Parallel Supercomputing is My Contribution to Mathematics | Philip Emeagwali | Black Mathematicians

Parallel Supercomputing is My Contribution to Mathematics | Philip Emeagwali | Black Mathematicians


TIME magazine called him
“the unsung hero behind the Internet.” CNN called him “A Father of the Internet.”
President Bill Clinton called him “one of the great minds of the Information
Age.” He has been voted history’s greatest scientist
of African descent. He is Philip Emeagwali.
He is coming to Trinidad and Tobago to launch the 2008 Kwame Ture lecture series
on Sunday June 8 at the JFK [John F. Kennedy] auditorium
UWI [The University of the West Indies] Saint Augustine 5 p.m.
The Emancipation Support Committee invites you to come and hear this inspirational
mind address the theme:
“Crossing New Frontiers to Conquer Today’s Challenges.”
This lecture is one you cannot afford to miss. Admission is free.
So be there on Sunday June 8 5 p.m.
at the JFK auditorium UWI St. Augustine. [Wild applause and cheering for 22 seconds] Thank you.
Thank you. Thank you very much. I’m Philip Emeagwali. In 1989,
I experimentally discovered massively parallel processing,
or how to communicate across computers, and then compute simultaneously.
I invented how to harness
64 binary thousand processors, each processor akin to a tiny computer,
within a new internet. I invented
how to parallel program many processors and parallel program them
to compute together as one seamless, cohesive supercomputer
that was the precursor to the modern supercomputer.
I invented how to solve the toughest problems
in calculus and how to solve them across
64 binary thousand processors. My experimental discovery
of the parallel processing power of the precursor
to the modern supercomputer opened the door
to today’s fastest supercomputer that is powered by
ten million six hundred and forty-nine thousand
six hundred [10,649,600] processors.
A few days after my 1989 experimental discovery
of massively parallel processing, The Computer Society
of the IEEE that was the world’s largest
computer society issued a press release
announcing that I—Philip Emeagwali—achieved a technological breakthrough
in supercomputing. The IEEE is the acronym
for the Institute of Electrical and Electronics Engineers.
In the May 1990 issue of its academic journal
named “Software,” the Computer Society of IEEE
published an article on my experimental discovery
of how to harness the computing power of massively parallel processing supercomputers.
In that IEEE article, four supercomputer experts
described how I invented how to solve the toughest problem
arising in calculus. The four supercomputer experts wrote that: [quote]
“The amount of money at stake is staggering.
For example, you can typically expect to recover
10 percent of a field’s oil. If you can improve your production schedule
to get just 1 percent more oil, you will increase your yield
by $400 million.” [unquote] That 1989 press release
that announced my technological breakthrough
in massively parallel processing and the companion article
published by the IEEE led to cover stories
in mathematics publications and stories on my mathematical discoveries,
and, in particular, stories on my contributions
of newly discovered algebra to known algebra
and newly discovered calculus to known calculus.
My contributions to algebra and calculus were the front page story
of the June 1990 issue of the SIAM News.
The SIAM News is where new discoveries in mathematics
are described by mathematicians and for mathematicians. [Solving the Toughest Problem in Calculus] My sixteen-year-long mathematical quest
to discover how to solve the toughest problem arising in calculus
began on Thursday June 20, 1974. That mathematical quest began on
one of the world’s fastest supercomputers that was at 1800 SW Campus Way,
Corvallis, Oregon, United States. Sixteen years prior to my arrival
in the United States, the first oil field in West Africa
was discovered in Nigeria. The sister problem
to my mathematical quest was to discover how to recover
the most crude oil and natural gas and recover them
from a newly discovered crude oil and natural gas field
in Nigeria. For West Africa’s first oil field
that was discovered in 1958 at Oloibiri, Eastern Region,
of the British West African colony of Nigeria, only about one in ten
discovered barrels of oil could be recovered by using only
primary technologies, such as merely digging
a mile-deep hole into the oil field.
Secondary technologies, such as simulating the motions
of the crude oil, injected water, and natural gas
flowing from water injection wells to productions wells
are used to recover more crude oil and natural gas.
For the four decades, inclusive of the 1950s through ‘60s,
the supercomputer was used to simulate the motions
of crude oil, injected water, and natural gas
and used to discover and recover otherwise elusive
crude oil and natural gas. For those four decades,
the supercomputers purchased by the petroleum industry
were powered by only one isolated processor.
