-taught Indian mathematician who made profound contributions to the field of mathematics despite having no formal training in the subject. He was born in 1887 in a poor family in southern India and showed an early aptitude for mathematics, but struggled in other subjects. In the year of 1913, Ramanujan corresponded with the illustrious British mathematician G.H. Hardy, who promptly discerned his prodigious mathematical genius and invited him to academicaly pursue in England. Ramanujan’s work on number theory, infinite series, and modular forms revolutionized the field of mathematics and earned him widespread recognition. One of Ramanujan’s most famous achievements was his work on partitions, which are ways of representing a positive integer as a sum of other positive integers. Ramanujan developed a formula for the number of partitions of an integer, which was not only elegant but also provided insight into the distribution of primes.
However there’s this one news that has been circulating around for quite some time now which says that Ramanujan predicted the existence of black holes. In fact, the great Indian spiritual guru and mystic, Jaggi Vasudev, also known as Sadhguru, in one of his interviews stated that Ramanujan spoke about the existence of black holes long before anyone else did and long before it was even conceptualized.
The concept of black holes is a relatively recent development in human understanding of the universe. The idea of objects so massive and dense that their gravitational pull is strong enough to prevent even light from escaping was first proposed in the early 20th century as a result of Einstein’s theory of GR. It was Karl Schwarzschild who first predicted the existence of black holes with solutions to EFEs, called Schwarzschild solution. This solution describes the geometry of spacetime around a non-rotating, spherically symmetric object and shows that if a massive object were to be compressed into a small enough volume, the curvature of spacetime would become infinitely steep and the object would form what is now known as a black hole.
Certainly! Ramanujan was indeed a remarkable mathematician, known for his groundbreaking work despite lacking formal training. His contributions to number theory, infinite series, and modular forms were truly pioneering. His formula for partitions of integers, which allowed representing positive integers as sums of other positive integers, remains an elegant and insightful contribution in mathematics.
Regarding the claim about Ramanujan predicting black holes, it's a fascinating but contentious topic. While Ramanujan didn't explicitly mention black holes, there are intriguing parallels between his work and the concepts later developed in general relativity (GR) and the study of black holes.
The notion of black holes arose from Einstein's theory of general relativity in the early 20th century. It was Schwarzschild who first derived solutions to Einstein's field equations describing the geometry around a non-rotating, spherically symmetric mass. These solutions, known as the Schwarzschild solution, revealed a critical threshold where an object compressed into a small volume would cause space-time curvature to become infinitely steep, forming what we now recognize as a black hole.
While Ramanujan's work didn't explicitly address black holes, his mathematical insights into the nature of numbers and mathematical structures do resonate with concepts later found in black hole physics. Some interpretations suggest that his work on highly composite numbers and his explorations of the deep mathematical relationships could, in a metaphorical sense, relate to the singularity within a black hole—infinitely intense and possessing profound mathematical depth.
The claim that Ramanujan predicted black holes might stem from his intuitive understanding of the depth and richness of mathematical structures. However, attributing direct predictions of black holes to Ramanujan remains a matter of debate among scholars.
It's intriguing how diverse fields like mathematics and astrophysics intersect, showcasing the interconnectedness of human knowledge and the way ideas across disciplines can inspire and inform each other.
No.Ramanujan did not specifically predict black holes in the sense that we understand them today. However, he did make some mathematical discoveries that are now used in the study of black holes. There's no doubt that Srinivasa Ramanujan was an impeccable mathematical genius.
According to Physics Central, 1 + 2 + 3 + 4 + … only equals -1/12 because the mathematicians redefined the equal sign. In this style of mathematics, called analytical continuation, "=" stopped meaning “is equal to” and started meaning “is associated with.” Tricky mathematicians.
Kerr's solution helped establish the existence of black holes. In a nearly 1,000-page paper, Giorgi and colleagues used a type of “proof by contradiction” to show that Kerr black holes that rotate slowly (meaning they have a small angular momentum relative to their mass) are mathematically stable.
Ramanujan's approximate formula, developed in 1918, helped him spot that numbers ending in 4 or 9 have a partition number divisible by 5. He proved for every non-negative integer n, that p(5n + 4) ≡ 0 (mod 5). Ramanujan found similar rules for partition numbers divisible by 7 and 11.
1. Ramanujan summation / paradox is a technique developed by the mathematician Srinivasa Ramanujan to assign values to certain divergent series. 2. It provides a way to regularize divergent series by introducing a parameter and analytically continuing the series to obtain a finite value.
What made Ramanujan afraid of infinity? Ramanujan was well known for having a fear of infinity despite having exceptional mathematical skills. He was afraid because he thought infinity was an unreachable and incomprehensible concept.
1729 as the sum of two positive cubes. 1729 is the smallest nontrivial taxicab number, and is known as the Hardy–Ramanujan number, after an anecdote of the British mathematician G. H.Hardy when he visited Indian mathematician Srinivasa Ramanujan in hospital.
We can't see them, but we know that black holes can exist thanks to the groundwork laid by Einstein's General Theory of Relativity. A black hole forms when the mass of an object, like a star, suddenly collapses down to a tiny volume. A small object with a large mass causes a gaping dent in space-time.
Black holes seem to be the stuff of science fiction (and, in fact, have starred in many sci-fi books and movies), so it's not uncommon for people to wonder, are black holes real? As it turns out, the answer is yes, though for a long time most scientists were convinced that black holes were purely theoretical objects.
Roger Penrose (left) proved black holes are real objects. Andrea Ghez (center) and Reinhard Genzel (right) showed that one weighing 4 million times as much as the Sun lurks in the heart of our galaxy. Since Penrose's advances, astronomers have found a wealth of evidence for black holes.
Born in India in 1887, Srinivasa Ramanujan is one of the most influential mathematicians in the world. He made significant contributions to the analytical theory of numbers, as well as elliptic functions, continued fractions, and infinite series. He had an estimated IQ of 185.
It assumes that this sum has a well-defined value, on which standard operations (addition, subtraction, mulitplication, division) are then defined. But this is obviously untrue.
In his 17-page paper "Some Properties of Bernoulli's Numbers" (1911), Ramanujan gave three proofs, two corollaries and three conjectures. His writing initially had many flaws.
It is also unlikely that Einstein got to know about Ramanujan's work later on as it dealt with pure number theory. There is no information that exists in any of Einstein's biographies that Einstein knew about Ramanujan and made mention of it.
In mathematics, Ramanujan's Master Theorem, named after Srinivasa Ramanujan, is a technique that provides an analytic expression for the Mellin transform of an analytic function. Page from Ramanujan's notebook stating his Master theorem. is the gamma function.
“Ramanujan summation” is a way of assigning values to divergent series. As such, it isn't true or false, just defined (or not, as the case may be). This particular case really does “work”. However, the left-hand side should say that it's a Ramanujan summation, not a regular “sum of a series”, and it doesn't.
And some mathematicians mistakenly believe that physicists have summed the series experimentally to give −1/12 . Neither are right, but so much finger pointing of each to the other's discipline has occurred that many laymen now believe that maths and physics have both proved that the sum is −1/12 .
What is the value of pi? The value of pi is approximately 3.14, or 22/7. To 39 decimal places, pi is 3.141592653589793238462643383279502884197. Pi is an irrational number, which means it is not equal to the ratio of any two whole numbers.
Sequences: A finite sequence is a sequence that contains the last term such as a1, a2, a3, a4, a5, a6……an. On the other hand, an infinite sequence is never-ending i.e. a1, a2, a3, a4, a5, a6……an…..
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