Mathematicians Project

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Mathematicians Project

• Dany Gonzalez
• Joe Kennedy
• Joe Puchner
• Randy Spaulding

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• Maria Agnesi (Italian, 1718-1799)
• Was very religious, wanted to become a nun
• Wrote a book on differential calculus
• Also wrote Instituzioni analitiche ad uso della
  gioventù italiana, a book on systemic algebra
• This book contains discussion about a cubic curve
  now know as the "witch of Agnesi
• About this It took much skill and sagacity to
  reduce, as the author has done, to almost uniform
  methods these discoveries scattered among the
  works of modern mathematicians and often
  presented by methods very different from each
  other. Order, clarity and precision reign in all
  parts of this work. ... We regard it as the most
  complete and best made treatise.
• Pope Benedict XIV wrote to her, praising her for
  her advancements in mathematics in Italy
• He appointed her to honorary reader at the
  University of Bologna.
• She was a very religious and very scholarly
  woman, and she devoted her life to mathematics
  and religion

3

• Mohammed al-Khowarizmi (Arabic, c. 790-850)
• First to use zero as a place holder
• "Algorithm" derives from his name
• Considered the first to write a book on algebra
• Came up with six standard forms of equations
• 1. Squares equal to roots. 2. Squares equal to
  numbers. 3. Roots equal to numbers. 4. Squares
  and roots equal to numbers e.g. x2 10 x
  39 5. Squares and numbers equal to roots e.g.
  x2 21 10 x 6. Roots and numbers equal to
  squares e.g. 3 x 4 x2
• Wrote books on geography and astronomy
• Considered one of the greatest mathematicians of
  all time
• Al-Khwarizmi's algebra is regarded as the
  foundation and cornerstone of the sciences. In a
  sense, al-Khwarizmi is more entitled to be called
  "the father of algebra" than Diophantus another
  mathematician because al-Khwarizmi is the first
  to teach algebra in an elementary form and for
  its own sake, Diophantus is primarily concerned
  with the theory of numbers.

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• Charles Babbage (English, 1791-1871)
• Originated the modern analytic computer
• Educated at private schools in England, loved
  mathematics from an early age.
• He is credited for providing the basic thinking
  behind modern computers
• I was sitting in the rooms of the Analytical
  Society, at Cambridge, my head leaning forward on
  the table in a kind of dreamy mood, with a table
  of logarithms lying open before me. Another
  member, coming into the room, and seeing me half
  asleep, called out, Well, Babbage, what are you
  dreaming about?" to which I replied "I am
  thinking that all these tables" (pointing to the
  logarithms) "might be calculated by machinery.
• He later published Reflections on the Decline of
  Science in England, which caused the formation of
  the British Association for the Advancement of
  Science.

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• Bernoulli Family (Swiss, 1600s and 1700s)
• They immigrated to Switzerland from the
  Netherlands to flee from Spanish oppression.
• Accomplishments
• Daniel Bernoullis Principle Energy is
  conserved in a moving fluid- this can explain why
  an airplane can fly, and why a baseball pitcher
  can throw a curveball.
• Jacob First to use the term integral and was
  one of the first to use polar coordinates.
• Johann Studied reflection and refraction of
  light.
• Johann II Studied heat and light.
• Johann III Wrote numerous books on number
  theory, probability, and astronomy.
• Nature always tends to act in the simplest way.
  -Daniel Bernoulli

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• Janos Bolyai (Hungarian, 1802-1860)
• Was a genius from a very early age ... when he
  was four he could distinguish certain geometrical
  figures, knew about the sine function, and could
  identify the best known constellations. By the
  time he was five he had learnt, practically by
  himself, to read. He was well above the average
  at learning languages and music. At the age of
  seven he took up playing the violin and made such
  good progress that he was soon playing difficult
  concert pieces.
• Wrote a complete treatise on non-Euclidean
  Geometry
• Developed complex geometric numbers
• Could speak nine languages and performed the
  violin in Vienna.
• There is a crater on the moon named after him

7

• George Boole (English, 1815-1864)
• Created Boolean Algebra (which many consider the
  foundation of computer science)
• In Boolean algebra, he incorporated logic into
  mathematics
• He also wrote books about differential equations
  and the calculus of finite differences
• He also discovered general methods in probability
• His work was highly recognized- he was given
  honorary degrees from the University of Dublin
  and the University of Oxford.
• I can speak confidently to the fact of his being
  not only well-versed in the highest branches of
  mathematics, but possessed of original power for
  their extension which gives him a very
  respectable rank among their English cultivators
  of this day.
• He died after he caught a cold when walking to
  teach a class in the rain

