Indian mathematician Ramanujan dead at age 32 only. If he was alive longer, how would math have changed today?

I've read a different version of the 1729 story, in which someone was visiting him and they remarked on the unremarkable quality of the number, which Ramanujan contradicted with the interpretation you give [roughly]. There's certainly a chance he had played with such numbers earlier and remembered previous reasoning, rather than coming up with it on the spot. Even the story I read is a bit apocryphal; it should really have a reliable citation.

I also remember reading a slightly different version of your house number problem, where Ramanujan says that he immediately knew the solution must be a continued fraction, and solved the whole class of problems. That version didn't actually describe the problem, and I have trouble following your description; sorry.

It's probable that Ramanujan only wrote his conclusions in his notebooks, having worked the results out elsewhere. I'm interested in the 5 formulas you say haven't been proven: could you list them?

I find that not having access to a computer forces ingenuity in performing calculations. For instance, in the story about Gauss summing the numbers from 1 to 100, if he had access to a scripting language he might have just had a computer find the answer instead of figuring out the triangular number formula. In any case, perhaps the lack of access to computers helped Ramanujan in some way.

I don't believe your assertion that he never showed any proof of his work. I wish I had access to some of his published work to see for myself.

Ramanujan was very rare and had an amazing intuition. Comparing him to current university math students is like comparing them to Gauss--it's an unfair comparison.

How would math be different if he had survived for longer? It's completely unclear. He probably would have continued making numerous deep and surprising discoveries related to analytic number theory. Perhaps something would have been groundbreaking, or perhaps they would just be interesting curiosities. Who can say?

I'm not sure that the Asker wants a rational answer. Who can tell what a bright person may or may not have done later in life? Quite a few young geniuses have burnt themselves out by the age of 30. Even the great Isaac Newton collapsed into alchemy and spiritualism, coupled with political hatred, later in life.

Just to set the record straight, Srinivasa Iyengar Ramanujan (22 December 1887 – 26 April 1920) was an Indian mathematician with almost no formal training in pure mathematics. He sort-of discovered mathematics at the age of 10 or 11, and had a natural ability to conceptualize and synthesize functions and relationships.

He made important but largely unrecognised contributions to mathematical analysis, number theory, infinite series and recursive fractions. Ramanujan's talent WAS recognised by the English mathematician Professor G.H. Hardy and he became Ramanujan's mentor and tutor. Hardy thought that Ramanujan was of the same natural ability as Gauss, Euler, Cauchy, Newton and Leibniz. I would put him in the same class as L'Hopital, Bernoulli and Galois.

But don't be overwhelmed by his abilities and the mystery of his achievements. Much of what he wrote was conjecture, and not all his formulae have yet been linked to problems by formal analysis. The possibility exists that some of his formulae do not solve the problems but are interesting starting points.

As to those 5 unproven formulas: While Ramanujan was indisputably a genius and prodigy in one, he produced and published a disproportionately large number of formulas which are simply wrong. So it is very possible that some or all of those formulas are also wrong.

The tragedy of Ramanujan's early death is probably not in the additional original thoughts he would have had. What mathematics really lost in him is probably a half a dozen incredibly powerful theorems and countless Lemmas and Corollaries that would have followed.

See, Ramanujan flatly refused to leave India when requested, only yielding with much insistence from Hardy. So most of his writing was steeped in the mathematical culture of India. And while in the early 1900s Indian mathematicians were starting to communicate in ways that were more "acceptable" to the Western establishment, India has a very long history of not proving the statements in the publications.

In his death, we lost many of these theorems of incredible depth simply because he had not written them down. I believe a quote of Hardy's is most relevant here. He said Ramanujan's theorems "must be true because, if they were not true, no one would have had the imagination to invent them." He is right, Ramanujan clearly had a pure intuition as to what should and should not be true about numbers. If we had more time to dig into his thought processes, we probably would have found some inner workings there. He was not divinely inspired, but he was very quick, and he was almost certainly as intimately familiar with numbers as he was his own self

edit: And yes, he had no training. And yes, he said things that were false. That doesn't make him a fraud, or a carny-style "magic calculator!" He was a veritable genius - you have to take his background into consideration, but that is true for everyone who does research.

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Indian mathematician Ramanujan dead at age 32 only. If he was alive longer, how would math have changed today?

Ramanujan met a road accident and was taken to hospital.

His math professor and police had come there to ask questions about who hit him. He told them that a taxi with this number 1729 hit him.

they asked, "how do you remember this number?"

he said, "it is the smallest number such...

Galois died at 20, and did far more to advance modern algebra than Ramanujan (or arguably any other mathematician). He might have been a genius, but he was unschooled. Intelligence can only take you so far toward greatness, and sadly it isn't all that far.

probably not by much: his work was done here, and it was his time to go. how he died provides a huge clue: malnutrition/dysentery is an incorrect diagnosis. he exhibited all the classic signs of a kundalini awakening. iow, through his math work, ramanujan became a buddha.

Ramanujan Death

he is NOT recognized in world of math. He NEVER went to college or school. Therefore he did not have any degree. Hence he was not educated. Mathematician requires phd in mathematics. Since he never went to school and just scribbled stuff on paper with pencil, using his own mind (that too at home), he is clearly not mathematician. the man has zero credibility. His so called, "math professor" you mention himself did not go to any college or university. These are all frauds

Thanks. It was very informative.