benjamin dickman
@benjamindickman.bsky.social
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
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
Pinned
(PDF) Curriculum. Creativity in the Mathematics Classroom
PDF | This chapter investigates the emergent creativity of a single mathematics project carried out across multiple years and contexts with students... | Find, read and cite all the research you need ...
www.researchgate.net
an academicky update:
i finally got a preprint ("UNCORRECTED PROOF") for a chapter i wrote!
www.researchgate.net/publication/...
this is Chapter 5 (Curriculum. Creativity in the Mathematics Classroom) from:
Creative Contexts: Our Worlds as Actors in the Dynamics of Change
(ISBN: 978-3-032-12282-7)
i finally got a preprint ("UNCORRECTED PROOF") for a chapter i wrote!
www.researchgate.net/publication/...
this is Chapter 5 (Curriculum. Creativity in the Mathematics Classroom) from:
Creative Contexts: Our Worlds as Actors in the Dynamics of Change
(ISBN: 978-3-032-12282-7)
[me after being inexplicably granted access to the hyperuranion]
me: wow, so this is the so-called "Platonic realm"!
perfect circle:
perfect square:
me: lmao do y'all ever call it the "Friend Zone"???
me: wow, so this is the so-called "Platonic realm"!
perfect circle:
perfect square:
me: lmao do y'all ever call it the "Friend Zone"???
November 25, 2025 at 11:30 PM
[me after being inexplicably granted access to the hyperuranion]
me: wow, so this is the so-called "Platonic realm"!
perfect circle:
perfect square:
me: lmao do y'all ever call it the "Friend Zone"???
me: wow, so this is the so-called "Platonic realm"!
perfect circle:
perfect square:
me: lmao do y'all ever call it the "Friend Zone"???
yesterday students showed me math from something called "TickTock" (i think it's like SnapGram). it involved moving whiteboard markers to change their arrangements from 4321 to 1234; here it is in typed form:
with one X and O switch, convert:
X X X X O X X X O X X O X
to its reverse! #iTeachMath ♾️
with one X and O switch, convert:
X X X X O X X X O X X O X
to its reverse! #iTeachMath ♾️
November 25, 2025 at 2:29 PM
yesterday students showed me math from something called "TickTock" (i think it's like SnapGram). it involved moving whiteboard markers to change their arrangements from 4321 to 1234; here it is in typed form:
with one X and O switch, convert:
X X X X O X X X O X X O X
to its reverse! #iTeachMath ♾️
with one X and O switch, convert:
X X X X O X X X O X X O X
to its reverse! #iTeachMath ♾️
Article ❌🔓:
archive.ph/coei4
If you can access The Atlantic, the piece can be found here:
www.theatlantic.com/ideas/2025/1...
‘A Recipe for Idiocracy’
What happens when even college students can’t do math anymore?
By Rose Horowitch
archive.ph/coei4
If you can access The Atlantic, the piece can be found here:
www.theatlantic.com/ideas/2025/1...
‘A Recipe for Idiocracy’
What happens when even college students can’t do math anymore?
By Rose Horowitch
November 24, 2025 at 10:02 PM
Article ❌🔓:
archive.ph/coei4
If you can access The Atlantic, the piece can be found here:
www.theatlantic.com/ideas/2025/1...
‘A Recipe for Idiocracy’
What happens when even college students can’t do math anymore?
By Rose Horowitch
archive.ph/coei4
If you can access The Atlantic, the piece can be found here:
www.theatlantic.com/ideas/2025/1...
‘A Recipe for Idiocracy’
What happens when even college students can’t do math anymore?
By Rose Horowitch
I'm going to try that thing where you live-post through (hopefully) solving the problem. What's that called? #MathOutLoud? #RealTimeMath?
1/🧵
1/🧵
consider a subset of the first N positive integers:
S ⊆ {1, ..., N}
call S "mid" if, for every integer n, if n-1 and n+1 are elements of S, then n is in S.
#MathSky 🧮 #iTeachMath ♾️
example: if N=5, the set {2,3,4,5} is a mid subset.
⭐️ find a formula f(N) for the # of mid subsets of {1, ..., N} ⭐️
S ⊆ {1, ..., N}
call S "mid" if, for every integer n, if n-1 and n+1 are elements of S, then n is in S.
#MathSky 🧮 #iTeachMath ♾️
example: if N=5, the set {2,3,4,5} is a mid subset.
