

After 100 Years, Ramanujan Gap Filled (2013) - bladecatcher
http://blog.wolfram.com/2013/05/01/after-100-years-ramanujan-gap-filled/

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throwaway88760
At first I thought the comments saying "this is not a proof" were being
sarcastic, but I guess readers are simply not aware.

Ramanajuan derived a lot of his mathematical writings from intuition and
seldom had proofs to the level of Western expectations.

It's nice that his "lost" formulae have been verified, but more important
would be an understanding of the intuition behind them.

I'm hoping that would lead to tools for lighter-weight proofs than the recent
heavy-weight and impenetrable Weil et al proofs.

~~~
pierrec
That he seldom had proofs to the level of Western expectations, whatever that
means, is an odd assumption to make. You should have read the (captivating)
paper that was on the front page two days ago.

" _The notebooks contain almost no proofs. Perhaps there are about 10-20
results for which Ramanujan sketches a proof, often only with one sentence.
There are several reasons for the absence of proofs.

1\. Ramanujan was probably influenced by the style of Carr's book _[his
primary source for learning mathematics in his youth] _.

2\. Like most Indian students in his time, Ramanujan worked primarily on a
slate. Paper was very expensive. Thus, after rubbing out his proofs with his
sleeve, Ramanujan recorded only the final results in his notebooks.

3\. Ramanujan never intended that his notebooks be made available to the
mathematical public. They were his personal compilation of what he had
discovered. If someone had asked him how to prove a particular result in the
notebooks, undoubtedly Ramanujan could supply a proof._

[...]

 _It should be emphasized that Ramanujan doubtless thought like any other
mathematician; he just thought with more insight than most of us._ "

\- Bruce C. Berndt, An Overview of Ramanujan's Notebooks

[http://www.math.uiuc.edu/~berndt/articles/aachen.pdf](http://www.math.uiuc.edu/~berndt/articles/aachen.pdf)

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monochromatic
I don't really understand this article. It reads like pop science because of
all the elided details, but no layperson could possibly understand it. But I'm
not sure how much an expert would really out of it either. The stuff about
"having solutions for a particular function" is just nonsense.

Also, can _anyone_ actually decipher the handwritten stuff?

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_dark_matter_
Here's their method:

>First, calculate a numerical value for the point of interest. Second,
conjecture a closed algebraic form for this number. Third, express the
algebraic number as nested radicals. Finally, check the conjectured form with
many digits of accuracy.

But this isn't a proof. It's just empirical evidence. At least it seems to me
- I'm no mathematician.

~~~
shasta
Keep reading. "An actual proof can be accomplished using modular equations. "

