REPOST: Quantum Computing & Brahmagupta: From Zero to Qubits

Episode Transcript
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(00:00):
In case you can't hear it, right outside
my studio, there is a lot of construction
going on.
As a result, I'm going to roll with
it and I'm going to spare you the
noise.
That said, today is going to be another
repost.
One of my favorite podcasts is about quantum
computing and Brahmagupta.

(00:21):
Quantum computing is rapidly evolving from a theoretical
dream to a transformative force in the real
world.
In early 2025, Microsoft introduced its Majorana 1
chip, built on breakthrough topoconductor materials, which could
pave the way for more stable and scalable

(00:42):
quantum systems.
Around the same time, Google's Willow processor demonstrated
powerful error correction across 105 superconducting qubits, solving
problems beyond the reach of today's fastest classical
supercomputers.
These developments aren't just technological milestones, they signal

(01:04):
a new era in which quantum tools can
accelerate drug discovery, revolutionize climate modeling, optimize global
logistics, and reshape cybersecurity.
And what's remarkable is how the roots of
this quantum future reached deep into our mathematical
past.
Over 1300 years ago, the Indian mathematician Brahmagupta

(01:29):
revolutionized number theory by formalizing the use of
zero and defining the rules for positive and
negative numbers.
These were concepts that laid the groundwork for
binary systems.
Today's quantum computing builds upon that foundation, using
quantum bits, qubits, that exist not just in

(01:50):
zero or one, but in complex superpositions of
both.
In many ways, Brahmagupta's legacy lives on at
the cutting edge of science, proving that history
and innovation are forever entangled.
So without further ado, enjoy this repost on
quantum computing and Brahmagupta.

(02:12):
And until next time, hopefully, it'll be a
little more quieter.
Carpe diem, my friends.
I'm going to start my podcast with a
digression, because today I read some very exciting
news.
The National Science Foundation has awarded the University

(02:34):
of California, Berkeley, $25 million to create a
multi-university institute that will advance quantum science
to create quantum computers.
This excites me because it's going to take
math to a whole new level and make
it powerful beyond numbers and words.
Though quantum computing is young, the opportunities that

(02:57):
it presents are truly mind-blowing.
Unlike the conventional computers that we use today,
where information is stored as bits, quantum computers
store information and data as qubits, also known
as quantum bits.
You see, the computer that you use today
is streaming electrical pulses that represent ones or
zeros.
Though quantum computers also use zeros and ones,

(03:19):
they also use superposition and entanglement to create
a third state of qubits that represent a
zero and a one simultaneously.
We don't have quantum computers for public use
yet because we're still executing computational operations on
a small number of qubits.
Furthermore, these processes require a computer to operate

(03:41):
at negative 460 degrees Fahrenheit, also known as
negative 273 degrees Celsius, also known as zero
Kelvin.
Quantum computers are going to be the future
of computing.
Used today, they can solve problems that would
take a conventional computer billions of years to
solve because they are thousands of times faster.

(04:02):
Because of their power, they'll be able to
break encryptions.
However, also because of their power, they will
be able to create unhackable systems.
Also, instead of using electricity like our conventional
computers do, quantum computers will use quantum tunneling
for power.
As a result, quantum computers will reduce the
consumption of power that a computer generates.

(04:24):
But to me, the most exciting thing that
a quantum computer can do is find a
product representation for the solution of Pell's equation
in polynomial time.
To simplify that statement, polynomial time is the
time it takes to do a computation depending
on the amount of inputted data.
That is actually irrelevant to this podcast, but
it's good to know for interesting party conversation.

(04:45):
What is relevant is that a quantum computer
can find a product representation for the solution
of Pell's equation.
You see, Pell's equation, also known as the
Pell-Fermat equation, is any Diophantine equation of
the form x squared minus ny squared equals
one, where the variable n represents a positive

(05:06):
non-square integer.
In this equation, solutions are solved for x
and y.
I'll post the equation on my website so
that you actually have a visual of what
the equation looks like.
But when the equation is presented in Cartesian
coordinates and n is positive, it's also shown
as a hyperbola, and when n is negative,
it's an ellipse.
I'll show that also on my website at

(05:28):
mathsciencehistory.com.
This particular equation, according to Joseph Lagrange, has
infinite integer solutions as long as the variable
n is not a perfect square and x
and y are integers.
Though Diophantine equations have been around since the
mathematician Diophantus presented his work called Arithmetica around
250 CE, it wasn't until 628 when Brahmagupta

(05:52):
discovered an integer solution to this equation when
n equals 92.
Brahmagupta was a tremendous mathematician.
The world-renowned science historian George Sarton stated
that Brahmagupta was, quote, one of the greatest
scientists of his race and the greatest of
all time, unquote.
Brahmagupta was born in 598 CE in India.

(06:15):
In 628, he wrote and improved the treatise
of Brahma called Brahmasutasiddhanta.
The book consists of 24 chapters and has
1008 verses.
It includes astronomy, algebra, geometry, trigonometry, and algorithmics.
The solution to the reference Diophantine equation is
found in chapter 8 of Brahmasutasiddhanta.