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• Brahmagupta (Indian, 598-670)
• The greatest Indian mathematician of the time
• Understood number theory (debt is a negative
  number, fortune is a positive number)
• A debt minus zero is a debt. A fortune minus
  zero is a fortune. Zero minus zero is a zero. A
  debt subtracted from zero is a fortune. A
  fortune subtracted from zero is a debt. The
  product of zero multiplied by a debt or fortune
  is zero. The product of zero multiplied by zero
  is zero. The product or quotient of two fortunes
  is one fortune. The product or quotient of two
  debts is one fortune. The product or quotient of
  a debt and a fortune is a debt. The product or
  quotient of a fortune and a debt is a debt.
• He also made significant advances in astronomy
  writing about the longitudes of the planets the
  three problems of diurnal rotation lunar
  eclipses solar eclipses risings and settings
  the moon's crescent and conjunctions of the
  planets.

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• Rene Descartes (French, 1596-1650)
• Came up with Cartesian Geometry (analytical
  geometry)
• The basis is Cartesian coordinates (x,y)
• This was the first ever link between Euclidean
  geometry and algebra.
• It is the study of geometry using a coordinate
  plane and principles of algebra and analysis
• Was also a very famous philosopher
• Driven to understand being and existence
• Very famous quote Cogito Ergo Sum (I think
  therefore I am).
• Key thinker of the scientific revolution

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• Leonhard Euler (Swiss, 1707-1783)
•  Leonhard was born to a family of religion who's
  father was a pastor. He went to the Paris
  academy and thats where he began working on his
  scholarly pieces.
• Accomplishments-
• Published a book Mechanica in 1736
• Won the Grand Prize at Paris Academy
• 1759- took over the Berlin Academy
• Chairman of physics in the Academy in St
  Petersburg
• Director of geography at St. Petersburg Academy
• Solved the problem of the Bridges of Königsberg
• The problem was to find a path through the city
  that would cross each of 7 bridges once and only
  once. The islands could not be reached by any
  route other than the bridges, and every bridge
  must have been crossed completely every time.
• Euler proved that the problem has no solution.
• "For since the fabric of the universe is most
  perfect and the work of a most wise Creator,
  nothing at all takes place in the universe in
  which some rule of maximum or minimum does not
  appear."

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• Pierre De Fermat (French, 1601-1665)
• Accomplishments-
• He received a degree in civil law in Toulouse and
  received a spot in parliament
• Changed his name to Pierre de Fermat after
  receiving this recognition
• Wrote Plane Roci
• Most known for Fermat's Last Theorem- The first
  proof of this theorem was discovered in 1995!
• New Account of Discoveries in the Science of
  Numbers
• Fluent in four languages
• I have found a very great number of exceedingly
  beautiful theorems.

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• Leonardo Pisano Fibbonaci (Italian, c. 1170-1250)
• Accomplishments
• Liber abaci-Focused on forgotten math skills
• Fibonacci's number sequences 1,1, 2, 3, 5, 8,
  13, 21 (sum of the previous two numbers)
• Liber quadratorum-examining Pythagorean triples
• Practica geometriae-Chapter 8 of Euclid's elemnts
• Published over 6 math books in his career
• ... the serious and learned Master Leonardo
  Bigollo ....

13

• Evariste Galois (French, 1811-1832)
• Accomplishments
• Annales de mathématiques- book on continued
  fractions
• the condition that an equation be soluble by
  radicals-paper written but teacher died before
  could be recognized for it
• Galois theory-study of polynomial equations
• Submitted papers before he died which got
  recognition later
• Bulletin de Férussac- article written on Abels
  theory
• This pupil is sometimes obscure in expressing
  his ideas, but he is intelligent and shows a
  remarkable spirit of research

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• Johann Carl Friedrich Gauss (German, 1777-1855)
• Accomplishments
• Disquisitiones Arithmeticae- book on the number
  theory
• Wrote a dissertation on the fundamental theory of
  algebra
• Director of a observatory in Gottingen
• Theoria motus corporum coelestium in sectionibus
  conicis Solem ambientium- book on celestial
  bodies
• Disquisitiones generales circa superficies curva-
  another book written on geography
• Bestimmung der Genauigkeit der Beobachtungen
  explained statistical estimators
• Methodus nova integralium valores per
  approximationem inveniendi - book on approximate
  integration
• To praise it would mean to praise myself .

