Lightnews — Scholar-powered news

benjamin dickman

@benjamindickman.bsky.social

1.4K followers 410 following 2.5K posts

K-12 math educator 🪄♾️ Brookline to Nanjing to NYC Amherst College BA Fulbright Program x2 (🇨🇳+🇵🇭) Teachers College, Columbia University PhD past BU Wheelock (postdoc, Math Edu) cocreated original word game: #FiddleBrix http://tinyurl.com/bmdmaths

tinyurl.com

Posts Media Videos Starter Packs

Pinned

benjamin dickman @benjamindickman.bsky.social · 17d

my favorite #sensemaking excerpt

from:
Kegan, Robert. The evolving self: Problem and process in human development. Harvard University Press, 1982.

preview in google books:
books.google.com/books?id=SP3...

not overtly about 'mathematics' per se but w/e
#iTeachMath ♾️ #MathSky 🧮

screenshot of text beginning "these days my daughter" and ending with "parenthood, friendship, and love"

1 6

benjamin dickman @benjamindickman.bsky.social · 7h

i read Who's Afraid of Gender (previous school year) and it was hard reading in multiple ways (sadly prescient; dense and overly fond of the word phantasm)

benjamin dickman @benjamindickman.bsky.social · 10h

day 2 of LinkedOut games:
still playing them when I first wake up instead of when I'm fully awake; still xcl on phone

benjamin dickman @benjamindickman.bsky.social · 19h

as the good lord intended!!

yes, my initials are a nickname I sometimes use

and, correspondingly re: anagrams,

nickname BD = Ben Dickman

(capitalization held constant!)

benjamin dickman @benjamindickman.bsky.social · 19h

great #2solve pairing today for this Tue solve!

1 2

benjamin dickman @benjamindickman.bsky.social · 1d

totally agreed, xcl gotta be on ⌨️ and Zip Tango Queens on 📱

mixed on Sudoku, which isn't my strong suit

benjamin dickman @benjamindickman.bsky.social · 1d

LinkedOut games dropping a public leaderboard [for connections] is going to shift my playing style from wake up [first thing in the morning, still half asleep] to blitz [wait until later, play fully awake]. not sure if this is an improvement!

PS: play #FiddleBrix for true 🔡 joy!!
www.fiddlebrix.com

screenshot of fiddlebrix.com landing page; a 5x5 board contains the letters in play, beneath it are the tiles ("brix") spelling out FiddleBrix; beneath that is the phrase "A colorful daily word puzzle"; at the bottom are two buttons to download (one for Apple and one for Android)

3 3

benjamin dickman @benjamindickman.bsky.social · 2d

minimal #2solve for Monday 6 Oct 2025:

01001111 01010110 01000101 01010010 01000110 01001001 01010100 01010011 00100000 01010011 01001000 01000001 01010111 01001100

2 2

benjamin dickman @benjamindickman.bsky.social · 2d

see also the account written up by Terry Tao on Mathstodon:
mathstodon.xyz/@tao/1153167...

Terence Tao (@[email protected])

An update on my previous post https://mathstodon.xyz/@tao/115306424727150237 regarding how I was able to use modern AI to help solve a MathOverflow problem. Superficially, this story favors the "you ...

mathstodon.xyz

benjamin dickman @benjamindickman.bsky.social · 2d

🤨

1 3

benjamin dickman @benjamindickman.bsky.social · 3d

And that latter example is included in a Jan 2013 MathOverflow answer of mine:
mathoverflow.net/a/118023/22971

Elementary examples of the Weil conjectures

I'm looking for examples of the Weil conjectures---specifically rationality of the zeta function---that can be appreciated with minimal background in algebraic geometry. Are there varieties for wh...

mathoverflow.net

1 1

benjamin dickman @benjamindickman.bsky.social · 3d

idk what the norm is but I feel like they look pretty similar 🤔 and that a 2016 Master's Thesis would've surely included googling that would find my 2008 Undergrad Thesis ... 🧐

