
Ramanujan surprises again - yarapavan
https://plus.maths.org/content/ramanujan
======
livatlantis
Fascinating! This is exceptionally well-written. I can't imagine it being very
easy to communicate mathematical concepts and the excitement of the discovery
(!) in ways that even the uninitiated (like myself) can relate to.

His discovery (albeit not identified as such) contributed to laying the
foundation for work in string theory and he had no clue.

~~~
atmosx
If you liked this post, check the BBC podcast Series "A Brief History of
Mathematics"[1] and also "The Music of the Primes" from Amazon. It's from the
same author.

[1]
[http://www.bbc.co.uk/programmes/b00srz5b/episodes/downloads](http://www.bbc.co.uk/programmes/b00srz5b/episodes/downloads)

~~~
chris_wot
Anything by Marcus du Sautoy is awesome :-)

~~~
vikane
I think so!!

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strommen
> A box of manuscripts and three notebooks. That's all that's left of the work
> of Srinivasa Ramanujan

FYI, the three notebooks are available in PDF form here:
[http://www.math.tifr.res.in/~publ/ramanujan.html](http://www.math.tifr.res.in/~publ/ramanujan.html).
This warms my heart.

~~~
vinchuco
I wonder if someone has gone through the trouble of converting that monster
into LaTeX.

~~~
ics

        ics@kafka-mbp:~ ls -l ~/Projects | grep Ramanujan
        drwxr-xr-x   3 ics  staff        102 Nov  6 16:54 RamanujanManuscripts
    

Funny you should mention that... I haven't really dug in yet but I was looking
for a good reason to brush up on LaTeX and have been on a math reading tear
lately. I couldn't find any other attempts so if I make any progress I'll edit
or comment on this with a link.

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chris_wot
_...this is exactly what Ramanujan came up with. His work on the K3 surface he
discovered provided Ono and Trebat-Leder with a method to produce, not just
one, but infinitely many elliptic curves requiring two or three solutions to
generate all other solutions. It 's not the first method that has been found,
but it required no effort. "We tied the world record on the problem [of
finding such elliptic curves], but we didn't have to do any heavy lifting,"
says Ono. "We did next to nothing, expect recognise what Ramanujan did."_

There's a joke in Dr Who where the 11th Doctor (Matt Smith) gives a proof of
Fermat's Last Theorem to geniuses on earth in order to convince them he can
prevent annihilation by the Atraxi. He basically gives them "Fermat’s Theorem.
The proof. And I mean the real one. Never been seen before. Poor old Fermat
got killed in a duel before he could write it down. My fault. I slept in."

That always makes me wonder - was there and is there indeed a better, shorter
and more elegant proof than the one we have?

Who knows, maybe Ramanujan was on his way to developing one!

~~~
thrownaway2424
Maybe there's an inter-dimensional, pan-galactic conspiracy to come to Earth
and kill anyone who is about to reveal Fermat's marvelous proof.

~~~
chris_wot
Hence your throw away account, huh?

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clusterfoo
What a great case for pure research:

> "He was a whiz with formulas and I think [his aim was] to construct those
> near counter-examples to Fermat's last theorem. So he developed a theory to
> find these near misses, without recognizing that the machine he was
> building, those formulas that he was writing down, would be useful for
> anyone, ever, in the future."

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Asparagirl
_Hardy later described his collaboration with Ramanujan as "the one romantic
incident in my life"._

OMG, that is ridiculously romantic, and the linked bio of Hardy is amazing.
Please tell me there is a book or play or movie about Hardy, maybe along the
lines of the one Tom Stoppard wrote about Hardy's contemporary A E Housman.

~~~
jordigh
There's a movie with Jeremy Irons in the role of Hardy:

[http://jeremyirons.net/tag/g-h-hardy/](http://jeremyirons.net/tag/g-h-hardy/)

If you want more romance and mathematics, read about Galois.

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fredley
For such a legendary mathematician, it does beg the question of why his old
notes were not pored over before.

~~~
wbhart
They certainly were. Bruce Berndt is one example of a mathematician who has
spent an entire career proving the results found in Ramanujan's notebooks. He
has written a number of very thick books showing methods of proof for all his
results.

Notice that Ono says that only a few people knew about this stuff. Another way
of saying the same thing (the more usual way in my opinion) is that "this was
already known by the experts".

------
pthreads
That was a fascinating article.

There is a new biopic about Ramanujan. I wonder if anyone on HN knows when it
will be released in the US. So far it seems it is only at film festivals.

[http://tiff.net/festivals/festival15/galapresentations/the-m...](http://tiff.net/festivals/festival15/galapresentations/the-
man-who-knew-infinity)

~~~
Jaxan
I was very happy to see it today at a science film festival in my hometown.
It's a great movie. Very dramatical. But there seems to be little info known
about its release.

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crb002
What do the power series at top have to do with the equations at bottom?
McIlRoy of Unix pipe fame has a wonderful exposition on programming with power
series.
[http://www.cs.dartmouth.edu/~doug/powser.html](http://www.cs.dartmouth.edu/~doug/powser.html)

------
acjohnson55
The implied other side to the 1729 example, x^3 + y^3 = z^3 - 1 could also be
thought of as a special case w^3 + x^3 + y^3 = z^3 (well, they both can, if
the variables are integers). Since the more specific version has infinite
examples, so must this. But what about if we bump those exponents up to 4? Is
there a generalized Fermat's Last?

~~~
ixwt
Could this be further generalized to n integers raised to nth power added
together can have a number raised to nth power integer, hence why there is no
relationship such that x^3 + y^3 = z^3, but there are an infinite number of
x^3 + y^3 + z^3 = a^3 (where z in this case can work as +-1).

~~~
acjohnson55
That's what I was asking :)

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justifier
a month ago(o) i mused on the potential applications of understanding why
ramanujan was examining 'the smallest number expressible as a sum of two cubes
in two different ways'

what a great investigation

(o)
[https://news.ycombinator.com/item?id=10394669](https://news.ycombinator.com/item?id=10394669)

------
bliti
What a wonderful Saturday read. Thank you for posting.

The article does make a very interesting point I had never considered:
Mathematics as machines. Which absolutely makes sense when you see it from the
point of view of input-processing-output.

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S4M
Whenever I think of Ramanujan I wonder if he would get founding at this time.
I personally doubt someone so much ahead of his time would.

~~~
Ganz7
What?

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dashdart
I think he means funding.

~~~
S4M
Yeah, I meant funding, sorry for the spelling. Precisely, I meant that I am
afraid Ramanujan's ideas would seem so crazy that nobody would fund his
research.

~~~
eveningcoffee
Well, at least he could have enough paper at least.

~~~
shardinator
and get Indian food in Britain

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sanmon3186
ELI5 anyone please.

~~~
CamperBob2
RTFA, it's actually quite interesting and comprehensible.

