## Wednesday, June 6, 2012

### Wednesday Search Challenge (6/6/12): Who solves impossible problems... by accident?

Every so often you hear a story about some unwitting student solving a problem that they thought was part of their homework assignment, but was ACTUALLY an impossible-to-solve problem put on the whiteboard by their professor as an example.

Usually, the student is running late and wasn’t paying attention—or some such similar background detail that makes the story seem realistic. And the story is usually told about some famous mathematician--Newton, Einstein and Ramanujan are often mentioned.

But is this story (or some version of it) really true?

Question: Has some student accidentally  solved an impossible-problem by not knowing it was impossible?

If so, who, where, when, how... and what was the problem anyway?

The perfect answer won’t just repeat another apocryphal story, but will give a credible reference or two.  As Carl Sagan famously said, “extraordinary claims require extraordinary evidence.” [1]

Also, be sure to tell us how long it took you to find the answer AND the queries you used to drill your way towards the solution.

Search on!

________________________
[1] Carl Sagan  "Encyclopaedia Galactica,” episode 12 of “Cosmos”, original broadcast date, December 14, 1980; 01:24 minutes in. PBS.

1. That was trivial - snopes have done all the work :D

http://www.snopes.com/college/homework/unsolvable.asp

I searched for "Impossible problem solved by accident", and got the snopes article, with a good set of references, a setup for a movie, and further details.

Answer: George B. Dantzig, and the problems were two previously unsolved statistical analyses that he found written on the board, thinking they were part of a homework assignment.

See the article for a full list of sources - further searching seems to back this up quite nicely.

2. George Dantzig,UC Berekely, 1939, showed up late for a graduate level stats class

Searched for "student solves unsolvable math problem"

Got snopes article: http://www.snopes.com/college/homework/unsolvable.asp

3. George Dantzig, Berkely,1939, During my first year at Berkeley I arrived late one day to one of Neyman's classes. On the blackboard were two problems which I assumed had been assigned for homework. I copied them down. A few days later I apologized to Neyman for taking so long to do the homework -- the problems seemed to be a little harder to do than usual. I asked him if he still wanted the work. He told me to throw it on his desk. I did so reluctantly because his desk was covered with such a heap of papers that I feared my homework would be lost there forever."
"About six weeks later, one Sunday morning about eight o'clock, Anne and I were awakened by someone banging on our front door. It was Neyman. He rushed in with papers in hand, all excited: "I've just written an introduction to one of your papers. Read it so I can send it out right away for publication." For a minute I had no idea what he was talking about. To make a long story short, the problems on the blackboard which I had solved thinking they were homework were in fact two famous unsolved problems in statistics. That was the first inkling I had that there was anything special about them."

His studies were interrupted by the War but his dissertation was the solution to the two problems "I. Complete Form Neyman-Pearson Fundamental Lemma. II. On the Non-Existence of Tests of Student's Hypothesis Having Power Functions Independent of Sigma"

From http://www.umass.edu/wsp/statistics/tales/dantzig.html

There are multiple sources similar to this. Snopes.com led me to it with the search terms unsolvable problem and student. Took about 2-3 minutes to find all the information

4. [famous solved unsolvable problem] Took me to snopes! There I found George Danzig. http://www.snopes.com/college/homework/unsolvable.asp with credible references aplenty. An excellent reminder that any question beginning with "Have you ever heard about..." should be searched on snopes first! This probably took 30 seconds so I wonder if you were looking for something trickier.

5. found! i started off with good old google "student impossible solve" (elegant) and then added "example" and re-searched after finding this page on the first page of results for my first search. the re-search had a snopes page as my first result (http://www.snopes.com/college/homework/unsolvable.asp) which made me very happy, since i know they would cite references if true. and success! george dantzig, with all the gritty details and references. took about 5 minutes.

6. It looks like this was George Dantzig, in 1939 at Berkley. His professor put two equations on the board, George assumed they were homework and solved them over the next couple of days. His professor [Neyman] showed up at his house 6 weeks later asking him if he could publish the work. I found details of the story in both his obituary from the washington post (http://supernet.isenberg.umass.edu/photos/gdobit.html) and an excerpt from the College of Mathematics journal, found on snopes.com (http://www.snopes.com/college/homework/unsolvable.asp).

7. Search string "student solves impossible problem snopes"

8. This took me about 30min to complete.

It seems George Dantzig did this in 1939 while he was a graduate student at UC Berkeley.

First I started with a search on "Solve Impossible Math Problem". Which actually led me to http://www.snopes.com/college/homework/unsolvable.asp

There I learned of George Dantzig.

