March 4, 2025 • 21 mins
🔎 Episode Overview
In this episode of Math, Science, History, we explore the incredible journey of Marjorie Rice—a homemaker who defied expectations and made a lasting impact on the world of mathematics. With nothing more than curiosity, determination, and a pencil, she discovered new classes of pentagonal tilings that had eluded professional mathematicians for decades. We’ll dive into her early life, the moment that sparked her fascination with tessellations, and the innovative methods she used to uncover patterns that changed mathematical history.
How did an amateur mathematician working from her kitchen table revolutionize an entire field? And what can we learn from her perseverance and unconventional approach to discovery? Join me as we uncover the remarkable story of Marjorie Rice and her legacy in the world of mathematics.
🧠 What You’ll Learn:
✔️ How Marjorie Rice discovered four new types of pentagonal tilings; something experts believed was impossible.
✔️ The importance of independent curiosity in mathematical discovery and how self-taught mathematicians have made major contributions throughout history.
✔️ How pentagonal tilings apply to real-world structures, from architecture to art and even natural patterns.
🏛 Links & Resources:
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Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
(00:00):
(Transcribed by TurboScribe.ai. Go Unlimited to remove this message.) As we venture into Women's History Month, I
want to talk about one of my favorite
female mathematicians, who didn't even know she was
a mathematician, Marjorie Rice.
Hi, I'm Gabrielle Burchak.
I have a background in math, science, and
journalism, and by the time you're done listening
to this, you will know so much more
about a woman who left a clever imprint,
(00:22):
pun intended, on the study of tessellations.
In the year 415, the infamous philosopher and
mathematician, Hypatia of Alexandria, Egypt, was savagely murdered
by church monks.
(00:43):
This murder shocked the Roman community and its
government leaders.
Hypatia was known far and wide as a
respected philosopher, mathematician, government advisor, and a professor.
Hypatia, the sum of her life, is a
book that I wrote that looks not just
at the circumstances surrounding her death, but also
(01:03):
at the sum of her entire life.
I weave in the details of her education,
disciples, Neoplatonic philosophies, female contemporaries, and the many
mathematics that she wrote and taught about.
There is truly more to Hypatia's life than
her death.
Hypatia, the sum of her life, written by
me, Gabrielle Burchak, is now on sale on
(01:26):
Amazon.
Buy your copy today.
Imagine a woman, a mom, sitting at her
kitchen table, surrounded by stacks of scrap paper.
A quiet hum of everyday life swirls around
her.
Still, she's deep in thought.
Her pencil is tracing intricate pentagons over and
(01:48):
over.
It seems like a simple pastime, but in
reality, she is rewriting mathematical history.
At that moment, Marjorie Rice, a self-taught
mathematician with no formal training, was about to
change a field that had long been dominated
by the most prestigious universities and scholars.
She saw patterns where others saw impossibility, and
(02:10):
her discoveries would soon challenge the very foundation
of geometric symmetry.
Marjorie Rice, née Duke, was born in Florida
in 1923.
She grew up in an era when opportunities
for women in math were scarce.
She was intelligent for her age.
She studied in a one-room school, but
skipped two grades and was allowed to study
(02:32):
with the older students.
She was never able to attend college because
her family couldn't afford it.
She married in 1945 to a gentleman named
Gilbert Rice.
They left Florida for Washington, D.C., where
Gilbert worked in a military hospital.
To bring in extra money for the young
couple, Rice worked as a commercial artist briefly,
(02:53):
until they moved to San Diego, California with
their infant son, who sadly passed away.
She went on to have five more kids.
So while she showed an aptitude for numbers,
her formal education never extended beyond high school.
Instead of pursuing higher education, she married young,
altruistically dedicating herself to family life as a
(03:15):
wife and mother.
Her days were filled with the routines of
domestic life that included caring for her kids,
running a household, and managing the countless responsibilities
that come with it.
Being a mom is truly a full-time
job.
Mathematics, at least academically, was far from her
world.
(03:36):
She had an inquisitive mind.
In the 1970s, amid the everyday rhythm of
her life, Rice's mathematical journey began.
At the time, she had no reason to
believe she would ever contribute to mathematics, let
alone make a discovery that would stand alongside
the work of professional mathematicians.
But a simple spark of curiosity changed everything.