1 1

benjamin dickman @benjamindickman.bsky.social · 3d

others have assigned that in the past; not a bad idea for next summer's assignment !

benjamin dickman @benjamindickman.bsky.social · 3d

Koblitz did, which is the book that we both used... But the latter is one exercise among many

1 1

benjamin dickman @benjamindickman.bsky.social · 3d

this got me to google Dwork's Theorem since my undergrad thesis was un/acceptably called: On a Theorem of Dwork

I found another person wrote a Master's thesis about the same theorem 8 years after me; how similar do the examples look in these screenshots? 🤔

Screenshot of two examples related to Dwork's Theorem

Screenshot of text with three examples of Dwork's Theorem; compared the first and last here to the other image

1 1

benjamin dickman @benjamindickman.bsky.social · 3d

same Sunday #2solve (I thought the second word meant easy to steal but you're right that it just means small)(which, ofc, would also make it easier to steal)

1 1

benjamin dickman @benjamindickman.bsky.social · 3d

this table contains the various conclusions and links that seem to have stemmed mostly from this very nice wonder on MathOverflow:
mathoverflow.net/a/501203/22971

#MathSky 🧮 #iTeachMath ♾️

Is the least common multiple sequence $\text{lcm}(1, 2, \dots, n)$ a subset of the highly abundant numbers?

I've been comparing the sequence of the Least Common Multiple of the first $n$ integers, $L_n = \text{lcm}(1, 2, \dots, n)$, with the sequence of Highly Abundant Numbers (HA). The two sequences in

mathoverflow.net

1 3

benjamin dickman @benjamindickman.bsky.social · 3d

fascinating conjecture answered in the negative and elaborated:
mathoverflow.net/q/501066/22971

For numbers of the form:
lcm(1,2,...,n)

Conjecture:
All such numbers are "highly abundant" (n is HA means divisor sum n strictly > divisor sum for all naturals less than n)

MO: Eventually always false!

mathoverflow.net

1 1 7

benjamin dickman @benjamindickman.bsky.social · 3d

if my twittxr is visible to you they're in the 🔐 account here:
x.com/benjamindick...

x.com

benjamin dickman @benjamindickman.bsky.social · 3d

I assigned that reading this year, I posted the assignment somewhere on Bsky... Assigned Francis Su Mathematics for Human Flourishing the year before (summer reading for all HS students). Not sure what I'll do next...

1 4

benjamin dickman @benjamindickman.bsky.social · 3d

I had a lesson that I think a former LMS swallowed with readings about Algebra 2 and its necessity (or lack thereof)... ANAR was part of that. I may be able to locate it...

For NCLB etc definitely R Gutierrez on gap-gazing fetish

1 1

benjamin dickman @benjamindickman.bsky.social · 3d

I talk about it in decades so roughly
1960 New Math (without specifics of SMSG initial planning etc)
1970 Back to Basics Movement
1980 A Nation At Risk (have read intro with students... they enjoyed it??)
1990ish NCTM standards
2000ish NCLB
2010 CCSSM
2020ish Remote Teaching & DEI efforts

1 7

benjamin dickman @benjamindickman.bsky.social · 5d

same #2solve, not sure 🤔 definitely a word I look for in Boggle (as well as the dance w the same prefix)

benjamin dickman @benjamindickman.bsky.social · 5d

^yeah this is how I feel too lol

benjamin dickman @benjamindickman.bsky.social · 5d

by which I mean, if you have

ax²+bx+c

the p value (x coordinate of the vertex) isn't affected by c, so may as well set c=0

ax²+bx

this factors as

x(ax+b)

hence roots 0, -b/a

average of those roots is -b/2a

benjamin dickman @benjamindickman.bsky.social · 5d

to find p+q? or just p? bc yeah for p that's a fine method and definitely how I'd find the vertex of x²+x:

x(x+1) has roots 0, -1; so p = -½

still don't see a better way to find q than plugging in p, tho:
-½(½) = -¼

p+q = -½ + -¼ = -¾

now subtract 30

this is equivalent in my mind to using -b/2a

1 1