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.
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"
"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: 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…
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.
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)
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
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:
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…
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…
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.
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)
“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
royalsocietypublishing.org/toc/rsta/2020/…
Some of my favourite articles below!
#Ramanujan #PhilTransA
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