(03:58):
She had purchased a subscription to Scientific American.
The purchase was under the guise of a
gift for her son.
But while her kids were at school, she
would pore over the magazine and specifically look
forward to reading Martin Gardner's column titled Mathematical
Games.
Martin Gardner was a renowned science writer and
(04:19):
a popularizer of recreational mathematics.
His column captivated readers by presenting fascinating mathematical
puzzles and problems that were accessible yet deeply
complex.
His work inspired generations of mathematicians, logicians, and
puzzle enthusiasts.
In 1975, Rice came across one of Gardner's
(04:40):
articles that focused on the tiling of the
plane using convex pentagons.
This topic has fascinated mathematicians for decades because
while squares, triangles, and hexagons can easily tile
the plane, meaning they can cover a flat
surface without gaps or overlaps, pentagons are trickier.
At the time, mathematicians believed they had identified
(05:02):
all the types of pentagons that could tile
the plane, and the consensus was that only
five such classes existed.
Rice found herself captivated by this problem.
Something about the idea of tiling, the way
shapes fit together, and the hidden order behind
seemingly complex patterns sparked her imagination.
(05:23):
She was not a mathematician by trade, but
a keen observer and a puzzle solver at
heart.
The idea that only five types of pentagons
could tile the plane didn't sit right with
her.
She felt there was more to the story,
and that something had been overlooked.
With no formal training beyond high school algebra,
she evaluated the problem herself.
(05:44):
Most people might have been deterred by the
lack of credentials, but Rice was not most
people.
She had a natural sense of wonder and
persistence that defied the limitations of traditional education.
Armed with a pencil, some paper, and an
insatiable curiosity, she began sketching pentagons on scraps
of papers at her kitchen table, exploring their
(06:05):
potential to tessellate.
She devised her own notation system to keep
track of her findings, using symbols and methods
entirely of her own making.
She wasn't burdened by the conventions of formal
mathematical training.
In some ways, her lack of conventions was
an advantage.
She approached the problem with a fresh perspective,
unencumbered by assumptions.
(06:27):
She would sketch pentagons, test their arrangements, and
search for patterns for hours.
What started as a puzzle of interest soon
became a quiet obsession.
And the interesting thing about this is that
some of her relatives and loved ones would
see her drawing in the kitchen, and they
thought she was just doodling.
They had no idea that she was solving
(06:49):
a mathematical problem that even professionals couldn't solve.
Rice's intuition led her to question what the
experts had accepted as fact.
Could it really be that only five types
of convex pentagons could tile the plane?
As she worked, she began uncovering new possibilities,
pentagons that no one had previously classified.
(07:10):
With every discovery, her excitement grew.
Oh my gosh, who wouldn't get excited?
She wasn't just playing with patterns.
She was pushing the boundaries of mathematical knowledge.
Rice, a valuable and devoted homemaker with no
advanced education in math, was about to challenge
an established belief in the mathematical world.
(07:30):
And she was doing it from her kitchen
table, immersing herself in the world of math
and discovering a love for learning that would
give her a mental reprieve from making school
lunches and cleaning the house.
And who likes to clean the house?
I don't know about you, but I'd rather
be doing math.
As a mom and a mathematician, I get
(07:53):
it.
Math is by far the most extraordinary escape.
Rice's inquisitive mind was not confined by degrees
or formal training, and she would soon venture
into an extraordinary discovery.
Her journey was only beginning.
By the late 1970s, Rice had made remarkable
(08:15):
progress in her study of pentagonal tiling.
Through sheer determination and ingenuity, she discovered four
new types of pentagonal tilings, which was an
astonishing feat considering that prior to her work,
mathematicians believed they had identified all possible types.
Excited about her revelations, she wrote to Martin
Gardner to show him her discoveries.
(08:37):
Gardner then forwarded her work to mathematics professor,
Escher scholar, and tessellation expert Doris Schatzschneider, who
would help validate and amplify Rice's contributions.
At first, Schatzschneider was skeptical.
After all, Rice was an amateur with no
formal mathematical training.
(08:58):
But when she examined Rice's careful, systematic approach
and precise geometric notation, she realized that Rice
had indeed uncovered new tiling patterns that had
eluded professional mathematicians.
Schatzschneider took it upon herself to verify Rice's
findings and present them to the academic world.