⭐️ find a formula f(N) for the # of mid subsets of {1, ..., N} ⭐️
November 23, 2025 at 4:37 PM
no calc before uni but advisor put me on REU about p-adic dynamics; thought math PhD could be cool!
took Chinese as a sidequest but didn't study abroad; dormmate brought me to an info session on fellowships.
got a Fulbright to learn about Chinese math T training; back in US, got a PhD in Math Edu.
took Chinese as a sidequest but didn't study abroad; dormmate brought me to an info session on fellowships.
got a Fulbright to learn about Chinese math T training; back in US, got a PhD in Math Edu.
November 23, 2025 at 3:14 PM
no calc before uni but advisor put me on REU about p-adic dynamics; thought math PhD could be cool!
took Chinese as a sidequest but didn't study abroad; dormmate brought me to an info session on fellowships.
got a Fulbright to learn about Chinese math T training; back in US, got a PhD in Math Edu.
took Chinese as a sidequest but didn't study abroad; dormmate brought me to an info session on fellowships.
got a Fulbright to learn about Chinese math T training; back in US, got a PhD in Math Edu.
> Bernshteyn took a logic course with Anush Tserunyan... “She should take all the credit for me being in this field,” he said. “She really made it seem that logic and set theory is this glue that connects all different parts of math.” #MathSky 🧮
www.quantamagazine.org/a-new-bridge...
www.quantamagazine.org/a-new-bridge...
A New Bridge Links the Strange Math of Infinity to Computer Science | Quanta Magazine
Descriptive set theorists study the niche mathematics of infinity. Now, they’ve shown that their problems can be rewritten in the concrete language of algorithms.
www.quantamagazine.org
November 23, 2025 at 2:52 PM
> Bernshteyn took a logic course with Anush Tserunyan... “She should take all the credit for me being in this field,” he said. “She really made it seem that logic and set theory is this glue that connects all different parts of math.” #MathSky 🧮
www.quantamagazine.org/a-new-bridge...
www.quantamagazine.org/a-new-bridge...
33 more years until 11 23 58
time to start brainstorming 🧠⛈️ fun ways to celebrate
time to start brainstorming 🧠⛈️ fun ways to celebrate
November 23, 2025 at 6:57 AM
33 more years until 11 23 58
time to start brainstorming 🧠⛈️ fun ways to celebrate
time to start brainstorming 🧠⛈️ fun ways to celebrate
consider a subset of the first N positive integers:
S ⊆ {1, ..., N}
call S "mid" if, for every integer n, if n-1 and n+1 are elements of S, then n is in S.
#MathSky 🧮 #iTeachMath ♾️
example: if N=5, the set {2,3,4,5} is a mid subset.
⭐️ find a formula f(N) for the # of mid subsets of {1, ..., N} ⭐️
S ⊆ {1, ..., N}
call S "mid" if, for every integer n, if n-1 and n+1 are elements of S, then n is in S.
#MathSky 🧮 #iTeachMath ♾️
example: if N=5, the set {2,3,4,5} is a mid subset.
⭐️ find a formula f(N) for the # of mid subsets of {1, ..., N} ⭐️
November 22, 2025 at 2:32 PM
consider a subset of the first N positive integers:
S ⊆ {1, ..., N}
call S "mid" if, for every integer n, if n-1 and n+1 are elements of S, then n is in S.
#MathSky 🧮 #iTeachMath ♾️
example: if N=5, the set {2,3,4,5} is a mid subset.
⭐️ find a formula f(N) for the # of mid subsets of {1, ..., N} ⭐️
S ⊆ {1, ..., N}
call S "mid" if, for every integer n, if n-1 and n+1 are elements of S, then n is in S.
#MathSky 🧮 #iTeachMath ♾️
example: if N=5, the set {2,3,4,5} is a mid subset.
