Percentage of Ramanujan's conjectures that were proven correct
Today I read the following brief but insightful account of Ramanujan's approach to mathematics: https://www.imsc.res.in/~rao/ramanujan/images/KSRchap3.pdf and while reading this I wondered whether we have a lower-bound on the percentage of Ramanujan's conjectures which are correct.
I'm planning to get a copy of Ramanujan's notebooks. Meanwhile, the above question intrigues me.
ho.history-overview conjectures ramanujan
asked Dec 18 at 13:06
Aidan Rocke
350216
add a comment |
Today I read the following brief but insightful account of Ramanujan's approach to mathematics: https://www.imsc.res.in/~rao/ramanujan/images/KSRchap3.pdf and while reading this I wondered whether we have a lower-bound on the percentage of Ramanujan's conjectures which are correct.
I'm planning to get a copy of Ramanujan's notebooks. Meanwhile, the above question intrigues me.
ho.history-overview conjectures ramanujan
asked Dec 18 at 13:06
Aidan Rocke
350216
5
Side question, are there conjectures of him still open?
– Per Alexandersson
Dec 18 at 13:19
2
Dual question: mathoverflow.net/questions/288410/what-did-ramanujan-get-wrong/…
– Timothy Chow
Dec 18 at 16:45
add a comment |
Today I read the following brief but insightful account of Ramanujan's approach to mathematics: https://www.imsc.res.in/~rao/ramanujan/images/KSRchap3.pdf and while reading this I wondered whether we have a lower-bound on the percentage of Ramanujan's conjectures which are correct.
I'm planning to get a copy of Ramanujan's notebooks. Meanwhile, the above question intrigues me.
ho.history-overview conjectures ramanujan
asked Dec 18 at 13:06
Aidan Rocke
350216
Today I read the following brief but insightful account of Ramanujan's approach to mathematics: https://www.imsc.res.in/~rao/ramanujan/images/KSRchap3.pdf and while reading this I wondered whether we have a lower-bound on the percentage of Ramanujan's conjectures which are correct.
I'm planning to get a copy of Ramanujan's notebooks. Meanwhile, the above question intrigues me.
ho.history-overview conjectures ramanujan
ho.history-overview conjectures ramanujan
asked Dec 18 at 13:06
Aidan Rocke
350216
asked Dec 18 at 13:06
Aidan Rocke
350216
asked Dec 18 at 13:06
Aidan Rocke
350216
asked Dec 18 at 13:06
Aidan Rocke
350216
asked Dec 18 at 13:06
Aidan Rocke
350216
350216
5
Side question, are there conjectures of him still open?
– Per Alexandersson
Dec 18 at 13:19
2
Dual question: mathoverflow.net/questions/288410/what-did-ramanujan-get-wrong/…
– Timothy Chow
Dec 18 at 16:45
add a comment |
5
Side question, are there conjectures of him still open?
– Per Alexandersson
Dec 18 at 13:19
2
Dual question: mathoverflow.net/questions/288410/what-did-ramanujan-get-wrong/…
– Timothy Chow
Dec 18 at 16:45
5
5
Side question, are there conjectures of him still open?
– Per Alexandersson
Dec 18 at 13:19
Side question, are there conjectures of him still open?
– Per Alexandersson
Dec 18 at 13:19
2
2
Dual question: mathoverflow.net/questions/288410/what-did-ramanujan-get-wrong/…
– Timothy Chow
Dec 18 at 16:45
Dual question: mathoverflow.net/questions/288410/what-did-ramanujan-get-wrong/…
– Timothy Chow
Dec 18 at 16:45
add a comment |
1 Answer
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This interview with Prof. Bruce Berndt indicates the percentage of correct results from his notebooks to be greater than 99.7%. (See also this longer writeup.)
Between 1903 and 1914, before Ramanujan went to Cambridge, he compiled
3,542 theorems in the notebooks. I have gone through every entry in
the notebooks. If a result has already been proved in the literature,
then I just wrote the entry down and said that proofs can be found in
this literature and so on.There are a number of misprints. I did not
count the number of serious mistakes but it is an extremely small
number - maybe five or ten out of over 3,000 results. Considering that
Ramanujan did not have any rigorous training, it is really amazing
that he made so few mistakes.