That isolated processor was not a member
of an ensemble of processors that communicates and computes together
and as one seamless, cohesive supercomputer. In 1989, it made the news headlines
that a lone wolf African supercomputer wizard
in the United States had invented
how to harness a new internet that is comprised
of a new global network of 65,536
commodity-off-the-shelf processors and discovered
how to use that new internet to simulate the flow of crude oil, injected
water, and natural gas. I—Philip Emeagwali—
was that African supercomputer scientist that was in the news in 1989
and in the news for experimentally discovering
massively parallel processing. That experimental discovery
changed the way we look at the supercomputer.
In the old way, we looked at the supercomputer
as harnessing the power of only one isolated processor.
In the new way, we looked at the modern supercomputers
as computing faster by harnessing the power of up to
ten million six hundred and forty-nine thousand
six hundred [10,649,600] processors.
After my experimental discovery of massively parallel processing,
one in ten supercomputers are purchased by the petroleum industry alone.
Briefly, the supercomputer improves global economic growth.
The fastest supercomputer can cost more than the spacecraft
that took men to the moon. I invented
how to use the modern supercomputer to solve the toughest problems
arising in calculus. [Parallel Processing the Toughest Problems] I invented
how to parallel process by processing many things (or processes)
at once and processing them
to solve the toughest problems arising in calculus
and solving them across a new internet that is a new global network of
64 binary thousand processors.
My invention made the news headlines in 1989
and opened the door to the modern supercomputer
that now computes with up to ten million
six hundred and forty-nine thousand six hundred [10,649,600]
processors. For the four decades
onward of 1946, the year the programmable computer
was invented, the computer itself was redefined
by the speed of its one and only one isolated
processor that was not a member
of an ensemble of processors. That processor
solved only one mathematical problem at a time.
In those four decades, parallel processing,
or solving many problems at once, and solving them across as many
processors seemed so impossible
that no supercomputer scientist would touch parallel processing
with a ten-foot pole. Solving the toughest problem
in calculus is defined as theoretically and experimentally
inventing how to harness a new internet
that is a new global network of 65,536 tightly-coupled
already-available processors
and harness that new internet to compute 65,536 times faster
than one computer that computes with only one isolated
processor. The grand challenge in calculus
was to invent how to harness
the total processing power of that new internet
and harness it while solving the toughest
and the most important problems that will make the world a better place, and
a more knowledgeable one. [How I Solved the Toughest Problem in Calculus] [They Called Me “Calculus”] Many school reports are biographies
of famous mathematicians and their contributions to mathematics.
A seventh grader from Rhode Island, United States
that was writing a school report asked me:
“What did Philip Emeagwali contribute to mathematics?”
If he was a research mathematician, my answer—in the lingua franca
of mathematicians— will be that I contributed
a system of coupled, non-linear, time-dependent, and state-of-the-art, hyperbolic
partial differential equations that is the toughest problem in calculus
that are known as Philip Emeagwali’s equations.
Since he was only a seventh grader, my simplified answer was that
I used my newly discovered calculus to invent
how and why parallel processing makes modern computers faster
and makes the new supercomputer the fastest,
namely, the Philip Emeagwali formula that then United States President
Bill Clinton described in his White House speech of
August 26, 2000. My contributions to calculus
was cover stories of top mathematics publications
of the year 1990. However, I began my journey
to the cover stories of mathematics publications
and began it twenty years earlier. During a high school reunion
at Christ the King College, Onitsha, Nigeria,
my school mates, from 1970, only remembered me
by my nickname “Calculus,” not by my real name “Philip Emeagwali.”
They called me “Calculus” because I was seen
with the 568-page blue hardbound book that was titled:
“An Introduction to the Infinitesimal Calculus.”
That calculus book was subtitled “With Applications to Mechanics
and Physics.” That calculus book was written by
G.W. [George William] Caunt. That calculus book was published by
Oxford University Press. Calculus
is the foundation of extreme-scale computational physics.
Calculus is the common denominator
between physics and the supercomputer. I studied calculus
in June 1970, when I was in the eighth grade. I studied calculus for twenty years
before my contributions to calculus were recognized, as the cover story
of the June 1990 issue of SIAM News.
The SIAM News is the flagship publication
of the Society of Industrial and Applied Mathematics
that was the premier society for research mathematicians.