⭐️ find a formula f(N) for the # of mid subsets of {1, ..., N} ⭐️
an academicky update:
i finally got a preprint ("UNCORRECTED PROOF") for a chapter i wrote!
www.researchgate.net/publication/...
this is Chapter 5 (Curriculum. Creativity in the Mathematics Classroom) from:
Creative Contexts: Our Worlds as Actors in the Dynamics of Change
(ISBN: 978-3-032-12282-7)
i finally got a preprint ("UNCORRECTED PROOF") for a chapter i wrote!
www.researchgate.net/publication/...
this is Chapter 5 (Curriculum. Creativity in the Mathematics Classroom) from:
Creative Contexts: Our Worlds as Actors in the Dynamics of Change
(ISBN: 978-3-032-12282-7)
(PDF) Curriculum. Creativity in the Mathematics Classroom
PDF | This chapter investigates the emergent creativity of a single mathematics project carried out across multiple years and contexts with students... | Find, read and cite all the research you need ...
www.researchgate.net
November 20, 2025 at 6:24 PM
an academicky update:
i finally got a preprint ("UNCORRECTED PROOF") for a chapter i wrote!
www.researchgate.net/publication/...
this is Chapter 5 (Curriculum. Creativity in the Mathematics Classroom) from:
Creative Contexts: Our Worlds as Actors in the Dynamics of Change
(ISBN: 978-3-032-12282-7)
i finally got a preprint ("UNCORRECTED PROOF") for a chapter i wrote!
www.researchgate.net/publication/...
this is Chapter 5 (Curriculum. Creativity in the Mathematics Classroom) from:
Creative Contexts: Our Worlds as Actors in the Dynamics of Change
(ISBN: 978-3-032-12282-7)
me: we can write 5·4·3·2·1 as 5!, so, if it helps, we could use a modified exclamation mark with a + rather than a · below the vertical part to represent for e.g. 5 the expression 5+4+3+2+1
students:
students:
WHAT DOES THIS MEAN BENJAMIN DICKMAN??
November 19, 2025 at 11:59 PM
me: we can write 5·4·3·2·1 as 5!, so, if it helps, we could use a modified exclamation mark with a + rather than a · below the vertical part to represent for e.g. 5 the expression 5+4+3+2+1
students:
students:
*students feel blah about quadratics*
me:
me:
November 19, 2025 at 11:28 PM
*students feel blah about quadratics*
me:
me:
in base 10, sometimes two numbers with only 0s and 1s have a product of only 0s and 1s. e.g.
11010*100001 = 1101011010
➡️ under what conditions does this occur?
cc #MathSky 🧮 bcc #iTeachMath ♾️
11010*100001 = 1101011010
➡️ under what conditions does this occur?
cc #MathSky 🧮 bcc #iTeachMath ♾️
November 19, 2025 at 11:26 PM
in base 10, sometimes two numbers with only 0s and 1s have a product of only 0s and 1s. e.g.
11010*100001 = 1101011010
➡️ under what conditions does this occur?
cc #MathSky 🧮 bcc #iTeachMath ♾️
11010*100001 = 1101011010
➡️ under what conditions does this occur?
cc #MathSky 🧮 bcc #iTeachMath ♾️
Prealgebra
Algebra 1
Algebra 2
Linear Algebra
Abstract Algebra
Algebraic Geometry
Algebraic Number Theory
Algebraic Topology
Algebra
Algebraic Etymology
Algebraic Ontology
Algebraic Entomology
Algebraic Oenology
Algebraic Otology
Algebraic Philology
Algebraic Astrology
Postalgebra
Algebra 1
Algebra 2
Linear Algebra
Abstract Algebra
Algebraic Geometry
Algebraic Number Theory
Algebraic Topology
Algebra
Algebraic Etymology
Algebraic Ontology
Algebraic Entomology
Algebraic Oenology
Algebraic Otology
Algebraic Philology
Algebraic Astrology
Postalgebra
November 19, 2025 at 11:23 PM
Prealgebra
Algebra 1
Algebra 2
Linear Algebra
Abstract Algebra
Algebraic Geometry
Algebraic Number Theory
Algebraic Topology
Algebra
Algebraic Etymology
Algebraic Ontology
Algebraic Entomology
Algebraic Oenology
Algebraic Otology
Algebraic Philology
Algebraic Astrology
Postalgebra
Algebra 1
Algebra 2
Linear Algebra
Abstract Algebra
Algebraic Geometry
Algebraic Number Theory
Algebraic Topology
Algebra
Algebraic Etymology
Algebraic Ontology
Algebraic Entomology
Algebraic Oenology
Algebraic Otology
Algebraic Philology
Algebraic Astrology
Postalgebra
[finally integrating algebra & geometry]
me: now remember, when you have a function that sends x to ax²+bx+c, what role do the coefficients play?