Bruce Berndt, Ramanujan's Notebooks, parts I--V.
side question: The Ramanujan–Petersson conjecture for Maass forms is still open.
edited Dec 18 at 14:43
Josiah Park
887318
answered Dec 18 at 13:40
Carlo Beenakker
72.9k9164273
2
Of course the Ramanujan-Petersson conjecture for Maas forms is not actually Ramanujan's per se.
– Josiah Park
Dec 18 at 13:52
7
Do you really mean 0.997%? I guess that should read 99.7% of correct theorems.
– Manfred Weis
Dec 18 at 14:03
thank you @ManfredWeis , for correcting my silly typo.
– Carlo Beenakker
Dec 18 at 14:48
2
"really amazing" - is that one of those understatements mathematicians are fond of?
– davidbak
Dec 18 at 16:02
add a comment |
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This interview with Prof. Bruce Berndt indicates the percentage of correct results from his notebooks to be greater than 99.7%. (See also this longer writeup.)
Between 1903 and 1914, before Ramanujan went to Cambridge, he compiled
3,542 theorems in the notebooks. I have gone through every entry in
the notebooks. If a result has already been proved in the literature,
then I just wrote the entry down and said that proofs can be found in
this literature and so on.There are a number of misprints. I did not
count the number of serious mistakes but it is an extremely small
number - maybe five or ten out of over 3,000 results. Considering that
Ramanujan did not have any rigorous training, it is really amazing
that he made so few mistakes.
Bruce Berndt, Ramanujan's Notebooks, parts I--V.
side question: The Ramanujan–Petersson conjecture for Maass forms is still open.
edited Dec 18 at 14:43
Josiah Park
887318
answered Dec 18 at 13:40
Carlo Beenakker
72.9k9164273
2
Of course the Ramanujan-Petersson conjecture for Maas forms is not actually Ramanujan's per se.
– Josiah Park
Dec 18 at 13:52
7
Do you really mean 0.997%? I guess that should read 99.7% of correct theorems.
– Manfred Weis
Dec 18 at 14:03
thank you @ManfredWeis , for correcting my silly typo.
– Carlo Beenakker
Dec 18 at 14:48
2
"really amazing" - is that one of those understatements mathematicians are fond of?
– davidbak
Dec 18 at 16:02
add a comment |
This interview with Prof. Bruce Berndt indicates the percentage of correct results from his notebooks to be greater than 99.7%. (See also this longer writeup.)
Between 1903 and 1914, before Ramanujan went to Cambridge, he compiled
3,542 theorems in the notebooks. I have gone through every entry in
the notebooks. If a result has already been proved in the literature,
then I just wrote the entry down and said that proofs can be found in
this literature and so on.There are a number of misprints. I did not
count the number of serious mistakes but it is an extremely small
number - maybe five or ten out of over 3,000 results. Considering that
Ramanujan did not have any rigorous training, it is really amazing
that he made so few mistakes.
Bruce Berndt, Ramanujan's Notebooks, parts I--V.
side question: The Ramanujan–Petersson conjecture for Maass forms is still open.
edited Dec 18 at 14:43
Josiah Park
887318
answered Dec 18 at 13:40
Carlo Beenakker
72.9k9164273
2
Of course the Ramanujan-Petersson conjecture for Maas forms is not actually Ramanujan's per se.
– Josiah Park
Dec 18 at 13:52
7
Do you really mean 0.997%? I guess that should read 99.7% of correct theorems.
– Manfred Weis
Dec 18 at 14:03
thank you @ManfredWeis , for correcting my silly typo.
– Carlo Beenakker
Dec 18 at 14:48
2
"really amazing" - is that one of those understatements mathematicians are fond of?
– davidbak
Dec 18 at 16:02
add a comment |
This interview with Prof. Bruce Berndt indicates the percentage of correct results from his notebooks to be greater than 99.7%. (See also this longer writeup.)
Between 1903 and 1914, before Ramanujan went to Cambridge, he compiled
3,542 theorems in the notebooks. I have gone through every entry in
the notebooks. If a result has already been proved in the literature,
then I just wrote the entry down and said that proofs can be found in
this literature and so on.There are a number of misprints. I did not
count the number of serious mistakes but it is an extremely small
number - maybe five or ten out of over 3,000 results. Considering that
Ramanujan did not have any rigorous training, it is really amazing
that he made so few mistakes.