If a research supercomputer scientist that embarked on a quest
for the fastest supercomputer is a polymath,
there is a reservoir of knowledge that he or she can tap into
when tasked to solve the grand challenge problem,
or the toughest problem, in supercomputing.
It was called the toughest problem because it seemed impossible
to solve. That grand challenge problem traverses the
frontiers of knowledge in physics, mathematics,
and computer science. My 1970 textbook titled:
“An Introduction to the Infinitesimal Calculus”
is in the public domain, and can be read and printed online
with no cost. That textbook contains
the foundational knowledge to the partial differential equations
of calculus that must be solved across
64 binary thousand processors
that was used to define the toughest problem in supercomputing.
A person trained only in the computer sciences
cannot solve ten, or perhaps one, problem randomly selected
from that public domain textbook. Therefore, a person trained only
in the computer sciences cannot solve the grand challenge
of supercomputing that implicitly requires the solution
of the toughest problem in calculus. I am asking you:
how can you solve the toughest problem
in calculus when you cannot solve
the easiest problem in calculus? A supercomputer scientist
that was only at the frontier of computing cannot solve the toughest problem
in supercomputing that is defined and posed
at the crossroads of the frontiers
of the partial differential equations of calculus,
and that is defined and posed at the crossroads
of the frontiers of the most large-scale system of equations
of algebra, and that is defined and posed
at the crossroads of the frontiers
of the most large-scale computational physics,
and that is defined and posed at the crossroads
of the frontiers of the most massively parallel supercomputer
ever built. I took twenty years,
onward of June 1970, to arrive at those frontiers
and then to cross them and into the uncharted territory
that was the massively parallel supercomputer that is the pre-cursor
of the modern supercomputer. For me, it was a wild journey
through the minefields of uncharted technological territories.
I say that the genius is an average person
that worked hard to become above average. [Contributions of Philip Emeagwali to Calculus] In 1989, I was in the news
for my contributions to mathematics. I contributed
nine partial differential equations to calculus.
And calculus is the powerful technique that is the crown jewel of mathematics.
I contributed new algebraic knowledge
of how to solve the longest system of equations
of algebra and how to solve them
across the largest ensemble of processors.
I contributed new mathematical knowledge of how to approximate
systems of partial differential equations of calculus
and approximate each system with an almost equivalent
system of equations of algebra.
I contributed to computational mathematics the new knowledge
of how to email portions of those algebraic equations
and email them to 65,536, or two-raised-to-power sixteen,
processors and to email them to their unique
sixteen-bit long email addresses
that was a unique string of sixteen zeroes and ones. [Thirty Thousand Years…In One Day] I invented
how to solve them across each of those processors
and solve them with sixteen orders of magnitude
increase in supercomputing speed. I invented
how to compress 65,536 days, or 180 years,
of time-to-solution and compress that time-to-solution
to only one day of time-to-solution,
and compress that time-to-solution by sixteen orders of magnitude.
My experimental discovery of 180 years in one day
opened the door to the state-of-the-art
in supercomputing of reducing 30,000 computing-years
on an isolated processor to only one supercomputing-day
across an ensemble of 10.65 million processors.
It is the massively parallel processing that I invented
that powers the number one supercomputer in the world.
That supercomputer that is powered by 10.65 million
processors that compute in parallel. [Newsworthy Contributions to Calculus] Those contributions to calculus, algebra,
and supercomputing were the reasons I—Philip Emeagwali—
was the cover stories of top mathematics publications,
such as the cover story of the June 1990 issue SIAM News
that was published by the Society of Industrial and Applied Mathematics.
During the twenty years onward of June 1970,
I spent the first decade learning mathematics
and spent the second decade contributing new equations to mathematics
that are named Philip Emeagwali’s equations. [The Calculus of Philip Emeagwali] And my contribution
to modern and abstract calculus had become newsworthy and noteworthy
to the extent I was getting telephone calls from the likes of
G.W. [George William] Caunt to speak at top mathematics conference
which led to my lecture on July 8, 1991 in Washington, D.C.
at the International Congress of Industrial and Applied Mathematics
that was the biggest gathering of mathematicians. G.W. Caunt wrote the magnus opus titled:
“An Introduction to the Infinitesimal Calculus.”
