What are some noteworthy “mic-drop” moments in math?How did Cole factor $2^67-1$ in 1903What are some slogans that express mathematical tricks?What are some good resources for mathematical translation?What are some famous rejections of correct mathematics?What are some applications of other fields to mathematics?What are some good group theory references?What are some mathematical sculptures?Noteworthy achievements in and around 2010? What are some Applications of Teichmüller Theory?What are some deep theorems, and why are they considered deep?Higher Moments, what are they good for?
What are some noteworthy “mic-drop” moments in math?
How did Cole factor $2^67-1$ in 1903What are some slogans that express mathematical tricks?What are some good resources for mathematical translation?What are some famous rejections of correct mathematics?What are some applications of other fields to mathematics?What are some good group theory references?What are some mathematical sculptures?Noteworthy achievements in and around 2010? What are some Applications of Teichmüller Theory?What are some deep theorems, and why are they considered deep?Higher Moments, what are they good for?
$begingroup$
Oftentimes in math the manner in which a solution to a problem is announced becomes a significant chapter/part of the lore associated with the problem, almost being remembered more than the manner in which the problem was solved. I think that most mathematicians as a whole, even upon solving major open problems, are an extremely humble lot. But as an outsider I appreciate the understated manner in which some results are dropped.
The very recent example that inspired this question:
- In updating his homepage to a single, austere line, Tim Browning announced a solution to $a^3+b^3+c^3=33$ with $(a,b,c)inmathbbZ^3$ as $$(a,b,c)=(8866128975287528,-8778405442862239,-2736111468807040).$$ In the update, Dr. Browning did not even indicate that this is/was a semi-famous open problem, nor did he indicate that the cubes actually sum to $33$, apparently leaving it as an exercise for the reader.
Other examples that come to mind include:
- In 1976 after Appel and Hakken had proved the Four Color Theorem, Appel etched on the University of Illinois' math department blackboard "Modulo careful checking, it appears that four colors suffice." The statement "Four Colors Suffice" was used as the stamp for the University of Illinois at least around 1976.
- In 1697 Newton famously offered an "anonymous solution" to the Royal Society to the Brachistochrone problem that took him a mere evening/sleepless night to resolve. I think the story is noteworthy also because Johanne Bernoulli is said "recognized the lion by his claw."
- As close to a literal "mic-drop" as I can think of, after noting in his 1993 lectures that Fermat's Last Theorem was a mere corollary of the work presented, Andrew Wiles famously ended his lecture by stating "I think I'll stop here."
What are other noteworthy examples of such announcements in math that are, in some sense, memorable for being understated? Say to an outsider in the field?
Cole's silent 1903 lecture factoring Mersenne prime $M_67$ would be a good contender, if it were actually true. Watson and Crick's famous ending of their DNA paper, "It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material," has a bit of the same feel...
soft-question big-list
$endgroup$
|
show 1 more comment
$begingroup$
Oftentimes in math the manner in which a solution to a problem is announced becomes a significant chapter/part of the lore associated with the problem, almost being remembered more than the manner in which the problem was solved. I think that most mathematicians as a whole, even upon solving major open problems, are an extremely humble lot. But as an outsider I appreciate the understated manner in which some results are dropped.
The very recent example that inspired this question:
- In updating his homepage to a single, austere line, Tim Browning announced a solution to $a^3+b^3+c^3=33$ with $(a,b,c)inmathbbZ^3$ as $$(a,b,c)=(8866128975287528,-8778405442862239,-2736111468807040).$$ In the update, Dr. Browning did not even indicate that this is/was a semi-famous open problem, nor did he indicate that the cubes actually sum to $33$, apparently leaving it as an exercise for the reader.
Other examples that come to mind include:
- In 1976 after Appel and Hakken had proved the Four Color Theorem, Appel etched on the University of Illinois' math department blackboard "Modulo careful checking, it appears that four colors suffice." The statement "Four Colors Suffice" was used as the stamp for the University of Illinois at least around 1976.
- In 1697 Newton famously offered an "anonymous solution" to the Royal Society to the Brachistochrone problem that took him a mere evening/sleepless night to resolve. I think the story is noteworthy also because Johanne Bernoulli is said "recognized the lion by his claw."