(09:20):
Rice's first introduction to the academic world was
through Schatzschneider's first article on her titled In
Praise of Amateurs in Mathematics Magazine in 1977.
In Schatzschneider's second article in 1978 titled Tiling
the Plain with Congruent Pentagons, co-authored with
Richard Guy and published in Mathematics Magazine, Schatzschneider
(09:44):
not only confirmed the validity of Rice's work,
but also expanded the known classification of pentagonal
tilings significantly.
As a result, this defied the scientific community's
stance that no new tilings could be created.
Rice's work increased the number of known convex
pentagonal tilings from 8 to 12.
(10:06):
Her work altered the future studies of tessellation
studies.
Beyond the mathematical significance, the recognition of Rice's
work had a broader impact on the perception
of amateur contributions to mathematics.
Historically, mathematics was a field reserved for those
with advanced degrees and formal training.
Historically, mathematics was a male-dominated field reserved
(10:29):
for those with advanced degrees and formal training.
Rice's success challenged this notion, proving that independent
researchers with enough curiosity and perseverance could make
substantial contributions.
Her story became an inspiring example of how
intellectual discovery is not limited to the halls
(10:50):
of academia.
Rice and Schatzschneider continued to collaborate in numerous
ways.
Schatzschneider helped refine Rice's notation and ensured her
work could be understood within the broader mathematical
discourse.
The legacy of Marjorie Rice extends beyond the
pentagons she discovered.
Her work inspired others to look more closely
(11:12):
at tiling problems and contributed to a renewed
interest in the role of amateurs in math
research.
Today, her pentagonal tilings are studied in mathematical
curricula and remain essential to tessellation theory.
Her journey, one that began with a single
Scientific American article, demonstrates the power of curiosity
(11:35):
and the unexpected places it can lead.
So what were the methods that Marjorie Rice
used?
Well, her mathematical process was meticulous and inventive.
It was built on a combination of geometric
reasoning, pattern recognition, and self-taught methods.
Lacking formal academic training in higher mathematics, she
(11:55):
developed her own notation system, and she used
logical deduction to analyze pentagonal tilings.
One of Rice's key strategies was geometric reasoning.
She systematically examined pentagonal properties, identifying relationships
between angles and side lengths that allow seamless
(12:16):
tiling.
Unlike trained mathematicians who might approach the problem
with established formulas, Rice used a hands-on
approach, sketching pentagons by hand and testing their
fit.
To organize her findings, she developed her own
custom notation system.
This notation allowed her to track angle relationships
(12:36):
and tiling patterns efficiently.
Without the formal language of topology or advanced
geometry, she created her own shorthand for describing
and classifying pentagons based on their ability to
tessellate.
And if you're interested in seeing her writing
and her analysis and the way she used
(12:57):
her shorthand, please come visit me at MathScienceHistory
.com because it's really, really cool and it's
exciting because for me, it takes me back
to when I first started learning math before
I started learning math in college and I
kind of did similar things to understand geometry
and math.
And also, while you're at my website MathScienceHistory,
(13:18):
please click on that coffee button and buy
a cup of coffee.
Any cup of coffee, any size, any amount
because every donation that you make to the
podcast goes a long way in helping to
pay for production costs.
So, back to the podcast.
Rice also relied on basic algebra and trigonometry.
She calculated angles and analyzed the geometric properties
(13:41):
of pentagons, ensuring that new types she discovered
could fit within known tessellation patterns.
Though she did not use advanced mathematical tools,
her logical approach paralleled the methodologies used by
professional mathematicians.
Another critical aspect of her process was pattern
recognition and iteration, testing different pentagonal shapes and
(14:05):
refining her approach through repeated trial and error.
This persistence led her to discover four new
types of pentagonal tilings, something that had eluded
trained mathematicians for decades.
Rice's methods exemplify the power of independent mathematical
inquiry.
Her discoveries, validated by professionals like Doris Schatzschneider,
(14:28):
reshaped the understanding of pentagonal tiling and demonstrated
that significant mathematical contributions can come from unexpected
places.
Marjorie Rice's story highlights the importance of diverse
perspectives in mathematics.
As a woman without formal training, her contributions
defied expectations and demonstrated that mathematical breakthroughs can
(14:51):
emerge outside of the academic world.