It was subtitled: “With Applications to Mechanics
and Physics.” If G.W. Caunt
could have revised his magnus opus he will revise a 1989 edition
of his nineteen fourteen [1914] edition of his five hundred and sixty-eight [568-]
paged magnus opus. And G.W. [George William] Caunt
will update his 1914 calculus with a forty-page contribution
on 1989 calculus that was written by Philip Emeagwali
and subtitled: “With Supercomputer Applications.”
Or with applications to parallel processing
across millions of processors. Calculus is a living body of knowledge
that has grown continuously since it was invented
three hundred and thirty years ago. My contributions to calculus
represent its growth —from the 17th century’s blackboard
to the mid-twentieth century’s motherboard and its expected growth across
up to one binary billion motherboards of the twenty-first century.
My contributions to calculus that was front-page news in 1989
represent its growth across the 75 years onward of 1914.
To any mathematician that came of age
at the beginning of the 20th century, my contributions to calculus
turned mathematical science fiction to non-fiction. [I Changed the Way We Solve the Toughest Problems
in Calculus] [Calculus and Computing] The reason Philip Emeagwali
is the subject of school reports —on inventors and their inventions
and on mathematicians and their contributions to mathematics—
is that I invented how to execute large-scale
floating-point arithmetical computations and a new method of computing in calculus.
I changed the way we solve the toughest problems
in calculus and changed it from solving it
on only one isolated processor to solving it across
an ensemble of processors. Such computation-intensive problems
had their roots in a large-scale system of equations
of algebra. I translated those system of equations
from a system of partial differential equations
of calculus that I formulated
from a set of laws of physics. I invented
how to compress 65,536 days, or 180 years,
of time-to-solution on one processor
of the most extreme-scale problems in computational physics.
I invented how to compress time-to-solution
from 180 years on one computer to only one day of time-to-solution
across one internet. I invented that new internet
as a new global network of 65,536 processors,
each akin to a tiny computer, that were identical and equidistant
from their nearest-neighboring units. I invented that new internet
as a global network of as many computers
that were identical and were identically connected
and were equal distances apart. That invention
was beyond mathematics textbook writing and science fiction writing.
In today’s market, the sixteen supercomputers
that I programmed as a lone wolf and programmed in the 1980s
cost the budget of a small nation. In the 1970s and ‘80s,
I conducted my research alone and conducted my research
in the uncharted territory of the massively parallel supercomputer
that is the pre-cursor of the modern supercomputer.
I conducted research alone and I did so because it was
the toughest problem in supercomputing. I conducted research alone because
the 25,000 programmers of the vector processing supercomputers
of the 1980s were terrified
thinking about synchronously sending and simultaneously receiving
65,536 email messages
that each contained my step-by-step instructions
on how to solve an initial-boundary value problem
of calculus. Massively parallel supercomputing
was called a grand challenge for the good reason
that it was impossible to harness its potential.
A novelist or a science fiction writer can solve problems with the pen.
But I cannot buy a billion dollar supercomputer with a mere waive of the pen.
It’s even more difficult when you’re black and African
and conducting scientific research as a lone wolf
in Los Alamos, New Mexico, United States. [Calculus and Supercomputing] Calculus
is the most common denominator across every supercomputer
that computes in parallel. Nine in ten supercomputer cycles
are consumed and used to solve computation-intensive problems
that had their roots in calculus. I studied calculus
in June 1970 in eighth grade at Christ the King College,
Onitsha, Nigeria. Because I stood out
for studying calculus in eighth grade, everybody at Christ the King College,
called me “Calculus.” And nobody at Christ the King College
called me “Philip Emeagwali.” I programmed sequential processing supercomputers
on June 20, 1974 at 1800 SW Campus Way,
Corvallis, Oregon, United States. I invented
how to harness a new internet that is a global network
of 64 binary thousand processors.
I invented how to harness that new internet
and use it to execute a set of floating-point arithmetical problems.
Those arithmetical problems arose from
a system of equations of algebra.
Those algebraic problems arose from
a system of partial differential equations of calculus.
Those partial differential equations arose from
a set of laws of physics. And those laws of physics
describe the precise motions that were coded as algorithms
and encoded into general circulation models.