- As close to a literal "mic-drop" as I can think of, after noting in his 1993 lectures that Fermat's Last Theorem was a mere corollary of the work presented, Andrew Wiles famously ended his lecture by stating "I think I'll stop here."
What are other noteworthy examples of such announcements in math that are, in some sense, memorable for being understated? Say to an outsider in the field?
Cole's silent 1903 lecture factoring Mersenne prime $M_67$ would be a good contender, if it were actually true. Watson and Crick's famous ending of their DNA paper, "It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material," has a bit of the same feel...
soft-question big-list
$endgroup$
2
$begingroup$
The tale about Cole seems to have no basis in fact and was just a legend propagated by E. T. Bell, who was a former PhD student of Cole. Cole did have a real method of discovering the factorization (the answers to mathoverflow.net/questions/207321/… include a link to Cole's article) and it was not the "three years of Sundays" that Bell wrote. I therefore don't think the Cole story should be among your examples.
$endgroup$
– KConrad
1 hour ago
2
$begingroup$
The example of how Ramanujan's results came to the attention of Hardy and Littlewood is fairly well documented, and would be a better choice than Cole's "story".
$endgroup$
– KConrad
1 hour ago
1
$begingroup$
I'd say Yitang Zhang's submission in 2013 was pretty understated. Gerhard "Would This Be An Example?" Paseman, 2019.03.10.
$endgroup$
– Gerhard Paseman
1 hour ago
$begingroup$
@GerhardPaseman I think that's a good answer for posting - especially in light of his comments "I believe one could make it sharper" when people asked him if he thought $k < 70,000,000$ could be reduced.
$endgroup$
– Mark S
1 hour ago
$begingroup$
"etched" suggests to me an irreversible change to the blackboard. Other sources give different accounts. Robin Wilson, Four Colors Suffice, writes, "He celebrated their achievement by placing a notice on the department's blackboard...." Steven Miller, Mathematics of Optimization, writes, "Appel famously celebrated this achievement by writing the words ... on the blackboard...."
$endgroup$
– Gerry Myerson
26 mins ago
|
show 1 more comment
$begingroup$
Oftentimes in math the manner in which a solution to a problem is announced becomes a significant chapter/part of the lore associated with the problem, almost being remembered more than the manner in which the problem was solved. I think that most mathematicians as a whole, even upon solving major open problems, are an extremely humble lot. But as an outsider I appreciate the understated manner in which some results are dropped.
The very recent example that inspired this question:
- In updating his homepage to a single, austere line, Tim Browning announced a solution to $a^3+b^3+c^3=33$ with $(a,b,c)inmathbbZ^3$ as $$(a,b,c)=(8866128975287528,-8778405442862239,-2736111468807040).$$ In the update, Dr. Browning did not even indicate that this is/was a semi-famous open problem, nor did he indicate that the cubes actually sum to $33$, apparently leaving it as an exercise for the reader.
Other examples that come to mind include:
- In 1976 after Appel and Hakken had proved the Four Color Theorem, Appel etched on the University of Illinois' math department blackboard "Modulo careful checking, it appears that four colors suffice." The statement "Four Colors Suffice" was used as the stamp for the University of Illinois at least around 1976.
- In 1697 Newton famously offered an "anonymous solution" to the Royal Society to the Brachistochrone problem that took him a mere evening/sleepless night to resolve. I think the story is noteworthy also because Johanne Bernoulli is said "recognized the lion by his claw."
- As close to a literal "mic-drop" as I can think of, after noting in his 1993 lectures that Fermat's Last Theorem was a mere corollary of the work presented, Andrew Wiles famously ended his lecture by stating "I think I'll stop here."
What are other noteworthy examples of such announcements in math that are, in some sense, memorable for being understated? Say to an outsider in the field?
Cole's silent 1903 lecture factoring Mersenne prime $M_67$ would be a good contender, if it were actually true. Watson and Crick's famous ending of their DNA paper, "It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material," has a bit of the same feel...
soft-question big-list
$endgroup$
Oftentimes in math the manner in which a solution to a problem is announced becomes a significant chapter/part of the lore associated with the problem, almost being remembered more than the manner in which the problem was solved. I think that most mathematicians as a whole, even upon solving major open problems, are an extremely humble lot. But as an outsider I appreciate the understated manner in which some results are dropped.