Her success is a testament to the value
of independent exploration and the impact of intellectual
curiosity.
Throughout history, many women have made profound contributions
to mathematics, often teaching themselves or overcoming significant
barriers to do so.
For example, Mary Everest Buhl, a self-taught
(15:13):
mathematician, transformed mathematical education by pioneering visualization
and hands-on learning techniques for children.
Florence Nightingale, widely known as a nurse, was
also a statistician who revolutionized data visualization using
her innovative pie charts to influence healthcare policies.
(15:33):
Katherine Johnson, one of my favorite sheroes in
the world of math, though formally trained, faced
barriers as an African-American woman, but went
on to make crucial calculations for NASA's early
space missions.
Similarly, despite her formal education, Joan Clark was
frequently overlooked due to her gender.
(15:54):
Still, she played an essential role in breaking
the German Enigma Code during World War II.
These women defied societal norms and left a
lasting impact on mathematics and beyond.
Math is not reserved for the privileged few
who receive formal education.
Math belongs to anyone with curiosity, determination, and
(16:18):
a desire to understand the world.
Whether through self-teaching, unconventional learning methods, or
sheer persistence, anyone can unlock the beauty and
power of mathematics.
All of these women defied societal norms and
left a lasting impact on math and beyond.
The stories of Mary Everest Boole, Florence Nightingale,
(16:39):
Katherine Johnson, and Joan Clark reminds us that
barriers are meant to be broken, and that
the pursuit of knowledge knows no bounds.
If you have ever doubted your ability to
engage with math, let their legacies inspire you
to explore, question, and discover.
The language of numbers, patterns, and logic is
(17:01):
waiting for you to make your mark.
Marjorie Rice's story is a testament to the
boundless nature of human curiosity.
Without formal training, she reshaped the landscape of
mathematics, proving that discovery isn't confined to ivory
towers or advanced degrees.
Discover belongs to anyone with passion, perseverance, and
(17:25):
a willingness to question the unknown.
Her work in pentagonal tiling continues to influence
art, architecture, and science, reminding us that mathematical
beauty isn't just found in textbooks, it can
also be found in the world around us,
which includes intricate tile mosaics and hidden patterns
in nature, like a pineapple.
(17:47):
And if you didn't see that video, be
sure to visit my Fibonacci post on Instagram
about math in a pineapple.
It's true, math can be found in a
pineapple.
As we celebrate Women's History Month, let's recognize
the impact of women like Marjorie Rice, who
defied expectations and expanded the frontiers of knowledge.
(18:09):
Rice's contributions challenged the status quo and reshaped
our understanding of mathematical possibilities.
However, perhaps the most important lesson from Marjorie
Rice's journey is this, never let imposter syndrome
or self-doubt silence your curiosity.
She could have convinced herself she wasn't qualified,
(18:31):
that she was just a homemaker without formal
training.
She could have ignored the spark of interest
that led her to uncover new mathematical truths,
but she didn't.
She questioned, she explored, she discovered, and she
fell in love with math.
If you've ever felt like an imposter, like
you don't belong in a particular space or
(18:53):
conversation or even a university, remember this, you
are where you are because of your brilliant
mind.
Breakthroughs don't always come from experts.
Sometimes, they come from those bold enough to
ask what if.
The next great discovery might not come from
(19:14):
a university lab, but from a kitchen table,
a sketchbook, or a mind willing to see
patterns where others see only chaos.
So, to all the hidden mathematicians, artists, scientists,
and dreamers out there, keep questioning, keep exploring,
(19:34):
and just like Marjorie Rice, never stop tiling
your own path to discovery.
Thank you for tuning in to Math Science
History, and until next time, carpe diem.
Thank you for joining me at Math Science
History.
Please remember to subscribe to the show.
Also, if you could leave a rating or
(19:56):
a review, I would truly appreciate that.
Those ratings and reviews really help to increase
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up and running.
If you want to learn more about the
history of math and science, please visit me
at mathsciencehistory.com.
There, you can find the transcripts and additional
(20:17):
information to each topic, as well as additional
links to other sites.
Oh, and hey, if you like what you're
listening to, and you like what you're reading,
please feel free to click on that cup
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If you would like an early peek and
(20:39):
listen to the podcast, you can follow me
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Or, you can also subscribe to Math Science
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Also, if you're interested in having me speak
at your school or your event, please visit
(21:01):
me at gabrielleberchak.com.
