Today is 131st birthday of #Ramanujan, celebrated as #NationalMathematicsDay in India.
This year is also the 100th anniversary of his election as FRS.
131 is a palindromic and permutable prime with 113 and 311.
Can also be stated as the sum of 3 consecutive primes 41 + 43 + 47.
#Ramanujan's letter to Hardy is an all-time classic -
"I beg to introduce myself to you as a clerk"
"I have no University education"
"I have not trodden through the conventional ... but I am striking out a new path"
"I have made a special investigation of divergent series"
There are ~ 4 photos #Ramanujan according to
"Ramanujan: Essays and Surveys" by Bruce Berndt and co.
bookstore.ams.org/hmath-22
Ramanujan's Lost Notebook series here:
springer.com/series/7261
#Ramanujan's papers in digitised form can be found here @TrinCollLibCam trin.cam.ac.uk/library/wren-d…
Some fascinating quotes from the talks at #Ramanujan symposium organised by @royalsociety
royalsociety.org/science-events…
On #Ramanujan's annotation from Bruce Berndt talk - "Living with Ramanujan for forty years." Also laminated pages of Ramanujan's Notebook.
Managed to get a photo with both Bruce Berndt and George Andrews: two people who were most instrumental in advancing Ramanujan's work.
Paul Erdos passed on #Hardy's rating of mathematicians
If mathematicians are rated on the basis of pure talent on a scale from 0 to 100
#Hardy gave himself a score of 25
#Littlewood 30
#Hilbert 80
#Ramanujan 100
Source: Bruce C. Berndt in Ramanujan's Notebooks: Part I (1994)
Initially, #Ramanujan mostly studied two books:
1. Carr's Synopsis of Pure and Applied Mathematics
2. Loney's trigonometry
Carr’s book is like an encyclopedia with a lot of formulas but no proofs.
Ramanujan imitated the style and probably felt formulas are left for him to prove
In his first letter to Hardy - #Ramanujan proved that
1+2+3+...=-1/12
This is also called Ramanujan Summation, different from Ramanujan Sums.
(first proof of this is probably from #Euler ~ 1760)
More about proof here:
More about #Ramanujan's Prime, Sums and Summation at @Wikipedia
en.wikipedia.org/wiki/Ramanujan…
en.wikipedia.org/wiki/Ramanujan…
en.wikipedia.org/wiki/Ramanujan…
And Hardy-Ramanujan number (1729 = 1^3 + 12^3 = 9^3 + 10^3).
Also recounted in the movie #TheManWhoKnewInfinity
en.wikipedia.org/wiki/1729_(num…
During his 5 years in Cambridge/England, #Ramanujan published ~30 papers that founded the basis of modern maths. A few of them:
1. Prime numbers
2. Hypergeometric series
3. Elliptic functions
4. Partitions
5. Probabilistic Number Theory
janus.lib.cam.ac.uk/db/node.xsp?id…
During his last year, when #Ramanujan knew he was dying, he worked even crazier.
The work is summarised in the "Last Notebook"
springer.com/gb/book/978038…
These are 138 sheets of paper containing over 600 mathematical formulas without proof. Each proof starts a new field in maths.
Finally, #Ramanujan predicted his death (like everyone...:)
“I have made a serious mathematical assessment of my own horoscope, and there is no doubt about it: I will die before I reach the age of thirty-five.”
Ramanujan died at the age of 32 = 2^5 (1887-1920)
Link to @RSocPublishing special issue in celebration of the centenary of Srinivasa Ramanujan's election as FRS.
royalsocietypublishing.org/toc/rsta/2020/…
Some of my favourite articles below!
#Ramanujan #PhilTransA
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