## Historical Development of Mathematics

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Historical Development of Mathematics

M.Ö2000

500

EGYPT & MESOPOTAMIA

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INDIAN-ISLAMRENAISANCE

500

ANCIENTGREECE

1700

17TH 18TH CENTURY

1900

MODERN AGE

"Math is Our Life" project team presents

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Historical Development of Mathematics

EGYPT & MESOPOTAMIA

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The world is made up of patterns and sequences: the day becomes night, the landscapes are constantly changing, the phases of the moon and the seasons. One of the reasons mathematics arose was the need to understand and explain the patterns by which nature is driven. Some of the most banal mathematical concepts are deep in the human brain, and are also observed in other animal species. For the latter, assessing the distance of food or predator is a factor that makes the difference between life and death. The one who put these simple concepts together, bound them together, began to count, and thus gave birth to the entire mathematical universe is man. Our prehistoric ancestors would have had a general sensitivity about the sums, and would have instinctively known the difference between, say, one and two antelopes. But the intellectual leap from the concrete idea of two things to the invention of a symbol or word for the abstract idea of "two" was lasting. Even today, there are isolated hunter-gatherer tribes in the Amazonia that have only words for "one," "two" and "many," and others that only have words for numbers up to five. In the absence of established agriculture and trade, there is no need for a formal system of numbers.

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Birth of mathematics

Mathematics does not have a clearly defined beginning, but the occurrence of mathematics is closely related to human evolution. People may have developed certain mathematical skills even before the occurrence of writing. The oldest mathematical object is the Lebombo Bone, a baboon's fibula with 29 notches, discovered in the Lebombo mountains of South Africa and dates back to 43,000 B.C.

The oldest object that proves the existence of a method of calculation is the bone in Ishango, Democratic Republic of Congo, which dates back to 20,000 B.C. It has been said that the marks on the object, a series of incisions arranged on three columns along the bone, are not random and that it is probably some kind of counting tool used to perform simple mathematical procedures. During the Egyptian predynasties of the 5th millennium B.C. some geometric paintings appeared.

The Egyptians and pre-dynastic Sumerians represented geometric patterns on their artifacts as early as the 5th B.C., also some megalithic societies in northern Europe in the 3rd millennium B.C. Mathematics itself initially developed largely in response to bureaucratic needs when civilizations established and developed agriculture – for measuring plots of land, taxing individuals, etc. – and this took place for the first time in the Sumerian and Babylonian civilizations of Mesopotamia (approximately, modern Iraq) and in ancient Egypt.

There is evidence of basic arithmetic and geometric notations on petroglyphs at the Knowth and Newgrange funeral mounds in Ireland (dating from approximately 3500 B.C., respectively 3200 B.C.). They use a repeated zigzag glyph for counting, a system that continued to be used in the UK and Ireland in the first millennium B.C.

Stonehenge, a Neolithic ceremonial and astronomical monument in England dating back to around 2300 B.C., also undoubtedly presents examples of the use of 60 and 360 in the measurements of the circle, a practice that probably developed quite independently of the sexagesimal counting system of the ancient Sumerians and Babylonians.

There are many theories that have been discovered by mathematicians solely on the basis of introspection, thought, mental calculus, without previously being observed in nature. The fact that it was then concluded that they describe so wonderfully the world in which we live is the great mystery. In fact, it was precisely this fact that got people thinking: If through our own mind, starting from certain simple mathematical theories, verifiable by experiment and observation, we mentally develop new theories, then is Mathematics invented by us or just discovered?

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INDIAN-ISLAM- RENAISANCE

Omar Khayyam

Fibonacci

Fermat

Descartes

Newton

Harezmi

Leonardo Fibonacci

Leonardo of Pisa (1170-1250)

Fibonacci Sequence

References

Biography

The Golden Ratio φ

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Leonardo Fibonacci of Pisa is the foremost Mathematician in pre-Renaissance Europe.