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• Hypatia (Egyptian, c. 370-415)
• Accomplishments-
• Hypatia became head of the Platonist school at
  Alexandria
• Taught philosophy of Neoplatonism
• Focused mainly on Christian students to teach
• Assisted her father in writing Almagest
• She undertook original mathematical research
• Synesius letters have been kept to admire the
  work of Hypatia
• ... by her eloquence and authority ... attained
  such influence that Christianity considered
  itself threatened ...

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• Johann Kepler (German, 1571-1630)
• Accomplishments-
• Best known for three principles of planetary
  motion
• attend the University of Tbingen
• The More Reliable Bases of Astrology- rejected
  theory that stars guide human life
• The New Star in the Foot of the Serpent
  Bearer-described the supernova that was
  witnessed by Kepler
• Was able to explain how glasses work
• Proposed the elliptical orbit, equality of areas,
  and the Harmonics of the World principles
• I much prefer the sharpest criticism of a single
  intelligent man to the thoughtless approval of
  the masses.

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• Felix Klein (German, 1849-1925)
• Accomplishments
• Attended University of Bonn
• Über die Transformation der allgemeinen Gleichung
  des zweiten Grades zwischen Linien-Koordinaten
  auf eine kanonische Form- written on line
  geometry
• Appointed to professor at Erlangen
• Klein wrote a major four volume classic on
  automorphic and elliptic modular functions
• Klein was elected to the Royal Society
• The London Mathematical Society awarded him their
  De Morgan Medal
• Every one who understands the subject will agree
  that even the basis on which the scientific
  explanation of nature rests is intelligible only
  to those who have learned at least the elements
  of the differential and integral calculus, as
  well as analytical geometry.

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• Gottfried Leibniz (German, 1646-1716)
• Philosopher and mathematician
• Developed infinitesimal calculus (disputed with
  Newton as to who really discovered calculus)
• Study of extremely small lengths and areas (i.e.
  the slopes of curves and the areas underneath
  them
• discovered the mechanics (the Leibniz wheel)
  behind the first mechanical calculator, the
  arithmometer, patented by Thomas de Clomar

• nearly 150 years later
• Refined the binary number system, the basis of
  all modern computers, nearly 250 years before its
  time
• devised the Leibniz formula for pi
• 1 - 1/3 1/5 - 1/7 1/9 - ..... p/4
• I also take it as granted that every created
  thing, and consequently the created monad also,
  is subject to change, and indeed that this change
  is continual in each one.

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• Nikolai Lobachevsky (Russian, 1792-1856)
• mathematician and geometer
• founder of hyperbolic geometry (also called
  Lobachevskian geometry)
• non-Euclidean geometry
• does not follow Euclids parallel postulate
• postulate states that with any given line and
  point not on that line, there is one line that
  goes through the point and does not intersect
  that line
• based on geometry that is set on a saddle-shaped
  plane (hyperbolic paraboloid)
• the point used in Euclids parallel postulate has
  2 lines that go through it while not intersecting
  the separate line
• had the Lobachevsky Prize for superior
  mathematicians named after himself.
• There is no branch of mathematics, however
  abstract, which may not some day be applied to
  phenomena of the real world.

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• Marin Mersenne (French, 1588-1648)
• Theologian, philosopher, mathematician, and music
  theorist
• Studied Mersenne primes, where positive integers
  one less than a power of two, in which the power
  must be prime, yield another prime number
• 47 Mersenne primes are known
• formula helped in finding the largest known prime
  number
• 12,978,189 digits long
• Helpful for determining strength of computers
  computing capability by programming the computer
  to find a Mersenne prime
• Was the first to determine the speed of sound in
  air by measuring the return of an echo. His final
  product was in error by only 10
• Animals do not so much act as be put into
  action, and that objects make an impression on
  their senses such that it is necessary for them
  to follow it just as it is necessary for the
  wheels of a clock to follow the weights and the
  spring that pulls them.

