Percentage of Ramanujan's conjectures that were proven correct












7












$begingroup$


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







share|cite|improve this question









$endgroup$








  • 5




    $begingroup$
    Side question, are there conjectures of him still open?
    $endgroup$
    – Per Alexandersson
    Dec 18 '18 at 13:19






  • 3




    $begingroup$
    Dual question: mathoverflow.net/questions/288410/what-did-ramanujan-get-wrong/…
    $endgroup$
    – Timothy Chow
    Dec 18 '18 at 16:45
















7












$begingroup$


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







share|cite|improve this question









$endgroup$








  • 5




    $begingroup$
    Side question, are there conjectures of him still open?
    $endgroup$
    – Per Alexandersson
    Dec 18 '18 at 13:19






  • 3




    $begingroup$
    Dual question: mathoverflow.net/questions/288410/what-did-ramanujan-get-wrong/…
    $endgroup$
    – Timothy Chow
    Dec 18 '18 at 16:45














7












7








7


3



$begingroup$


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







share|cite|improve this question









$endgroup$




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






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Dec 18 '18 at 13:06









Aidan RockeAidan Rocke

355216




355216








  • 5




    $begingroup$
    Side question, are there conjectures of him still open?
    $endgroup$
    – Per Alexandersson
    Dec 18 '18 at 13:19






  • 3




    $begingroup$
    Dual question: mathoverflow.net/questions/288410/what-did-ramanujan-get-wrong/…
    $endgroup$
    – Timothy Chow
    Dec 18 '18 at 16:45














  • 5




    $begingroup$
    Side question, are there conjectures of him still open?
    $endgroup$
    – Per Alexandersson
    Dec 18 '18 at 13:19






  • 3




    $begingroup$
    Dual question: mathoverflow.net/questions/288410/what-did-ramanujan-get-wrong/…
    $endgroup$
    – Timothy Chow
    Dec 18 '18 at 16:45








5




5




$begingroup$
Side question, are there conjectures of him still open?
$endgroup$
– Per Alexandersson
Dec 18 '18 at 13:19




$begingroup$
Side question, are there conjectures of him still open?
$endgroup$
– Per Alexandersson
Dec 18 '18 at 13:19




3




3




$begingroup$
Dual question: mathoverflow.net/questions/288410/what-did-ramanujan-get-wrong/…
$endgroup$
– Timothy Chow
Dec 18 '18 at 16:45




$begingroup$
Dual question: mathoverflow.net/questions/288410/what-did-ramanujan-get-wrong/…
$endgroup$
– Timothy Chow
Dec 18 '18 at 16:45










1 Answer
1






active

oldest

votes


















12












$begingroup$

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.






share|cite|improve this answer











$endgroup$









  • 2




    $begingroup$
    Of course the Ramanujan-Petersson conjecture for Maas forms is not actually Ramanujan's per se.
    $endgroup$
    – Josiah Park
    Dec 18 '18 at 13:52








  • 7




    $begingroup$
    Do you really mean 0.997%? I guess that should read 99.7% of correct theorems.
    $endgroup$
    – Manfred Weis
    Dec 18 '18 at 14:03










  • $begingroup$
    thank you @ManfredWeis , for correcting my silly typo.
    $endgroup$
    – Carlo Beenakker
    Dec 18 '18 at 14:48






  • 2




    $begingroup$
    "really amazing" - is that one of those understatements mathematicians are fond of?
    $endgroup$
    – davidbak
    Dec 18 '18 at 16:02











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1 Answer
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active

oldest

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1 Answer
1






active

oldest

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active

oldest

votes






active

oldest

votes









12












$begingroup$

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.






share|cite|improve this answer











$endgroup$









  • 2




    $begingroup$
    Of course the Ramanujan-Petersson conjecture for Maas forms is not actually Ramanujan's per se.
    $endgroup$
    – Josiah Park
    Dec 18 '18 at 13:52








  • 7




    $begingroup$
    Do you really mean 0.997%? I guess that should read 99.7% of correct theorems.
    $endgroup$
    – Manfred Weis
    Dec 18 '18 at 14:03










  • $begingroup$
    thank you @ManfredWeis , for correcting my silly typo.
    $endgroup$
    – Carlo Beenakker
    Dec 18 '18 at 14:48






