2,295 reputation
11342
bio website tc.columbia.edu/academics/…
location New York
age 28
visits member for 2 years
seen 13 hours ago

Benjamin Dickman is from Brookline, MA. After graduating from Amherst College, Dickman spent the following academic year in Nanjing, China, on a Fulbright Grant to study High School Mathematics Education. He returned to his host institution of Nanjing Normal University the following year on a Chinese government grant for Mandarin studies, and spent his free time becoming fluent in the Nanjing dialect. An avid Boggle player, Dickman is currently a National Science Foundation Graduate Fellow at Columbia University, pursuing his PhD in Mathematics Education.

Have you solved any of my puzzles? If so, send me an email!
Email: bmd2118[at]colunbia.edu. (Change n to m.)


15h
awarded  Yearling
Apr
4
answered A.J. Galitzer's Ph.D. thesis: On the moduli space of closed polygonal linkages on the 2-sphere
Mar
27
revised Elementary+Short+Useful
Removed first line asking for down-vote explanation; clearly it is not coming.
Mar
24
comment Matrix Transpose Similarility
Is the proof given here msp.org/pjm/1959/9-3/pjm-v9-n3-p25-p.pdf sufficiently "elementary"? Incidentally, note the remark on p.895 (pdf 4/7) comes from M. Newman; there was an earlier MO question answered using Smith's work (which you wish to avoid here...) that turned out to have a more elementary solution from M. Newman (mathoverflow.net/questions/151166/…). If the linked proof here does not suffice, perhaps Newman is the fellow to look to...
Mar
21
comment Finding closest point to a set of circles
With regard to Fermat's point etc, perhaps you can rig up a physical model to estimate where this point would be. See the related MO question mathoverflow.net/questions/104714/…
Mar
17
comment Analogues of P vs. NP in the history of mathematics
I think many were aware of (potential) equivalence (in ZF) between e.g. Zorn's Lemma and the Axiom of Choice, but there might be an example here if you do some digging: if not in terms of equivalence, then perhaps in terms of implied results. (Even today one formulation is frequently preferable over another depending on what one wishes to prove.)
Mar
16
answered Sources of Theorem drafts by the original author
Mar
3
awarded  Enlightened
Mar
3
awarded  Nice Answer
Mar
2
comment Number of vectors so that no two subset sums are equal
[So your results match up, thus far, with oeis.org/A214051.]
Mar
2
comment Number of vectors so that no two subset sums are equal
Surely someone has put the conjectured values into OEIS by now and seen oeis.org/A214051: 1, 1, 2, 4, 5, 7, 9, 12, 14, 16, 19, 21, 24, 27, 29, 32...
Feb
12
comment Is there a known solution to $f(x) = (1-x)f(x^2)$?
I think $1/f(x)$ gives the generating function for binary partitions. See, e.g., theory.cs.uvic.ca/inf/nump/BinaryPartition.html
Jan
19
comment Elementary group theory question
What's the motivation for the question? E.g., did you carry out computations for a lot of small groups and find such a statement to hold for them? (I'd be surprised if this is true for all finite groups...)
Jan
14
comment Probability two matching runs of coin tosses
Since all numerators are even, one might divide each by two and check OEIS. This gives oeis.org/A049539, which references: C. J. A. Jansen, Investigations on Nonlinear Stream cipher Systems: Construction and Evaluation Methods, Ph.D. Thesis, Delft University of Technology, The Netherlands, (1989), pp. 58-81. The thesis is available for free here: repository.tudelft.nl/assets/… (See, e.g., column 10, p.60; ii, p. 81.) Related are paths in a DeBruijn graph; but perhaps this is how you came to the problem initially...
Jan
11
comment How should you respond to a student who asks whether a very nice physical example constitutes a proof?
Just came across this (closed) question. Perhaps you would find this MO post to be of interest: mathoverflow.net/questions/104714/…
Jan
8
awarded  Benefactor
Jan
8
comment Probability that a stick randomly broken in five places can form a tetrahedron
I will be interested if there is a way to put in the last condition, and how far down this might bring the bound. It is clear to me that an explicit answer is very hard come-by! Thank you for giving the problem some thought.
Jan
7
comment Probability that a stick randomly broken in five places can form a tetrahedron
@AlexandreEremenko I'd hoped this was clarified by an earlier comment, which I re-paste here: I believe the problem in its original statement was meant only as a higher-dimension analogue of the 2D triangle one. Rephrasing from the linked MO post: "Pick five points uniformly at random on the stick, and break the stick at those points. What is the probability that the six segments obtained in this way form a tetrahedron?" If you see a more tractable problem under another reasonable interpretation, then I would be interested to see it!
Jan
7
reviewed Approve suggested edit on When is $L^2(X)$ separable?
Jan
4
comment Mathematical research published in the form of poems
Thanks for editing. I cannot speak to Indian mathematics, for my background in Asian languages is restricted to Chinese. For what it's worth, I think an earlier answer here makes the same questionable/unjustified claim about the poetry of Ancient Chinese mathematics: mathoverflow.net/a/153109/22971