21

• John Napier (Scottish, 1550-1617)
• mathematician, physicist, astronomer, and
  astrologer
• Devised the widely used mathematics of logarithms
• Used to simplify calculations
• Logb(xy)logb(x) logb(y)
• log(1000) 3 103
• Logarithms have many applications
• The shell of the sea creature nautilus displays a
  logarithmic spiral

• Measurements and charts in logarithmic scales
• Psychology relationship between stimulus and
  sensation
• Probability and statistics
• Chemistry entropy
• Music intervals
• Aside from mathematics
• Believed the world would end in 1688 or 1700

"Seeing there is nothing that is so troublesome
to mathematical practice.... than the
multiplications, divisions, square and cubical
extractions of great numbers, which besides the
tedious expense of time are... subject to many
slippery errors, I began therefore to consider
how I might remove those hindrances."
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• Sir Isaac Newton (English, 1643-1727)
• physicist, mathematician, astronomer, natural
  philosopher, alchemist, and theologian
• Devised the widely known concept of gravity and
  the three laws of motion
• gravity is the natural phenomenon by which
  physical bodies attract wiht a force proportional
  to their mass
• Laws of Motion
• If a body is at rest it remains at rest or if it
  is in motion it moves with uniform velocity until
  it is acted on by a resultant force.
• Force is equal to mass times acceleration
• For every action, there is an equal and opposite
  reaction

• Created the first practical reflecting telescope
• Combination of curved mirrors that reflect light
  and form an image
• Allows viewing of very large diameter objectives
• Worked with Leibniz in the development of
  calculus - the study of change
• Differential calculus - study of rates at which
  quantities change
• Integral Calculus - the determination,
  properties, and application of integrals
• Praised as one of the most influential people in
  human history
•  This most beautiful system The Universe could
  only proceed from the dominion of an intelligent
  and powerful Being.

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• Blaise Pascal (French, 1623-1662)
• mathematician, physicist, writer, and Catholic
  philosopher
• Was a child prodigy
• Devised Pascals Triangle
• a triangular array of numbers in which those at
  the ends of the rows are 1 and each of the others
  is the sum of the nearest two numbers in the row
• Has useful applications in binomial expansions
  and combinations
• Worked extensively in the fields of hydrodynamics
  and hydrostatics, mainly in the development of
  the principles of hydraulic fluids
• Invented the hydraulic press and the syringe

• The SI unit of pressure, the pascal, is named
  after Blaise Pascal for his contributions to the
  science behind pressure
• All human evil comes from a single cause, man's
  inability to sit still in a room.

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• Srinivasa Ramanujan (Indian, 1887-1920)
• mathematician
• Devised Ramanujan primes
• prime numbers that satisfy Ramanujans equation
  for counting primes
• Found the Hardy-Ramanujan number 1729
• the smallest number expressable as the sum of two
  cubes in two different ways
• Devised the Ramanujan theta function
• An equation for me has no meaning unless it
  expresses a thought of God.

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• Bernhard Riemann (German, 1826-1866)
• Mathematician
• developed ideas concerning the geometry of space
• has a large effect on modern physics
• created Riemannian geometry

• geometry in an area that is not necessarily flat,
  but infinitely close to flat
• introduced the Riemann zeta function
• developed theories of higher dimensions
• If only I had the theorems! Then I should find
  the proofs easily enough.