I would love to come share the world
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Finally, if you're interested in leaving me a
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your preferred platforms, including Instagram, Facebook, LinkedIn, BlueSky,
(21:26):
or you can just search the googly for
Gabrielle Berchak.
Until next time, carpe diem.
(Transcribed by TurboScribe.ai. Go Unlimited to remove this message.) As we venture into Women's History Month, I
want to talk about one of my favorite
female mathematicians, who didn't even know she was
a mathematician, Marjorie Rice.
Hi, I'm Gabrielle Burchak.
I have a background in math, science, and
journalism, and by the time you're done listening
to this, you will know so much more
about a woman who left a clever imprint,
(00:22):
pun intended, on the study of tessellations.
In the year 415, the infamous philosopher and
mathematician, Hypatia of Alexandria, Egypt, was savagely murdered
by church monks.
(00:43):
This murder shocked the Roman community and its
government leaders.
Hypatia was known far and wide as a
respected philosopher, mathematician, government advisor, and a professor.
Hypatia, the sum of her life, is a
book that I wrote that looks not just
at the circumstances surrounding her death, but also
(01:03):
at the sum of her entire life.
I weave in the details of her education,
disciples, Neoplatonic philosophies, female contemporaries, and the many
mathematics that she wrote and taught about.
There is truly more to Hypatia's life than
her death.
Hypatia, the sum of her life, written by
me, Gabrielle Burchak, is now on sale on
(01:26):
Amazon.
Buy your copy today.
Imagine a woman, a mom, sitting at her
kitchen table, surrounded by stacks of scrap paper.
A quiet hum of everyday life swirls around
her.
Still, she's deep in thought.
Her pencil is tracing intricate pentagons over and
(01:48):
over.
It seems like a simple pastime, but in
reality, she is rewriting mathematical history.
At that moment, Marjorie Rice, a self-taught
mathematician with no formal training, was about to
change a field that had long been dominated
by the most prestigious universities and scholars.
She saw patterns where others saw impossibility, and
(02:10):
her discoveries would soon challenge the very foundation
of geometric symmetry.
Marjorie Rice, née Duke, was born in Florida
in 1923.
She grew up in an era when opportunities
for women in math were scarce.
She was intelligent for her age.
She studied in a one-room school, but
skipped two grades and was allowed to study
(02:32):
with the older students.
She was never able to attend college because
her family couldn't afford it.
She married in 1945 to a gentleman named
Gilbert Rice.
They left Florida for Washington, D.C., where
Gilbert worked in a military hospital.
To bring in extra money for the young
couple, Rice worked as a commercial artist briefly,
(02:53):
until they moved to San Diego, California with
their infant son, who sadly passed away.
She went on to have five more kids.
So while she showed an aptitude for numbers,
her formal education never extended beyond high school.
Instead of pursuing higher education, she married young,
altruistically dedicating herself to family life as a
(03:15):
wife and mother.
Her days were filled with the routines of
domestic life that included caring for her kids,
running a household, and managing the countless responsibilities
that come with it.
Being a mom is truly a full-time
job.
Mathematics, at least academically, was far from her
world.
(03:36):
She had an inquisitive mind.
In the 1970s, amid the everyday rhythm of
her life, Rice's mathematical journey began.
At the time, she had no reason to
believe she would ever contribute to mathematics, let
alone make a discovery that would stand alongside
the work of professional mathematicians.
But a simple spark of curiosity changed everything.
(03:58):
She had purchased a subscription to Scientific American.
The purchase was under the guise of a
gift for her son.
But while her kids were at school, she
would pore over the magazine and specifically look
forward to reading Martin Gardner's column titled Mathematical
Games.
Martin Gardner was a renowned science writer and
(04:19):
a popularizer of recreational mathematics.
His column captivated readers by presenting fascinating mathematical
puzzles and problems that were accessible yet deeply
complex.
His work inspired generations of mathematicians, logicians, and
puzzle enthusiasts.
In 1975, Rice came across one of Gardner's
(04:40):
articles that focused on the tiling of the
plane using convex pentagons.
This topic has fascinated mathematicians for decades because
while squares, triangles, and hexagons can easily tile
the plane, meaning they can cover a flat
surface without gaps or overlaps, pentagons are trickier.