(06:36):
Though it seems like a simple process today,
he was solving for large numbers using Diophantus'
process of syncopated algebra, which was the process
of using simple symbolism before it evolved into
symbolic algebra.
As a result, in Brahmagupta's time, he only
had symbols that represented exponents, subtraction, and an
equal sign.

(06:56):
That was it.
Symbolic algebra wouldn't be used until the 16th
century.
The contribution of Brahmagupta's work to mathematics is
extensive.
For example, in arithmetic, we have the four
fundamental operations, which are addition, subtraction, multiplication, and
division.
Even though these fundamental operations had been around
for centuries, the current system that we know

(07:18):
of is based on the Hindu-Arabic number
system, and it appeared in Brahmasutasiddhanta.
We'll be right back after a quick word
from my advertisers.
And speaking of zeros and ones, Brahmasutasiddhanta was
the first existing book that treated zero as
a number and not just a placeholder.

(07:39):
Prior to this, in Ptolemaic mathematics, zero was
used only as a placeholder.
However, though Brahmagupta has contributed for treating zero
as a number, in 2017, research uncovered an
Indian manuscript that dates as far back as
200 CE, and it shows the use of
zero as a number.

(07:59):
So, regardless, we would not have been introduced
to this concept of zero as a number
if it wasn't for the work that Brahmagupta
presented in Brahmasutasiddhanta.
I'm going to post a video on my
website at MathScienceHistory.com, and it's from the
University of Oxford, and it shows the research
that uncovered the Bhakshali manuscript.

(08:20):
And it's really cool, and it's exciting, because
now we're understanding that zero was actually used
as a number further back, closer to 200
CE, in India at the same time that
the Romans were using zero as a placeholder.
Brahmagupta was also one of the first to
provide rules for multiplying negative numbers.

(08:42):
All of this played into several rules that
showed that the sum of two positives are
positive, 1 plus 1 equals 2.
The sum of two negatives are negative, negative
1 plus negative 1 equals negative 2.
The sum of a positive and a negative
is the difference, negative 1 plus 3 is
2.
And if the sum of a positive and

(09:02):
a negative are equal, the answer is zero,
negative 3 plus 3 equals zero.
Brahmagupta also described the process of zero and
negative numbers in multiplication.
He showed that the product of a negative
and a positive is negative, the product of
two negatives is a positive, the product of
two positives is positive, and he also showed

(09:22):
that the product of zero and a negative
is zero, and the product of a positive
and zero is also zero.
As far as triangles go, for the sides
of the right-angled triangle, he presented two
sets of the Pythagorean triples.
In geometry, he created an exact formula for
finding the area of cyclic quadrilaterals.

(09:43):
A cyclic quadrilateral is a quadrilateral that is
inscribed within a circle where all the vertices
sit on the single circle.
I'll post that formula and the process for
finding the area on my website as well.
His work with cyclic quadrilaterals led to Brahmagupta's
famous theorem, which stated that if a cyclic

(10:03):
quadrilateral has perpendicular diagonals, then the perpendicular to
a side from a point of intersection of
the diagonals bisects the opposite side.
There's actually a really great image that goes
with this, and I'll show that and the
mathematics that go with it as well.
So, he was phenomenal.
He contributed so much.
In astronomy, though he believed that the sun

(10:25):
orbited the earth, he presented an argument for
showing that the moon is closer to the
earth than the sun.
The evolution of mathematics is such a beautiful
one.
Brahmagupta's work helped to speed up the calculation
process of the Diophantine equation.
Today, we begin to move forward into a
new chapter of quantum computing, as the process

(10:46):
of crunching large numbers and data becomes faster
and easier.
And though we have many problems to correct,
including noise and error correction, and though we
may not see quantum computers for a while,
and though it is highly likely that quantum
computers may not outpace or even replace conventional
computers, initially, we are stepping into a new

(11:08):
chapter where even our fastest computers today will
become antiquated.
With this progress, the numbers that we understand
today may change by definition and representation.
As a result, as mathematicians and scientists, we
stand at a place in time that serves
as a marker for the future of mathematics.
Yeah, we stand along a linear path, specifically

(11:30):
at that point between history and the future,
where we can see all that brought us
here mathematically and all that will take us
to greater understandings.
Thank you for tuning in to Math Science
History.
If you enjoyed today's episode, please leave a
quick rating and review.
They really help the podcast.
You can find our transcripts at mathsciencehistory.com.

(11:54):
And while you're there, remember to click on
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supports a portion of our production costs and
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Again, thank you for tuning in, and until
next time, carpe diem.

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.css-14f5ked{margin:0;word-break:break-word;display:-webkit-box;-webkit-box-orient:vertical;box-orient:vertical;-webkit-line-clamp:2;overflow:hidden;}REPOST: Quantum Computing & Brahmagupta: From Zero to Qubits