The very recent example that inspired this question:
- In updating his homepage to a single, austere line, Tim Browning announced a solution to $a^3+b^3+c^3=33$ with $(a,b,c)inmathbbZ^3$ as $$(a,b,c)=(8866128975287528,-8778405442862239,-2736111468807040).$$ In the update, Dr. Browning did not even indicate that this is/was a semi-famous open problem, nor did he indicate that the cubes actually sum to $33$, apparently leaving it as an exercise for the reader.
Other examples that come to mind include:
- In 1976 after Appel and Hakken had proved the Four Color Theorem, Appel etched on the University of Illinois' math department blackboard "Modulo careful checking, it appears that four colors suffice." The statement "Four Colors Suffice" was used as the stamp for the University of Illinois at least around 1976.
- In 1697 Newton famously offered an "anonymous solution" to the Royal Society to the Brachistochrone problem that took him a mere evening/sleepless night to resolve. I think the story is noteworthy also because Johanne Bernoulli is said "recognized the lion by his claw."
- As close to a literal "mic-drop" as I can think of, after noting in his 1993 lectures that Fermat's Last Theorem was a mere corollary of the work presented, Andrew Wiles famously ended his lecture by stating "I think I'll stop here."
What are other noteworthy examples of such announcements in math that are, in some sense, memorable for being understated? Say to an outsider in the field?
Cole's silent 1903 lecture factoring Mersenne prime $M_67$ would be a good contender, if it were actually true. Watson and Crick's famous ending of their DNA paper, "It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material," has a bit of the same feel...
soft-question big-list
soft-question big-list
edited 1 hour ago
community wiki
Mark S
2
$begingroup$
The tale about Cole seems to have no basis in fact and was just a legend propagated by E. T. Bell, who was a former PhD student of Cole. Cole did have a real method of discovering the factorization (the answers to mathoverflow.net/questions/207321/… include a link to Cole's article) and it was not the "three years of Sundays" that Bell wrote. I therefore don't think the Cole story should be among your examples.
$endgroup$
– KConrad
1 hour ago
2
$begingroup$
The example of how Ramanujan's results came to the attention of Hardy and Littlewood is fairly well documented, and would be a better choice than Cole's "story".
$endgroup$
– KConrad
1 hour ago
1
$begingroup$
I'd say Yitang Zhang's submission in 2013 was pretty understated. Gerhard "Would This Be An Example?" Paseman, 2019.03.10.
$endgroup$
– Gerhard Paseman
1 hour ago
$begingroup$
@GerhardPaseman I think that's a good answer for posting - especially in light of his comments "I believe one could make it sharper" when people asked him if he thought $k < 70,000,000$ could be reduced.
$endgroup$
– Mark S
1 hour ago
$begingroup$
"etched" suggests to me an irreversible change to the blackboard. Other sources give different accounts. Robin Wilson, Four Colors Suffice, writes, "He celebrated their achievement by placing a notice on the department's blackboard...." Steven Miller, Mathematics of Optimization, writes, "Appel famously celebrated this achievement by writing the words ... on the blackboard...."
$endgroup$
– Gerry Myerson
26 mins ago
|
show 1 more comment
2
$begingroup$
The tale about Cole seems to have no basis in fact and was just a legend propagated by E. T. Bell, who was a former PhD student of Cole. Cole did have a real method of discovering the factorization (the answers to mathoverflow.net/questions/207321/… include a link to Cole's article) and it was not the "three years of Sundays" that Bell wrote. I therefore don't think the Cole story should be among your examples.
$endgroup$
– KConrad
1 hour ago
2
$begingroup$
The example of how Ramanujan's results came to the attention of Hardy and Littlewood is fairly well documented, and would be a better choice than Cole's "story".
$endgroup$
– KConrad
1 hour ago
1
$begingroup$
I'd say Yitang Zhang's submission in 2013 was pretty understated. Gerhard "Would This Be An Example?" Paseman, 2019.03.10.
$endgroup$
– Gerhard Paseman
1 hour ago
$begingroup$
@GerhardPaseman I think that's a good answer for posting - especially in light of his comments "I believe one could make it sharper" when people asked him if he thought $k < 70,000,000$ could be reduced.
$endgroup$
– Mark S
1 hour ago
$begingroup$
"etched" suggests to me an irreversible change to the blackboard. Other sources give different accounts. Robin Wilson, Four Colors Suffice, writes, "He celebrated their achievement by placing a notice on the department's blackboard...." Steven Miller, Mathematics of Optimization, writes, "Appel famously celebrated this achievement by writing the words ... on the blackboard...."