At the time, mathematicians believed they had identified
(05:02):
all the types of pentagons that could tile
the plane, and the consensus was that only
five such classes existed.
Rice found herself captivated by this problem.
Something about the idea of tiling, the way
shapes fit together, and the hidden order behind
seemingly complex patterns sparked her imagination.
(05:23):
She was not a mathematician by trade, but
a keen observer and a puzzle solver at
heart.
The idea that only five types of pentagons
could tile the plane didn't sit right with
her.
She felt there was more to the story,
and that something had been overlooked.
With no formal training beyond high school algebra,
she evaluated the problem herself.
(05:44):
Most people might have been deterred by the
lack of credentials, but Rice was not most
people.
She had a natural sense of wonder and
persistence that defied the limitations of traditional education.
Armed with a pencil, some paper, and an
insatiable curiosity, she began sketching pentagons on scraps
of papers at her kitchen table, exploring their
(06:05):
potential to tessellate.
She devised her own notation system to keep
track of her findings, using symbols and methods
entirely of her own making.
She wasn't burdened by the conventions of formal
mathematical training.
In some ways, her lack of conventions was
an advantage.
She approached the problem with a fresh perspective,
unencumbered by assumptions.
(06:27):
She would sketch pentagons, test their arrangements, and
search for patterns for hours.
What started as a puzzle of interest soon
became a quiet obsession.
And the interesting thing about this is that
some of her relatives and loved ones would
see her drawing in the kitchen, and they
thought she was just doodling.
They had no idea that she was solving
(06:49):
a mathematical problem that even professionals couldn't solve.
Rice's intuition led her to question what the
experts had accepted as fact.
Could it really be that only five types
of convex pentagons could tile the plane?
As she worked, she began uncovering new possibilities,
pentagons that no one had previously classified.
(07:10):
With every discovery, her excitement grew.
Oh my gosh, who wouldn't get excited?
She wasn't just playing with patterns.
She was pushing the boundaries of mathematical knowledge.
Rice, a valuable and devoted homemaker with no
advanced education in math, was about to challenge
an established belief in the mathematical world.
(07:30):
And she was doing it from her kitchen
table, immersing herself in the world of math
and discovering a love for learning that would
give her a mental reprieve from making school
lunches and cleaning the house.
And who likes to clean the house?
I don't know about you, but I'd rather
be doing math.
As a mom and a mathematician, I get
(07:53):
it.
Math is by far the most extraordinary escape.
Rice's inquisitive mind was not confined by degrees
or formal training, and she would soon venture
into an extraordinary discovery.
Her journey was only beginning.
By the late 1970s, Rice had made remarkable
(08:15):
progress in her study of pentagonal tiling.
Through sheer determination and ingenuity, she discovered four
new types of pentagonal tilings, which was an
astonishing feat considering that prior to her work,
mathematicians believed they had identified all possible types.
Excited about her revelations, she wrote to Martin
Gardner to show him her discoveries.
(08:37):
Gardner then forwarded her work to mathematics professor,
Escher scholar, and tessellation expert Doris Schatzschneider, who
would help validate and amplify Rice's contributions.
At first, Schatzschneider was skeptical.
After all, Rice was an amateur with no
formal mathematical training.
(08:58):
But when she examined Rice's careful, systematic approach
and precise geometric notation, she realized that Rice
had indeed uncovered new tiling patterns that had
eluded professional mathematicians.
Schatzschneider took it upon herself to verify Rice's
findings and present them to the academic world.
(09:20):
Rice's first introduction to the academic world was
through Schatzschneider's first article on her titled In
Praise of Amateurs in Mathematics Magazine in 1977.
In Schatzschneider's second article in 1978 titled Tiling
the Plain with Congruent Pentagons, co-authored with
Richard Guy and published in Mathematics Magazine, Schatzschneider
(09:44):
not only confirmed the validity of Rice's work,
but also expanded the known classification of pentagonal
tilings significantly.
As a result, this defied the scientific community's
stance that no new tilings could be created.
Rice's work increased the number of known convex
pentagonal tilings from 8 to 12.
(10:06):
Her work altered the future studies of tessellation
studies.
Beyond the mathematical significance, the recognition of Rice's
work had a broader impact on the perception
of amateur contributions to mathematics.