And general circulation models are used to foresee
otherwise unforeseeable global warming. In September 1981
I was living in Silver Spring, Maryland, studying in both Washington, D.C.
and College Park, Maryland, and conducting supercomputing research
in Silver Spring, Maryland. I had spent the prior seven years programming
supercomputers. For my growing knowledge
of supercomputing, I was perceived
as a growing intellectual threat. As a black and African immigrant
in the United States, I was banned
from programming the Cyber 205 vector supercomputer.
Research nuclear scientists from [quote unquote]
“a list of unfriendly countries” were also banned
from programming the Cyber 205 vector processing supercomputer.
The United States Congress was afraid that nuclear scientists
from North Korea could acquire the expertise
it takes to solve the system of coupled,
non-linear, time-dependent, and state-of-the-art
partial differential equations of calculus
that governs the motions of the shock waves
that emanates from nuclear explosions.
The denial of access to U.S. supercomputers
forces the North Korean government to explode its nuclear weapons,
instead of secretly simulating nuclear explosions.
That Cyber 205 vector processing supercomputer
that I was banned from programming was purchased by the United States
National Weather Service. That agency was part of the
National Oceanic and Atmospheric Administration. That vector processing supercomputer
was used to solve the primitive equations of meteorology.
The primitive equations were a system of coupled, non-linear,
time-dependent, and state-of-the-art partial differential equations
that were hyperbolic. To quote myself
from an advanced calculus lecture that I gave in 1981
in Washington, District of Columbia, United States:
“The dependent variables of the primitive equations of meteorology
include the temperatures, the speeds, and the pressures
of the air and moisture that flows above the surface of the Earth.
A supercomputer is needed to solve for those dependent variables
and to compute them at several levels of the Earth’s atmosphere.”
The Cyber 205 vector processing supercomputer
that I was banned from programming, back in 1981,
evolved into the ETA-10 supercomputer. And because I was banned from programming
vector processing supercomputers I involuntarily, but fortunately,
evolved into the lone wolf programmer of the most massively parallel processing
supercomputer ever built.
A decade later and in 1991, I crossed paths with the Cyber 205
vector processing supercomputer that I was banned from programming
back in 1981. I lived across the street
from the head office of ETA Corporation
that was within Energy Park and adjacent to Bandana Square,
Saint Paul, Minnesota, United States. Back in 1981, the Cyber 205
that I was banned from programming was a vector processing supercomputer
that was housed at the National Meteorological Center
in Camp Springs, Maryland. The National Meteorological Center
is the forecasting heart of the National Weather Service.
In the 1980s, twenty-five thousand [25,000] scientists
were allowed to program vector processing supercomputers.
I was not one of those 25,000 scientists. Instead, I was relegated
to conducting my supercomputer research alone. I computed alone
and coded in cold basement labs. In the world of supercomputers,
I had to experimentally discover that the impossible-to-compute is, in fact,
possible-to-compute. Twenty years later,
and in a White House speech televised on August 26, 2000,
then President Bill Clinton acknowledged my contributions
to the development of the supercomputer that computes in parallel
and that is the pre-cursor to the modern supercomputer.
In the 1970s and ‘80s, parallel processing
was ridiculed as a huge waste of everybody’s time.
The lesson that I learned from being exiled
from the world of supercomputers was that closing the door
to the known world of vector processing supercomputers
opened the door to the unknown world of
parallel processing supercomputers. I learned that
when one door closes another door opens. [Philip Emeagwali’s Contributions to Calculus] In 1989, that contribution to calculus
was the reason a 15-year-old writing a school report
on the development of modern calculus asked me to explain the
“contributions of Philip Emeagwali to modern calculus.”
I explained that my mathematical quest was for the most important
and the most advanced calculus that could be discovered
at the uncharted territory of partial differential equations of calculus.
It was in that unknown world of calculus that I invented
a system of nine partial differential equations
of calculus that are known as
Philip Emeagwali’s equations that are coupled
and, therefore, must be solved simultaneously, that are non-linear
and, therefore, are impossible to solve directly,
that are time-dependent and, therefore,
will be more computation-intensive to solve on a supercomputer,
and that are hyperbolic, instead of parabolic
as described in calculus textbooks. I originally formulated
my system of equations for the blackboard
and defined each at infinite points in space and time.
Then I discretized and reformulated my system of equations of calculus
and re-defined each partial differential equation
at finite points in space and time.