students: a² + b² = c²?
me:
students:
me: now remember, when you have a function that sends x to ax²+bx+c, what role do the coefficients play?
students: a² + b² = c²?
me:
students:
November 19, 2025 at 11:23 PM
[finally integrating algebra & geometry]
me: now remember, when you have a function that sends x to ax²+bx+c, what role do the coefficients play?
students: a² + b² = c²?
me:
students:
me: now remember, when you have a function that sends x to ax²+bx+c, what role do the coefficients play?
students: a² + b² = c²?
me:
students:
🌟Reminder🌟
Cannot say f(x)=x² is not injective aka one-to-one without explicitly stating its domain.
For example, the aforementioned function is one-to-one on the domain {-11,11}.
Cannot say f(x)=x² is not injective aka one-to-one without explicitly stating its domain.
For example, the aforementioned function is one-to-one on the domain {-11,11}.
November 19, 2025 at 11:21 PM
🌟Reminder🌟
Cannot say f(x)=x² is not injective aka one-to-one without explicitly stating its domain.
For example, the aforementioned function is one-to-one on the domain {-11,11}.
Cannot say f(x)=x² is not injective aka one-to-one without explicitly stating its domain.
For example, the aforementioned function is one-to-one on the domain {-11,11}.
students: wait is "PT" short for Pythagorean Theorem or Pascal's Triangle?
me: yeah
me: yeah
November 19, 2025 at 11:20 PM
students: wait is "PT" short for Pythagorean Theorem or Pascal's Triangle?
me: yeah
me: yeah
"It is the first time a mathematician has received NSW’s highest honour for scientific endeavour."
cc #iTeachMath × #MathSky!
cc #iTeachMath × #MathSky!
An article from @sydney.edu.au about today’s significant event #NSWPremiersPrizes news-opinion.sydney.edu.au/link/id/zzzz...
Nalini Joshi named 2025 NSW Scientist of the Year
Trailblazing mathematician Professor Nalini Joshi has been awarded the top scientific accolade in NSW for 2025.
news-opinion.sydney.edu.au
November 18, 2025 at 10:17 PM
"It is the first time a mathematician has received NSW’s highest honour for scientific endeavour."
cc #iTeachMath × #MathSky!
cc #iTeachMath × #MathSky!
this is my feeling about modulo (among gen pop)
Chirality is such a useful word for how rarely it is used in normal conversation.
November 17, 2025 at 3:03 AM
this is my feeling about modulo (among gen pop)
A few 👀 @catrionaagg.bsky.social geometry puzzles that definitely won't totally consume your Sunday or November or ...
Sunday night seems the right time to post a gallery of (I hope!) every one of Catriona's geometry puzzles.
notes.mathforge.org/notes/publis...
Give it a moment to load ... there's a *lot* of them!
#GeometryPuzzles #UKMathsChat #mathsky
notes.mathforge.org/notes/publis...
Give it a moment to load ... there's a *lot* of them!
#GeometryPuzzles #UKMathsChat #mathsky
Puzzle Gallery in Notes
notes.mathforge.org
November 16, 2025 at 6:28 PM
A few 👀 @catrionaagg.bsky.social geometry puzzles that definitely won't totally consume your Sunday or November or ...
every so often i recall that, 15 years ago in Fall 2010, i started a little storybook style introduction to Galois Theory:
imgur.com/a/galois-the...
i sent it out to the class & prof to ask if anyone was interested in my continuing; no one was. alas, i moved on thereafter.
well. it still reads ok!
imgur.com/a/galois-the...
i sent it out to the class & prof to ask if anyone was interested in my continuing; no one was. alas, i moved on thereafter.
well. it still reads ok!