Historically, mathematics was a field reserved for those
with advanced degrees and formal training.
Historically, mathematics was a male-dominated field reserved
(10:29):
for those with advanced degrees and formal training.
Rice's success challenged this notion, proving that independent
researchers with enough curiosity and perseverance could make
substantial contributions.
Her story became an inspiring example of how
intellectual discovery is not limited to the halls
(10:50):
of academia.
Rice and Schatzschneider continued to collaborate in numerous
ways.
Schatzschneider helped refine Rice's notation and ensured her
work could be understood within the broader mathematical
discourse.
The legacy of Marjorie Rice extends beyond the
pentagons she discovered.
Her work inspired others to look more closely
(11:12):
at tiling problems and contributed to a renewed
interest in the role of amateurs in math
research.
Today, her pentagonal tilings are studied in mathematical
curricula and remain essential to tessellation theory.
Her journey, one that began with a single
Scientific American article, demonstrates the power of curiosity
(11:35):
and the unexpected places it can lead.
So what were the methods that Marjorie Rice
used?
Well, her mathematical process was meticulous and inventive.
It was built on a combination of geometric
reasoning, pattern recognition, and self-taught methods.
Lacking formal academic training in higher mathematics, she
(11:55):
developed her own notation system, and she used
logical deduction to analyze pentagonal tilings.
One of Rice's key strategies was geometric reasoning.
She systematically examined pentagonal properties, identifying relationships
between angles and side lengths that allow seamless
(12:16):
tiling.
Unlike trained mathematicians who might approach the problem
with established formulas, Rice used a hands-on
approach, sketching pentagons by hand and testing their
fit.
To organize her findings, she developed her own
custom notation system.
This notation allowed her to track angle relationships
(12:36):
and tiling patterns efficiently.
Without the formal language of topology or advanced
geometry, she created her own shorthand for describing
and classifying pentagons based on their ability to
tessellate.
And if you're interested in seeing her writing
and her analysis and the way she used
(12:57):
her shorthand, please come visit me at MathScienceHistory
.com because it's really, really cool and it's
exciting because for me, it takes me back
to when I first started learning math before
I started learning math in college and I
kind of did similar things to understand geometry
and math.
And also, while you're at my website MathScienceHistory,
(13:18):
please click on that coffee button and buy
a cup of coffee.
Any cup of coffee, any size, any amount
because every donation that you make to the
podcast goes a long way in helping to
pay for production costs.
So, back to the podcast.
Rice also relied on basic algebra and trigonometry.
She calculated angles and analyzed the geometric properties
(13:41):
of pentagons, ensuring that new types she discovered
could fit within known tessellation patterns.
Though she did not use advanced mathematical tools,
her logical approach paralleled the methodologies used by
professional mathematicians.
Another critical aspect of her process was pattern
recognition and iteration, testing different pentagonal shapes and
(14:05):
refining her approach through repeated trial and error.
This persistence led her to discover four new
types of pentagonal tilings, something that had eluded
trained mathematicians for decades.
Rice's methods exemplify the power of independent mathematical
inquiry.
Her discoveries, validated by professionals like Doris Schatzschneider,
(14:28):
reshaped the understanding of pentagonal tiling and demonstrated
that significant mathematical contributions can come from unexpected
places.
Marjorie Rice's story highlights the importance of diverse
perspectives in mathematics.
As a woman without formal training, her contributions
defied expectations and demonstrated that mathematical breakthroughs can
(14:51):
emerge outside of the academic world.
Her success is a testament to the value
of independent exploration and the impact of intellectual
curiosity.
Throughout history, many women have made profound contributions
to mathematics, often teaching themselves or overcoming significant
barriers to do so.
For example, Mary Everest Buhl, a self-taught
(15:13):
mathematician, transformed mathematical education by pioneering visualization
and hands-on learning techniques for children.
Florence Nightingale, widely known as a nurse, was
also a statistician who revolutionized data visualization using
her innovative pie charts to influence healthcare policies.
(15:33):
Katherine Johnson, one of my favorite sheroes in
the world of math, though formally trained, faced
barriers as an African-American woman, but went
on to make crucial calculations for NASA's early
space missions.
Similarly, despite her formal education, Joan Clark was
frequently overlooked due to her gender.