$endgroup$
– Gerry Myerson
26 mins ago
2
2
$begingroup$
The tale about Cole seems to have no basis in fact and was just a legend propagated by E. T. Bell, who was a former PhD student of Cole. Cole did have a real method of discovering the factorization (the answers to mathoverflow.net/questions/207321/… include a link to Cole's article) and it was not the "three years of Sundays" that Bell wrote. I therefore don't think the Cole story should be among your examples.
$endgroup$
– KConrad
1 hour ago
$begingroup$
The tale about Cole seems to have no basis in fact and was just a legend propagated by E. T. Bell, who was a former PhD student of Cole. Cole did have a real method of discovering the factorization (the answers to mathoverflow.net/questions/207321/… include a link to Cole's article) and it was not the "three years of Sundays" that Bell wrote. I therefore don't think the Cole story should be among your examples.
$endgroup$
– KConrad
1 hour ago
2
2
$begingroup$
The example of how Ramanujan's results came to the attention of Hardy and Littlewood is fairly well documented, and would be a better choice than Cole's "story".
$endgroup$
– KConrad
1 hour ago
$begingroup$
The example of how Ramanujan's results came to the attention of Hardy and Littlewood is fairly well documented, and would be a better choice than Cole's "story".
$endgroup$
– KConrad
1 hour ago
1
1
$begingroup$
I'd say Yitang Zhang's submission in 2013 was pretty understated. Gerhard "Would This Be An Example?" Paseman, 2019.03.10.
$endgroup$
– Gerhard Paseman
1 hour ago
$begingroup$
I'd say Yitang Zhang's submission in 2013 was pretty understated. Gerhard "Would This Be An Example?" Paseman, 2019.03.10.
$endgroup$
– Gerhard Paseman
1 hour ago
$begingroup$
@GerhardPaseman I think that's a good answer for posting - especially in light of his comments "I believe one could make it sharper" when people asked him if he thought $k < 70,000,000$ could be reduced.
$endgroup$
– Mark S
1 hour ago
$begingroup$
@GerhardPaseman I think that's a good answer for posting - especially in light of his comments "I believe one could make it sharper" when people asked him if he thought $k < 70,000,000$ could be reduced.
$endgroup$
– Mark S
1 hour ago
$begingroup$
"etched" suggests to me an irreversible change to the blackboard. Other sources give different accounts. Robin Wilson, Four Colors Suffice, writes, "He celebrated their achievement by placing a notice on the department's blackboard...." Steven Miller, Mathematics of Optimization, writes, "Appel famously celebrated this achievement by writing the words ... on the blackboard...."
$endgroup$
– Gerry Myerson
26 mins ago
$begingroup$
"etched" suggests to me an irreversible change to the blackboard. Other sources give different accounts. Robin Wilson, Four Colors Suffice, writes, "He celebrated their achievement by placing a notice on the department's blackboard...." Steven Miller, Mathematics of Optimization, writes, "Appel famously celebrated this achievement by writing the words ... on the blackboard...."
$endgroup$
– Gerry Myerson
26 mins ago
|
show 1 more comment
2 Answers
2
active
oldest
votes
$begingroup$
I consider this manner as a mark of a professional mathematician: let others convey the excitement of a discovery. A good recent example was the submission of a paper on bounded gaps between primes. Much of the public excitement was generated by people other than the author, Yitang Zhang.
Gerhard "Can Be Excited In Private" Paseman, 2019.03.10.
$endgroup$
add a comment |
$begingroup$
The best known lower bound for the minimal length of superpermutations was announced by an anonymous user of a wiki mainly devoted to anime.
The story is told at Mystery Math Whiz and Novelist Advance Permutation Problem, and the publication is at A lower bound on the length of the shortest superpattern, with "Anonymous 4chan Poster" as the first author.
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "504"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathoverflow.net%2fquestions%2f325105%2fwhat-are-some-noteworthy-mic-drop-moments-in-math%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I consider this manner as a mark of a professional mathematician: let others convey the excitement of a discovery. A good recent example was the submission of a paper on bounded gaps between primes. Much of the public excitement was generated by people other than the author, Yitang Zhang.