  • 2




    $begingroup$
    "really amazing" - is that one of those understatements mathematicians are fond of?
    $endgroup$
    – davidbak
    Dec 18 '18 at 16:02
















12












$begingroup$

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.






share|cite|improve this answer











$endgroup$









  • 2




    $begingroup$
    Of course the Ramanujan-Petersson conjecture for Maas forms is not actually Ramanujan's per se.
    $endgroup$
    – Josiah Park
    Dec 18 '18 at 13:52








  • 7




    $begingroup$
    Do you really mean 0.997%? I guess that should read 99.7% of correct theorems.
    $endgroup$
    – Manfred Weis
    Dec 18 '18 at 14:03










  • $begingroup$
    thank you @ManfredWeis , for correcting my silly typo.
    $endgroup$
    – Carlo Beenakker
    Dec 18 '18 at 14:48






  • 2




    $begingroup$
    "really amazing" - is that one of those understatements mathematicians are fond of?
    $endgroup$
    – davidbak
    Dec 18 '18 at 16:02














12












12








12





$begingroup$

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.






share|cite|improve this answer











$endgroup$



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.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Dec 18 '18 at 14:43









Josiah Park

1,285320




1,285320










answered Dec 18 '18 at 13:40









Carlo BeenakkerCarlo Beenakker

75.3k9171280




75.3k9171280








  • 2




    $begingroup$
    Of course the Ramanujan-Petersson conjecture for Maas forms is not actually Ramanujan's per se.
    $endgroup$
    – Josiah Park
    Dec 18 '18 at 13:52








  • 7




    $begingroup$
    Do you really mean 0.997%? I guess that should read 99.7% of correct theorems.
    $endgroup$
    – Manfred Weis
    Dec 18 '18 at 14:03










  • $begingroup$
    thank you @ManfredWeis , for correcting my silly typo.
    $endgroup$
    – Carlo Beenakker
    Dec 18 '18 at 14:48






  • 2




    $begingroup$
    "really amazing" - is that one of those understatements mathematicians are fond of?
    $endgroup$
    – davidbak
    Dec 18 '18 at 16:02














  • 2




    $begingroup$
    Of course the Ramanujan-Petersson conjecture for Maas forms is not actually Ramanujan's per se.
    $endgroup$
    – Josiah Park
    Dec 18 '18 at 13:52








  • 7




    $begingroup$
    Do you really mean 0.997%? I guess that should read 99.7% of correct theorems.
    $endgroup$
    – Manfred Weis
    Dec 18 '18 at 14:03










  • $begingroup$
    thank you @ManfredWeis , for correcting my silly typo.
    $endgroup$
    – Carlo Beenakker
    Dec 18 '18 at 14:48






  • 2




    $begingroup$
    "really amazing" - is that one of those understatements mathematicians are fond of?
    $endgroup$
    – davidbak
    Dec 18 '18 at 16:02








2




2




$begingroup$
Of course the Ramanujan-Petersson conjecture for Maas forms is not actually Ramanujan's per se.
$endgroup$
– Josiah Park
Dec 18 '18 at 13:52






$begingroup$
Of course the Ramanujan-Petersson conjecture for Maas forms is not actually Ramanujan's per se.
$endgroup$
– Josiah Park
Dec 18 '18 at 13:52






7




7




$begingroup$
Do you really mean 0.997%? I guess that should read 99.7% of correct theorems.
$endgroup$
– Manfred Weis
Dec 18 '18 at 14:03




$begingroup$
Do you really mean 0.997%? I guess that should read 99.7% of correct theorems.
$endgroup$
– Manfred Weis
Dec 18 '18 at 14:03












$begingroup$
thank you @ManfredWeis , for correcting my silly typo.
$endgroup$
– Carlo Beenakker
Dec 18 '18 at 14:48




$begingroup$
thank you @ManfredWeis , for correcting my silly typo.
$endgroup$
– Carlo Beenakker
Dec 18 '18 at 14:48




2




2




$begingroup$
"really amazing" - is that one of those understatements mathematicians are fond of?
$endgroup$
– davidbak
Dec 18 '18 at 16:02




$begingroup$
"really amazing" - is that one of those understatements mathematicians are fond of?
$endgroup$
– davidbak
Dec 18 '18 at 16:02


















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