Google Search "George Dantzig" to find further proof led me to:

http://en.wikipedia.org/wiki/George_Dantzig
http://www-history.mcs.st-and.ac.uk/Biographies/Dantzig_George.html
D J Albers, G L Alexanderson and C Reid, More mathematical people. Contemporary conversations (Boston, MA, 1990).
D J Albers and C Reid, An interview with George B. Dantzig : the father of linear programming, College Math. J. 17 (4) (1986), 293-314.
http://www.umass.edu/wsp/statistics/tales/dantzig.html
http://www.ams.org/notices/200703/fea-cottle.pdf

All of these give the same story, that while he was at UC Berkley, he was late to class copied down two Statistical Problems from the board and thought they were homework problems. He handed them in and 6 weeks later his professor (Jerzy Neyman) said they were ready for publication.

Of course this story was later used in Good Will Hunting and Rushmore.

Methodology:

[ unsolved problem accidentally solved by student ]
The second search result leads to a snopes.com article at http://goo.gl/UqaIk about one George Bernard Dantzig (1914-2005) who worked out proofs to two then-unproved statistical theorems that he mistook to be homework problems after his professor had written them on a chalkboard in 1939.

The Wikipedia entry for George Dantzig points to the following reference:

Cottle, Richard; Johnson, Ellis; Wets, Roger, "George B. Dantzig (1914-2005)", Notices of the American Mathematical Society, v.54, no.3, March 2007. (Available at http://goo.gl/wSf5c )

which states:

"Arriving late to one of Neyman’s classes,Dantzig saw two problems written on the blackboard and mistook them for a homework assignment. He found them more challenging than usual, but managed to solve them and submitted them directly to Neyman. As it turned out, these problems were actually two open questions in the theory of mathematical statistics."

Time: 15 seconds to find the snopes.com article; another 10 minutes to read it and find the reference on Dantzig's Wikipedia page.

10. Took me around 30 seconds. I googled "impossible math problem solved" and read the third hit, from Snopes:

http://www.snopes.com/college/homework/unsolvable.asp

George Bernard Dantzig is the solver, and the article cites sources such as first-hand interviews with the solver.

11. A quick Google search for "student solves impossible problem" revealed a Snopes.com article (http://www.snopes.com/college/homework/unsolvable.asp) Searching for "george dantzig obituary" revealed the Washington Post obituary here:http://www.washingtonpost.com/wp-dyn/content/article/2005/05/18/AR2005051802171.html.

12. I just googled "student solves proof"

It came up on Snopes: http://www.snopes.com/college/homework/unsolvable.asp

Albers, Donald J. and Constance Reid.
"An Interview of George B. Dantzig: The Father of Linear Programming."
College Mathematics Journal. Volume 17, Number 4; 1986 (pp. 293-314).

Brunvand, Jan Harold. Curses! Broiled Again!
New York: W. W. Norton, 1989. ISBN 0-393-30711-5 (pp. 278-283).

Dantzig, George B.
"On the Non-Existence of Tests of 'Student's' Hypothesis Having Power Functions
Independent of Sigma."
Annals of Mathematical Statistics. No. 11; 1940 (pp. 186-192).

Dantzig, George B. and Abraham Wald. "On the Fundamental Lemma of Neyman and Pearson."
Annals of Mathematical Statistics. No. 22; 1951 (pp. 87-93).

Pearce, Jeremy. "George B. Dantzig Dies at 90."
The New York Times. 23 May 2005.

13. Found with one search of "student impossible problem" on google. First item was http://www.snopes.com/college/homework/unsolvable.asp

who: George Dantzig
where: University of California, Berkeley
when: 1939
how: statistics class in Neyman's class

14. 4 clicks, 3 minutes:

Google "true story inspiration for good will hunting"

Clicked the second link: http://www.forumgarden.com/forums/science/50269-real-good-will-hunting.html ....nope, different story

Scanned the page, fourth link down:
www.snopes.com/college/homework/unsolvable.asp

....snopes mentioned him by name: George Dantzig

Wikipedia from that point, read the "Mathematical statistics" subsection. 2 references listed in the Wikipedia entry.

15. George Dantzig, graduate student at UC Berkley in 1939. Near the beginning of class, professor wrote 2 famously unsolved statistical problems on the board. Arriving late, Dantzing believed this to be homework and, though it was "harder than usual," turned the solutions in a few days later.
Solved linear programming problems with the creation of the simplex algorithm. Later, when struggling for a thesis topic, the teacher just accepted these solutions in a binder.

started out with teacher/student impossible, problems, etc; moved to "real life good will hunting" but discovered it was a janitor with a high iq - not one that had solved a problem; switched to "real life good will hunting solved problem" to narrow the results). Snopes was the 3rd result with this and gave me the answer, Wikipedia confirmed.