Gerhard "Can Be Excited In Private" Paseman, 2019.03.10.
$endgroup$
add a comment |
$begingroup$
I consider this manner as a mark of a professional mathematician: let others convey the excitement of a discovery. A good recent example was the submission of a paper on bounded gaps between primes. Much of the public excitement was generated by people other than the author, Yitang Zhang.
Gerhard "Can Be Excited In Private" Paseman, 2019.03.10.
$endgroup$
add a comment |
$begingroup$
I consider this manner as a mark of a professional mathematician: let others convey the excitement of a discovery. A good recent example was the submission of a paper on bounded gaps between primes. Much of the public excitement was generated by people other than the author, Yitang Zhang.
Gerhard "Can Be Excited In Private" Paseman, 2019.03.10.
$endgroup$
I consider this manner as a mark of a professional mathematician: let others convey the excitement of a discovery. A good recent example was the submission of a paper on bounded gaps between primes. Much of the public excitement was generated by people other than the author, Yitang Zhang.
Gerhard "Can Be Excited In Private" Paseman, 2019.03.10.
answered 54 mins ago
community wiki
Gerhard Paseman
add a comment |
add a comment |
$begingroup$
The best known lower bound for the minimal length of superpermutations was announced by an anonymous user of a wiki mainly devoted to anime.
The story is told at Mystery Math Whiz and Novelist Advance Permutation Problem, and the publication is at A lower bound on the length of the shortest superpattern, with "Anonymous 4chan Poster" as the first author.
$endgroup$
add a comment |
$begingroup$
The best known lower bound for the minimal length of superpermutations was announced by an anonymous user of a wiki mainly devoted to anime.
The story is told at Mystery Math Whiz and Novelist Advance Permutation Problem, and the publication is at A lower bound on the length of the shortest superpattern, with "Anonymous 4chan Poster" as the first author.
$endgroup$
add a comment |
$begingroup$
The best known lower bound for the minimal length of superpermutations was announced by an anonymous user of a wiki mainly devoted to anime.
The story is told at Mystery Math Whiz and Novelist Advance Permutation Problem, and the publication is at A lower bound on the length of the shortest superpattern, with "Anonymous 4chan Poster" as the first author.
$endgroup$
The best known lower bound for the minimal length of superpermutations was announced by an anonymous user of a wiki mainly devoted to anime.
The story is told at Mystery Math Whiz and Novelist Advance Permutation Problem, and the publication is at A lower bound on the length of the shortest superpattern, with "Anonymous 4chan Poster" as the first author.
answered 1 hour ago
community wiki
Carlo Beenakker
add a comment |
add a comment |
Thanks for contributing an answer to MathOverflow!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathoverflow.net%2fquestions%2f325105%2fwhat-are-some-noteworthy-mic-drop-moments-in-math%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
2
$begingroup$
The tale about Cole seems to have no basis in fact and was just a legend propagated by E. T. Bell, who was a former PhD student of Cole. Cole did have a real method of discovering the factorization (the answers to mathoverflow.net/questions/207321/… include a link to Cole's article) and it was not the "three years of Sundays" that Bell wrote. I therefore don't think the Cole story should be among your examples.
$endgroup$
– KConrad
1 hour ago
2
$begingroup$
The example of how Ramanujan's results came to the attention of Hardy and Littlewood is fairly well documented, and would be a better choice than Cole's "story".
$endgroup$
– KConrad
1 hour ago
1
$begingroup$
I'd say Yitang Zhang's submission in 2013 was pretty understated. Gerhard "Would This Be An Example?" Paseman, 2019.03.10.
$endgroup$
– Gerhard Paseman
1 hour ago
$begingroup$
@GerhardPaseman I think that's a good answer for posting - especially in light of his comments "I believe one could make it sharper" when people asked him if he thought $k < 70,000,000$ could be reduced.
$endgroup$
– Mark S
1 hour ago
$begingroup$
"etched" suggests to me an irreversible change to the blackboard. Other sources give different accounts. Robin Wilson, Four Colors Suffice, writes, "He celebrated their achievement by placing a notice on the department's blackboard...." Steven Miller, Mathematics of Optimization, writes, "Appel famously celebrated this achievement by writing the words ... on the blackboard...."
$endgroup$
– Gerry Myerson
26 mins ago