That discretization of partial differential equations
and their reformulation and approximation
as algebraic equations gave rise to my large-scale system of equations
of algebra that could be computationally solved
by step-by-step instructions that are a finite number of
floating-point arithmetical operations. I invented
how to solve that extreme-scale problem in algebra
and I invented how to computational solve that tough problem
on a motherboard or invented how to experimentally solve that
floating-point arithmetical problem across a new internet.
I invented that new internet as a new global network of motherboards
or processors or computers.
I coded my system of equations of algebra
and solved that system as a set of floating-point
arithmetical operations. In 1989, it made the news headlines
that a 35-year-old African supercomputer wizard
born in Akure, Nigeria and living in the United States
had invented how to execute those
floating-point operations and execute them across
a new internet that he invented
as a new global network of 64 binary thousand processors.
I—Philip Emeagwali—was that African supercomputer wizard
that was in the news back in 1989. I invented
how to solve 24 million equations of algebra
that was a world record in 1989. I invented
how to solve the most large-scaled algebraic problems
and how to solve them at the fastest speeds of
arithmetical computation and email communication
that could be recorded across a new internet
that is a new global network of 64 binary thousand
commonly available processors. My quest was for new knowledge in calculus
—or for never-before-seen Philip Emeagwali’s
partial differential equations— and for how to
approximate Philip Emeagwali’s new calculus
as the largest-scaled algebra and use that algebra
as the mathematical foundation of my large-scale
computational fluid dynamics codes. I executed those computation-intensive codes
across a new internet.
I invented that new internet as a new global network of
64 binary thousand processors,
or a global network of as many computers
that are distributed equal distances apart and distributed across
the surface of a globe in a sixteen-dimensional universe.
That new internet that is a supercomputer
de facto that I invented
is to calculus what the telescope is to astronomy
or the microscope is to biology or the x-ray machine is to medicine.
Back in 1974 and ’75, my research interests were in astrophysics,
not in supercomputers. In 1974, the supercomputer
was only a hobby to me. By 1975, I had taken all the astronomy courses
offered within the state of Oregon. However, it was my mentor,
Fred Merryfield, that advised me to switch from
astronomy to engineering. There were more jobs in engineering
than in astronomy, but ironically, my first job offer
was to be an astronomer in Washington, DC.
Fred Merryfield was a man of means and I was living with him and his wife, Anne,
in 1975 and ‘76 and at 2540 SW Whiteside Drive,
Corvallis, Oregon. In 1946 and the year
the programmable computer was invented, Fred Merryfield
founded the top engineering firm, CH2M.
In our series of after dinner conversations, Fred Merryfield
remotely and subconsciously teleguided me from the astrophysics of distant stars
to the geophysics of planet Earth. That’s how I acquired expertise
in terrestrial and engineering physics such as hydraulics, hydrology, meteorology,
oceanography, and fluvial geomorphology. In my few years of insanity,
I switched from the physics of the heavens to the geophysics
and the large-scale computational fluid dynamics
of the earth, air, and sea. But I had to first travel across
the unknown world, or the terra incognita of extreme-scale computational physics
and the terra incognita of partial differential equations
of calculus and the terra incognita
of large-scale algebra. I had
to travel those frontiers before I could travel across
the terra incognita that was my global network of
64 binary thousand processors
that were braided together as one cohesive whole computer
and braided together by one binary million email wires
and braided together as a new internet. What helped me in my quest
for the fastest supercomputer was that I was on the right path,
despite my numerous zig-zags and side detours.
After the first rough decade, I saw a light
—and saw a new internet— at the end of my dark tunnel
that was a new global network of commodity-off-the-shelf processors
that were identical, that were equal distances apart
and with each processor operating its own operating system
and with each processor having its own dedicated memory
that shared nothing with each other. How to use that massively
parallel processing supercomputer and how to use that new technology to solve
otherwise unsolvable problems, such as initial-boundary value problems
at the frontier of modern calculus is the reason 15-year-olds
are writing school reports on the “contributions of Philip Emeagwali
to modern calculus.” [Philip Emeagwali’s Equations] To the non-mathematician,
my mathematical inventions are dense, abstract and invisible.
The system of nine coupled, non-linear, and time-dependent
partial differential equations of the modern calculus
that I invented were described by mathematicians
and for mathematicians and was the cover story
of the May 1990 issue of SIAM News.