16. George Dantzig - the theorems are described in these papers:

G. B. Dantzig, On the non-existence of tests of “Student’s” hypothesis having power functions in- dependent of sigma, Ann. Math. Stat. 11 (1940), 186–192.

G. B. Dantzig and A. Wald, On the fundamental lemma of Neyman and Pearson, Ann. Math. Stat. 22 (1951), 87–93.

Not impossible, just not solved at the time. Found the initial story by googling "solved impossible problem homework", then "george danzig unsolved problems", then "theorems george dantzig proved as homework". Took about 10 mins.

17. George Bernard Danzig solved a statistics problem that he believed to be a part of a homework assignment. They are more accurately not unsolvable problems, but unproven statistical theorems for which he worked out proofs. References to prove the validity of this claim are located at http://www.snopes.com/college/homework/unsolvable.asp, and the search was done in google by searching for "student solves impossible math problem" and clicking on the first link. It took about 20 seconds.

18. George Dantzig.

http://www.snopes.com/college/homework/unsolvable.asp

I just googled "dantzig unsolved problem student" which lead to the dantzig wikipedia entry (because i recalled that it was dantzig :)

but if you just google "unsolved problem student" it leads directly to the snopes entry about dantzig.

19. This was not that difficult (although it looked it). It took about 10 minutes to get the right answer (but 2 minutes or less to get my first try - and a few minutes checking to see if it was correct). So actual searching - 2-3 minutes.

My first attempts used Google with these search terms:
"solved by accident" "maths problem"
I made an assumption that the type of problem that would match would have to be a maths problem - as those are the ones that seem impossible to solve, but do get solved (e.g. like Fermat's last theorem).

That quickly brought up a very recent news story about Shouryya Ray, a schoolboy who reported solved a puzzle "posed by Sir Isaac Newton that have baffled mathematicians for 350 years".
http://www.dailymail.co.uk/news/article-2150225/Shouryya-Ray-solves-puzzles-posed-Sir-Isaac-Newton-baffled-mathematicians-350-years.html#ixzz1x34iFcSy

The problem with this is that on further searching it seems that the solution he came up with wasn't new, and as Ray was entering a competition I'm not sure that "accidental" is the right description for what Ray achieved.

So I carried on searching. I reasoned that the chances are that if this had happened, the mathematician would be known and important. So I tried:
"impossible problem" mathematicians solved

The story repeats the idea of whether this was an urban myth and says no - naming George Bernard Dantzig

Looking him up gave lots of references - all mentioning his solving an impossible problem as a student by turning up late and not knowing the problem was unsolved.

His obituary is as good a reference as any as it's from Stanford.
http://news.stanford.edu/news/2006/june7/memldant-060706.html and also http://www.stanford.edu/group/SOL/GBD/cottle-johnson-wets-2007.pdf

WHO: George Bernard Dantzig
WHERE: University of California, Berkeley
WHEN: 1939 (Source: http://en.wikipedia.org/wiki/George_Dantzig)
HOW: Dantzig arrived late to a lecture by the Statistics professor, Jerzy Neyman. He copied down two problems from the blackboard thinking that they were homework assignments. They were in fact open, unsolved questions - but Dantzig solved them (although he thought that they were harder than usual).
WHAT: Two statistical problems - one connected to "Student's" Hypothesis and power functions, and the 2nd to do with the Neyman Pearson lemma. (Reference 12 in http://www.stanford.edu/group/SOL/GBD/cottle-johnson-wets-2007.pdf)

20. 5 minutes - indian boy who solved math problem -> http://ibnlive.in.com/news/indian-boy-solves-350yearold-math-problem/261730-2.html

1. ...except he didn't. This is media hype

21. This may not be the "impossible" problem mentioned - but it seems that George Bernard Dantzig performed a similar feat in 1939 by creating proofs for as-yet unsolved statistics problems at UC Berkeley during a graduate-level stats exam.

http://www.snopes.com/college/homework/unsolvable.asp

Query: "Student solve impossible problem" from the lovely Drive-in google intro page.