Galois Theory
Discover the magic of the internet at Imgur, a community powered entertainment destination. Lift your spirits with funny jokes, trending memes, entertaining gifs, inspiring stories, viral videos, and ...
imgur.com
November 15, 2025 at 7:33 PM
every so often i recall that, 15 years ago in Fall 2010, i started a little storybook style introduction to Galois Theory:
imgur.com/a/galois-the...
i sent it out to the class & prof to ask if anyone was interested in my continuing; no one was. alas, i moved on thereafter.
well. it still reads ok!
imgur.com/a/galois-the...
i sent it out to the class & prof to ask if anyone was interested in my continuing; no one was. alas, i moved on thereafter.
well. it still reads ok!
new NEW @cshor.org pset 🥳
🔗:
drive.google.com/file/d/1mk6R...
alt text:
Screenshots of pages 1, 2, 3, and 7 (first three & last)
I haven't even read the problems but I cosign/cosine them nevertheless
#iTeachMath ♾️ #MathSky 🧮
🔗:
drive.google.com/file/d/1mk6R...
alt text:
Screenshots of pages 1, 2, 3, and 7 (first three & last)
I haven't even read the problems but I cosign/cosine them nevertheless
#iTeachMath ♾️ #MathSky 🧮
November 13, 2025 at 8:52 PM
new NEW @cshor.org pset 🥳
🔗:
drive.google.com/file/d/1mk6R...
alt text:
Screenshots of pages 1, 2, 3, and 7 (first three & last)
I haven't even read the problems but I cosign/cosine them nevertheless
#iTeachMath ♾️ #MathSky 🧮
🔗:
drive.google.com/file/d/1mk6R...
alt text:
Screenshots of pages 1, 2, 3, and 7 (first three & last)
I haven't even read the problems but I cosign/cosine them nevertheless
#iTeachMath ♾️ #MathSky 🧮
the following identity can, and generally is, proved by mathematical induction:
1³+2³+...+n³ = (n(n+1)/2)²
but it can also be proved by summing the entries of an n×n times table, for the RHS is the row sums and the LHS is the sum over backwards L-shaped regions. DO NOT REPEAT THIS INSIGHT
1³+2³+...+n³ = (n(n+1)/2)²
but it can also be proved by summing the entries of an n×n times table, for the RHS is the row sums and the LHS is the sum over backwards L-shaped regions. DO NOT REPEAT THIS INSIGHT
November 13, 2025 at 1:25 AM
the following identity can, and generally is, proved by mathematical induction:
1³+2³+...+n³ = (n(n+1)/2)²
but it can also be proved by summing the entries of an n×n times table, for the RHS is the row sums and the LHS is the sum over backwards L-shaped regions. DO NOT REPEAT THIS INSIGHT
1³+2³+...+n³ = (n(n+1)/2)²
but it can also be proved by summing the entries of an n×n times table, for the RHS is the row sums and the LHS is the sum over backwards L-shaped regions. DO NOT REPEAT THIS INSIGHT
another great read from mpershan! you don't have to like him or respect him or even tolerate him, but it's worth giving his blog posts a glance
#iTeachMath ♾️
#iTeachMath ♾️
I wrote about shallow, vague, fuzzy definitions of "conceptual understanding" and a better way to think about it. pershmail.substack.com/p/understand...
"Understanding" Shouldn't Be Vague or Mysterious
Let's do some pedagogy.
pershmail.substack.com
November 11, 2025 at 10:09 PM
another great read from mpershan! you don't have to like him or respect him or even tolerate him, but it's worth giving his blog posts a glance
#iTeachMath ♾️
#iTeachMath ♾️
whoa
@jedediyah.com , just got it today via hardcopy ILL, and scanned it. TONS of resources and citations in it. Shocking amount actually. Here is a link so you can download it. www.dropbox.com/scl/fi/ieeo7...
www.dropbox.com
November 11, 2025 at 2:07 AM
whoa
who is more likely to win, according to your intuition, in a game of war?
Scenario 1:
Player A with 4 aces
Player B with the other 48 cards
Scenario 2:
Player A with 4 aces and 4 kings
Player B with the other 44 cards
cc #iTeachMath ♾️ #MathSky 🧮
Scenario 1:
Player A with 4 aces
Player B with the other 48 cards
Scenario 2:
Player A with 4 aces and 4 kings
Player B with the other 44 cards
cc #iTeachMath ♾️ #MathSky 🧮
November 7, 2025 at 6:31 PM
who is more likely to win, according to your intuition, in a game of war?
Scenario 1:
Player A with 4 aces
Player B with the other 48 cards
Scenario 2:
Player A with 4 aces and 4 kings
Player B with the other 44 cards
cc #iTeachMath ♾️ #MathSky 🧮
Scenario 1:
Player A with 4 aces
Player B with the other 48 cards
Scenario 2:
Player A with 4 aces and 4 kings
Player B with the other 44 cards
cc #iTeachMath ♾️ #MathSky 🧮