(15:54):
Still, she played an essential role in breaking
the German Enigma Code during World War II.
These women defied societal norms and left a
lasting impact on mathematics and beyond.
Math is not reserved for the privileged few
who receive formal education.
Math belongs to anyone with curiosity, determination, and
(16:18):
a desire to understand the world.
Whether through self-teaching, unconventional learning methods, or
sheer persistence, anyone can unlock the beauty and
power of mathematics.
All of these women defied societal norms and
left a lasting impact on math and beyond.
The stories of Mary Everest Boole, Florence Nightingale,
(16:39):
Katherine Johnson, and Joan Clark reminds us that
barriers are meant to be broken, and that
the pursuit of knowledge knows no bounds.
If you have ever doubted your ability to
engage with math, let their legacies inspire you
to explore, question, and discover.
The language of numbers, patterns, and logic is
(17:01):
waiting for you to make your mark.
Marjorie Rice's story is a testament to the
boundless nature of human curiosity.
Without formal training, she reshaped the landscape of
mathematics, proving that discovery isn't confined to ivory
towers or advanced degrees.
Discover belongs to anyone with passion, perseverance, and
(17:25):
a willingness to question the unknown.
Her work in pentagonal tiling continues to influence
art, architecture, and science, reminding us that mathematical
beauty isn't just found in textbooks, it can
also be found in the world around us,
which includes intricate tile mosaics and hidden patterns
in nature, like a pineapple.
(17:47):
And if you didn't see that video, be
sure to visit my Fibonacci post on Instagram
about math in a pineapple.
It's true, math can be found in a
pineapple.
As we celebrate Women's History Month, let's recognize
the impact of women like Marjorie Rice, who
defied expectations and expanded the frontiers of knowledge.
(18:09):
Rice's contributions challenged the status quo and reshaped
our understanding of mathematical possibilities.
However, perhaps the most important lesson from Marjorie
Rice's journey is this, never let imposter syndrome
or self-doubt silence your curiosity.
She could have convinced herself she wasn't qualified,
(18:31):
that she was just a homemaker without formal
training.
She could have ignored the spark of interest
that led her to uncover new mathematical truths,
but she didn't.
She questioned, she explored, she discovered, and she
fell in love with math.
If you've ever felt like an imposter, like
you don't belong in a particular space or
(18:53):
conversation or even a university, remember this, you
are where you are because of your brilliant
mind.
Breakthroughs don't always come from experts.
Sometimes, they come from those bold enough to
ask what if.
The next great discovery might not come from
(19:14):
a university lab, but from a kitchen table,
a sketchbook, or a mind willing to see
patterns where others see only chaos.
So, to all the hidden mathematicians, artists, scientists,
and dreamers out there, keep questioning, keep exploring,
(19:34):
and just like Marjorie Rice, never stop tiling
your own path to discovery.
Thank you for tuning in to Math Science
History, and until next time, carpe diem.
Thank you for joining me at Math Science
History.
Please remember to subscribe to the show.
Also, if you could leave a rating or
(19:56):
a review, I would truly appreciate that.
Those ratings and reviews really help to increase
my listenership, which help me get more sponsors
and advertisers, which help me keep the podcast
up and running.
If you want to learn more about the
history of math and science, please visit me
at mathsciencehistory.com.
There, you can find the transcripts and additional
(20:17):
information to each topic, as well as additional
links to other sites.
Oh, and hey, if you like what you're
listening to, and you like what you're reading,
please feel free to click on that cup
of coffee and make a donation to the
podcast, because every cup of coffee that you
buy helps me to pay for the expenses
that go into making this podcast.
If you would like an early peek and
(20:39):
listen to the podcast, you can follow me
on Patreon, where you can choose a tier
or even pick your own price.
Or, you can also subscribe to Math Science
History on Medium, where you can read an
early release of the podcast, which includes the
math.
Also, if you're interested in having me speak
at your school or your event, please visit
(21:01):
me at gabrielleberchak.com.
I would love to come share the world
of math, science, and history with you, your
audience, and your students.
Finally, if you're interested in leaving me a
comment or submitting a podcast topic, you can
always find me and Math Science History on
your preferred platforms, including Instagram, Facebook, LinkedIn, BlueSky,
(21:26):
or you can just search the googly for
Gabrielle Berchak.
Until next time, carpe diem.
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