22. George Bernard Dantzing

took a very short time

5:42 PM
student solves impossible problem - Google Search

5:41 PM
student solved unknown problem - Google Search

5:41 PM
solved unknown problem - Google Search

5:41 PM
solve unknown problem - Google Search

led me to
http://www.snopes.com/college/homework/unsolvable.asp

full story is there

23. http://www.snopes.com/college/homework/unsolvable.asp

24. The student was George Bernard Dantzig, and he 'solved two open problems in statistical theory which he had mistaken for homework after arriving late to a lecture of Jerzy Neyman.' (see his wikipedia page)

Sources

- http://www.snopes.com/college/homework/unsolvable.asp

- http://en.wikipedia.org/wiki/George_Dantzig (yes wikipedia IS credible)

- D J Albers, G L Alexanderson and C Reid, More mathematical people. Contemporary conversations (Boston, MA, 1990).

- Time taken: about 2 mins to find a result, 8 mins for the sources -

25. It took under 1 minute, same way as previous commenters.

An Indian/German student, Shouryya Ray, was recently credited in the press with solving an old problem posed by Newton 350 years ago. I was curious, I found a neat paper written by Prof. Dr. Ralph Chill and Prof. Dr. JÃ¼rgen Voigt disproving the claim.

“Nevertheless all his steps are basically known to experts, and we emphasize that he did not solve an open problem posed by Newton.”

26. I took a slightly different route but also came up with Dantzig:

I went to books.google.com and searched for: "newton unsolvable problem chalkboard"

The second result -- http://books.google.com/books?id=qCehlw21nwgC&pg=PA279&dq=newton+unsolvable+problem+chalkboard&hl=en&sa=X&ei=dVHQT4SKKuXW2AXewqHaDA&ved=0CDwQ6AEwAQ#v=onepage&q=newton%20unsolvable%20problem%20chalkboard&f=false -- from a book about urban legends has the Dantzig tale too, however, it also has a related story of 23-year old University of Chicago student Robert Garisto who discovered an error in Newton's equations which were at the time 350 years old. Interesting.

Total search time < 1 minute.

27. http://goo.gl/B2LZq
Shouryya Ray
Dresden, Germany

28. I started (incorrectly) thinking that this had something to do with your earlier post about The Egg of Columbus or Gordian Knot. After wasting a few minutes on that I started typing in Google [student solves...] Autocomplete suggested [student solves unsolvable math problem]

That took me to the Snopes article about George Dantzig. I was thinking it would be an urban legend and was surprised to find that it was labeled True. http://www.snopes.com/college/homework/unsolvable.asp

I tried to fact check their references by trying to find a copy of the article in the College Mathematics Journal
["An Interview of George B. Dantzig: The Father of Linear Programming"]

I tried looking for it at http://www.maa.org/pubs/cmj.html
and saw that they have many of their issues available through JSTOR. After checking every library system I have access to I had to give up. None of my libraries offer JSTOR access.

I was able to find a few obituaries that tell his story from the interview about solving the unsolvable problems.
Source Citation
Rubenstein, Steve. "George Bernard Dantzig -- Stanford math professor." San Francisco Chronicle 16 May 2005: B3. Gale Biography In Context. Web. 6 June 2012.
Document URL

For the question: Has some student accidentally  solved an impossible-problem by not knowing it was impossible? YES

29. 5 mins or so:

Search "students solving impossible problems", grin past the lifehacker link and read the snopes entry
Coorelate their version by searching for "dantzig credible source"
Found a 1999 CNN chatpage with Jan Harold Brunvand who credit an interview with Professor Dantzig
Then searched "jan harold brunvand dantzig" and found an extract from "A Digression on Urban Legends and 'Falsehood'" citing Brunvand's book "The Choking Doberman" on page 282.

I think that is more of the perfect answer. Thanks

30. It is interesting as a new reader to note how many of my fellow researchers chose to verify their answer after finding it on snopes.

I learned to research in the days before full text online. Using a source as authoritative as snopes (15 year track record, touchstone of popular online research) I eyeball the citations to make sure it doesn't look like the Mikkelsons have lost their minds, but I don't bother to double-check them any more than I would have double-checked the printed citations in a trusted source in 1989.

Is this old fashioned of me? Since it only takes five more minutes to verify the citations of a trusted source, I could see adopting the practice of checking them before considering my work done -- but I also see a whole lot of five minutes spent verifying that yep, trustworthy sources are trustworthy. Thoughts?

1. I tend to double-check everything--even Snopes, even the NYTimes--it's not that I'm distrustful, it's because I've found that everyone (including me!) make mistakes. Often it's unintentional, but given that it's pretty quick and usually fairly simple to verify through a second source, I think it's a good practice. So, just as you said, "it only take five more minutes to verify the citations..." and maybe another couple of minutes to get another, different source to crosscheck.

I've just found too many errors in "usually trustworthy" sources. So I *always* check again.