Bruce Berndt, Ramanujan's Notebooks, parts I--V.
side question: The Ramanujan–Petersson conjecture for Maass forms is still open.
edited Dec 18 at 14:43
Josiah Park
887318
answered Dec 18 at 13:40
Carlo Beenakker
72.9k9164273
This interview with Prof. Bruce Berndt indicates the percentage of correct results from his notebooks to be greater than 99.7%. (See also this longer writeup.)
Between 1903 and 1914, before Ramanujan went to Cambridge, he compiled
3,542 theorems in the notebooks. I have gone through every entry in
the notebooks. If a result has already been proved in the literature,
then I just wrote the entry down and said that proofs can be found in
this literature and so on.There are a number of misprints. I did not
count the number of serious mistakes but it is an extremely small
number - maybe five or ten out of over 3,000 results. Considering that
Ramanujan did not have any rigorous training, it is really amazing
that he made so few mistakes.
Bruce Berndt, Ramanujan's Notebooks, parts I--V.
side question: The Ramanujan–Petersson conjecture for Maass forms is still open.
edited Dec 18 at 14:43
Josiah Park
887318
answered Dec 18 at 13:40
Carlo Beenakker
72.9k9164273
edited Dec 18 at 14:43
Josiah Park
887318
edited Dec 18 at 14:43
Josiah Park
887318
edited Dec 18 at 14:43
Josiah Park
887318
887318
answered Dec 18 at 13:40
Carlo Beenakker
72.9k9164273
answered Dec 18 at 13:40
Carlo Beenakker
72.9k9164273
answered Dec 18 at 13:40
Carlo Beenakker
72.9k9164273
72.9k9164273
2
Of course the Ramanujan-Petersson conjecture for Maas forms is not actually Ramanujan's per se.
– Josiah Park
Dec 18 at 13:52
7
Do you really mean 0.997%? I guess that should read 99.7% of correct theorems.
– Manfred Weis
Dec 18 at 14:03
thank you @ManfredWeis , for correcting my silly typo.
– Carlo Beenakker
Dec 18 at 14:48
2
"really amazing" - is that one of those understatements mathematicians are fond of?
– davidbak
Dec 18 at 16:02
add a comment |
2
Of course the Ramanujan-Petersson conjecture for Maas forms is not actually Ramanujan's per se.
– Josiah Park
Dec 18 at 13:52
7
Do you really mean 0.997%? I guess that should read 99.7% of correct theorems.
– Manfred Weis
Dec 18 at 14:03
thank you @ManfredWeis , for correcting my silly typo.
– Carlo Beenakker
Dec 18 at 14:48
2
"really amazing" - is that one of those understatements mathematicians are fond of?
– davidbak
Dec 18 at 16:02
2
2
Of course the Ramanujan-Petersson conjecture for Maas forms is not actually Ramanujan's per se.
– Josiah Park
Dec 18 at 13:52
Of course the Ramanujan-Petersson conjecture for Maas forms is not actually Ramanujan's per se.
– Josiah Park
Dec 18 at 13:52
7
7
Do you really mean 0.997%? I guess that should read 99.7% of correct theorems.
– Manfred Weis
Dec 18 at 14:03
Do you really mean 0.997%? I guess that should read 99.7% of correct theorems.
– Manfred Weis
Dec 18 at 14:03
thank you @ManfredWeis , for correcting my silly typo.
– Carlo Beenakker
Dec 18 at 14:48
thank you @ManfredWeis , for correcting my silly typo.
– Carlo Beenakker
Dec 18 at 14:48
2
2
"really amazing" - is that one of those understatements mathematicians are fond of?
– davidbak
Dec 18 at 16:02
"really amazing" - is that one of those understatements mathematicians are fond of?
– davidbak
Dec 18 at 16:02
add a comment |
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5
Side question, are there conjectures of him still open?
– Per Alexandersson
Dec 18 at 13:19
2
Dual question: mathoverflow.net/questions/288410/what-did-ramanujan-get-wrong/…
– Timothy Chow
Dec 18 at 16:45