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Thales of Miletus  -Born in about 624 BC in Asia
Minor, now Turkey.-Recognized as the first Greek
philosopher.-Taught Anaximander, a famous
philosopher.-First Natural Philosopher in the
Milesian School. -He rejected mythological
explanations of things, and therefore is
sometimes called the father of
science.-Correctly predicted the eclipse of the
sun in 585 BC.-died in around 547 BC in Asia
Minor. Nothing is more active than thought, for
it travels over the universe, and nothing is
stronger than necessity for all must submit to
it.
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John Von Neumann -Born in December 28 1903 in
Budapest, Hungary.-Taught in both the United
States and Europe.-Was one of the 6 original
math professors in Princeton, one of the others
being Albert Einstein.-Was the co-editor of the
Annals of Mathematics and Compositio
Mathematica.-Awarded the Bocher Prize from the
American Mathematical Society. -Many regard him
as the greatest modern mathematician because of
his contributions to functional analysis, quantum
mechanics, continuous geometry, economics, game
theory, hydrodynamics, statistics, and computer
science.-Died in February 8 1957 in Washington
DC. Any one who considers arithmetical methods
of producing random digits is, of course, in a
state of sin.
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Andrew Wiles -Born in April 11 1953 in
Cambridge, England.-Spent most of his life
trying to prove the Shimura-Taniyama conjecture,
knowing it would prove Fermats last
theorem.-Spent 2 years in Oxford as a Royal
Society Research member.-Eventually proved
Fermat's theorem and was awarded the Shaw Prize
for Mathematical Sciences in 2005.-Got an
asteroid named after him, asteroid 9999
Wiles.-Named Sir Andrew Wiles later in his
life. I realized that anything to do with
Fermat's Last Theorem generates too much
interest.
29
Zeno of Elea -Born in about 490 BC in Elea, now
southern Italy.-not much known about
Zeno.-studied with Parmenides in Elea. -it is
said that he visited Socrates and Parmenides met
with Zeno in Athens.-argued that something
without magnitude cannot exist.-Often got in
arguments with Plato and Aristotle. -He posed
paradoxes to challenge mathematical views of the
time.-Died in 425 BC in Elea. "My writing is an
answer to the partisans of the many... with a
view to showing that the hypothesis of the many,
if examined in sufficient detail, leads to even
more absurd results that the hypothesis of the
One."
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Archimedes -Born in 287 BC in Sicily.-invented
the device known as Archimedes screw in
Egypt.-Wrote many books about geometry.-wrote a
book One Plane Equilibriums, Sphere and Cylinder,
On Spirals and so on.-Approximated pi extremely
accurately-while pursuing many things,
Archimedes always said that his biggest interest
was mathematics.-helped build many machines
according to King Herod. -Claimed he could move
the world with a simple lever.-died in 212 BC in
Sicily. Give me a place to stand, and I will
move the world
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Euclid -born in about 325 BC.-considered the
most important early mathematician.-Most famous
for his book The Elements, which describes
geometry.-His book The Elements consisted of 13
books.-His book begins with definitions and 5
postulates.-So influential that most of his
students wrote books about him.-died in about
265 BC in Alexandria, Egypt. The laws of nature
are but the mathematical thoughts of God.
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Pythagoras -Born in about 569 BC in Samos,
Ionia.-described as the first pure
mathematician.-the 2 people that had a big
influence on him were Thales and
Anaximander.-not much known about his childhood
or actual work.-famous for the Pythagorean
theorem.-discovered irrationals.-first to be
able to construct the first 3 solids but not the
last 2.-taught that the earth was a sphere and
was at the center of the universe.-died in about
475 BC. The oldest, shortest words - "yes" and
"no" - are those which require the most
thought.
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Jean Le Rond d'Alembert  -born in November 17 in
Paris, France.-had to take care of himself for
most of his life because his father died when he
was 9.-helped improve Newtons definition of
force. -Studied laws and dynamics of motions and
fluids-Went from the Paris Academy to the Berlin
Academy because of disagreements with
classmates.-was wanted as the President of the
Berlin Academy but declined.-died in October 29
1783 in Paris. The imagination in a
mathematician who creates makes no less
difference than in a poet who invents. Of all
the great men of antiquity, Archimedes may be the
one who most deserves to be placed beside
Homer.
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• QUIZ!

1. Who came up with a theorem that wasnt proved
   until over 300 years after his death?
2. Who proved the above theorem?
3. Which mathematician wanted to become a nun?
4. Which mathematician used paradoxes as proofs?
5. Which mathematician studied laws and dynamics of
   motions and fluids?
6. Which mathematician came up with the theorem that
   states a² b² c²?
7. This mathematician has a branch of math named
   after him _______ean Geometry.
8. This German mathematician wrote about celestial
   bodies and statistical estimators.
9. This mathematician was Egyptian.
10. The _______ Theory is a study on polynomial
    equations.
11. This mathematician wrote a whole treatise on
    non-Euclidean Geometry.
12. Which modern mathematician contributed to
    functional analysis, quantum mechanics,
    continuous geometry, economics, game theory,
    hydrodynamics, statistics, and computer science?
13. Which mathematician came up with a series where
    the next number is the sum of the previous two?
14. This mathematician wrote a major four volume
    classic on automorphic and elliptic modular
    functions.
15. This mathematician came up with three laws about
    planetary motion.
16. This mathematician and philosopher is also known
    as the father of science.

35

• QUIZ!

1. This mathematician solved the Bridges of
   Konigsberg.
2. These two mathematicians are disputed as being
   the inventors of calculus.
3. This mathematician is considered the father of
   computer science.
4. This mathematician is considered the father of
   the analytical computer.
5. This Indian mathematician understood positive and
   negative number theory.
6. This Arabic mathematician was the first to use
   zero as a placeholder.
7. This mathematical family fled from the
   Netherlands to avoid Spanish oppression.
8. This mathematician was also a philosopher, known
   for the quote, I think, therefore I am.
9. This mathematician founded hyperbolic geometry.
10. This mathematician was the first to calculate the
    speed of sound.
11. This mathematician invented logarithms.
12. This mathematician has a unit of pressure named
    after him.
13. This mathematician discovered Ramanujan primes.
14. This mathematician created geometry in an area
    that is not necessarily flat, but infinitely
    close to flat.
15. This Greek mathematician approximated pi
    extremely accurately.