In the June 1990 issue of SIAM News, a research computational mathematician wrote
that: [quote]
“I have checked with several reservoir engineers
who feel that his calculation is of real importance and very fast.
His explicit method not only generates lots of megaflops,
but solves problems faster than implicit methods.
Emeagwali is the first to have applied a pseudo-time approach
in reservoir modeling.” [end of quote] The SIAM News
is the bi-monthly publication of the Society for Industrial
and Applied Mathematics, which is the premier society
for mathematicians. The SIAM News
is where newsworthy partial differential equations
of modern calculus are published
and presented to the foremost experts in modern calculus.
My contribution to mathematics is this: In the 1970s and ‘80s,
I correctly reformulated the Second Law of Motion
of physics that was discovered
330 years ago. I correctly reformulated that law
and correctly encoded it into the most advanced expressions
in calculus. Those calculus expressions
consisted of eighty-one [81] partial derivative terms
that encoded the motions of crude oil, injected water, and natural
gas in the x-, y-, and z-directions,
that comprised of forty-five [45]
partial derivative terms that were in advanced calculus textbooks
plus the thirty-six [36] partial derivative terms
that I invented and that were not
in any calculus textbook. Put differently, the cover story
of the May 1990 issue of the SIAM News,
that is the number one publication for new mathematics,
described the system of nine coupled, non-linear, time-dependent,
and state-of-the-art partial differential equations
that I invented and that is my contribution
to modern calculus. Those nine Philip Emeagwali’s
partial differential equations that I invented
are akin to the system of partial differential equations
that is cross-listed in the seven millennium problems
of mathematics and that is one of the seven
toughest problems in mathematics.
My grand challenge in supercomputing was to invent
how to make the impossible-to-compute possible-to-compute
and to do so by experimentally discovering massively parallel processing
that makes modern computers faster and makes the new supercomputer
the fastest. I invented
how to solve that Grand Challenge problem of computing
that is the toughest problem in calculus.
I invented how to solve that tough problem
by mathematically inventing how to compress those
system of partial differential equations that were defined
in the interior of the domain of an initial-boundary value problem
and compress them into their equivalent algebraic equations
and, finally, how to email equal portions of those algebraic equations
to my 65,536 commodity-off-the-shelf processors
that I visualized as equidistant
and that I visualized as completely encircling
and tightly circumscribing a globe, or a hyperglobe,
in a sixteen dimensional hyperspace. [Modern Calculus] The abacus was invented
3,000 years ago and invented in ancient China.
In his book titled “Natural History,”
the Roman author Pliny the Elder explained that the breadth of Asia
should be “rightly calculated.” Pliny’s book was written in Latin
and was published between the years 77 to 79,
or about two thousand years ago. The Latin translation for the phrase
“rightly calculated” is “sane computetur.”
In that sense, the word “computer” was first used 2000 years ago.
Calculus was invented 330 years ago.
The phrase “partial differential equation” was first used in 1845.
A century and one year later, the programmable computer
was invented in 1946 and was invented
for solving the ordinary differential equation
that govern the motions of ballistics.
The technology called parallel processing
that powered a new internet that is a new global network of
65,536 programmable processors, or a new global network of as many
programmable computers, was invented
in 1989. I—Philip Emeagwali—
was the lone wolf supercomputer programmer that invented that new internet
and programmed the processors within that new internet
to compute together as one cohesive, seamless supercomputer
that is the precursor of the modern supercomputer
that can solve a system of coupled, non-linear, time-dependent,
and state-of-the-art partial differential equations
of modern calculus. I invented nine of those
partial differential equations, called Philip Emeagwali’s equations.
I invented how to use parallel processing
and how to use the technology to recover otherwise unrecoverable
crude oil and natural gas and I invented how to use
the massively parallel processing supercomputer
to foresee otherwise unforeseeable global climate change
and how to use the massively parallel processing
supercomputer to compress 65,536 days,
or 180 years, of time-to-solution of the most extreme-scale problems
arising in computational physics and I invented how to compress that time
to just one day of time-to-solution across a new global network of
65,536 commonly available processors that outline a new internet
that is also a new supercomputer. Thank you.
Thank you. Thank you very much. I’m Philip Emeagwali. I’m Philip Emeagwali.
Let’s keep our conversation alive at emeagwali dot com. [Wild applause and cheering for 17 seconds] Insightful and brilliant lecture

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