LIBER ABBACI

The 13th Century Italian Leonardo of Pisa, better known by his nickname Fibonacci, was perhaps the most talented Western mathematician of the Middle Ages.Little is known of his life except that he was the son of a customs offical and, as a child, he travelled around North Africa with his father, where he learned about Arabic mathematics.On his return to Italy, he helped to disseminate this knowledge throughout Europe, thus setting in motion a rejuvenation in European mathematics, which had lain largely dormant for centuries during the Dark Ages.In particular, in 1202, he wrote a hugely influential book called “Liber Abaci” (“Book of Calculation”), in which he promoted the use of the Hindu-Arabic numeral system, describing its many benefits for merchants and mathematicians alike over the clumsy system of Roman numerals then in use in Europe. Despite its obvious advantages, uptake of the system in Europe was slow (this was after all during the time of the Crusades against Islam, a time in which anything Arabic was viewed with great suspicion), and Arabic numerals were even banned in the city of Florence in 1299 on the pretext that they were easier to falsify than Roman numerals. However, common sense eventually prevailed and the new system was adopted throughout Europe by the 15th century, making the Roman system obsolete. The horizontal bar notation for fractions was also first used in this work (although following the Arabic practice of placing the fraction to the left of the integer).

https://www.storyofmathematics.com/medieval_fibonacci.htmlhttp://matematik.dpu.edu.tr/tr/index/sayfa/3118/leonardo-fibonacci

Liber AbaciPractica GeometriaFlosLiber Quadratorum

In the 1750s, Robert Simson noted that the ratio of each term in the Fibonacci Sequence to the previous term approaches, with ever greater accuracy the higher the terms, a ratio of approximately 1 : 1.6180339887 (it is actually an irrational number equal to (1 + √5)⁄2 which has since been calculated to thousands of decimal places). This value is referred to as the Golden Ratio, also known as the Golden Mean, Golden Section, Divine Proportion, etc, and is usually denoted by the Greek letter phi φ (or sometimes the capital letter Phi Φ). Essentially, two quantities are in the Golden Ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The Golden Ratio itself has many unique properties, such as 1⁄φ = φ – 1 (0.618…) and φ2 = φ + 1 (2.618…), and there are countless examples of it to be found both in nature and in the human world.A rectangle with sides in the ratio of 1 : φ is known as a Golden Rectangle, and many artists and architects throughout history (dating back to ancient Egypt and Greece, but particularly popular in the Renaissance art of Leonardo da Vinci and his contemporaries) have proportioned their works approximately using the Golden Ratio and Golden Rectangles, which are widely considered to be innately aesthetically pleasing. An arc connecting opposite points of ever smaller nested Golden Rectangles forms a logarithmic spiral, known as a Golden Spiral. The Golden Ratio and Golden Spiral can also be found in a surprising number of instances in Nature, from shells to flowers to animal horns to human bodies to storm systems to complete galaxies.It should be remembered, though, that the Fibonacci Sequence was actually only a very minor element in “Liber Abaci” – indeed, the sequence only received Fibonacci’s name in 1877 when Eduouard Lucas decided to pay tribute to him by naming the series after him – and that Fibonacci himself was not responsible for identifying any of the interesting mathematical properties of the sequence, its relationship to the Golden Mean and Golden Rectangles and Spirals, etc.

Fibonacci is best known, though, for his introduction into Europe of a particular number sequence, which has since become known as Fibonacci Numbers or the Fibonacci Sequence. He discovered the sequence – the first recursive number sequence known in Europe – while considering a practical problem in the “Liber Abaci” involving the growth of a hypothetical population of rabbits based on idealized assumptions. He noted that, after each monthly generation, the number of pairs of rabbits increased from 1 to 2 to 3 to 5 to 8 to 13, etc, and identified how the sequence progressed by adding the previous two terms (in mathematical terms, Fn = Fn-1 + Fn-2), a sequence which could in theory extend indefinitely.The sequence, which had actually been known to Indian mathematicians since the 6th Century, has many interesting mathematical properties, and many of the implications and relationships of the sequence were not discovered until several centuries after Fibonacci’s death. For instance, the sequence regenerates itself in some surprising ways: every third F-number is divisible by 2 (F3 = 2), every fourth F-number is divisible by 3 (F4 = 3), every fifth F-number is divisible by 5 (F5 = 5), every sixth F-number is divisible by 8 (F6 = 8), every seventh F-number is divisible by 13 (F7 = 13), etc. The numbers of the sequence has also been found to be ubiquitous in nature: among other things, many species of flowering plants have numbers of petals in the Fibonacci Sequence; the spiral arrangements of pineapples occur in 5s and 8s, those of pinecones in 8s and 13s, and the seeds of sunflower heads in 21s, 34s, 55s or even higher terms in the sequence; etc.

PIERRE DE FERMAT

But it is impossible to divide a cube into two cubes, or a fourth power into fourth powers, or generally any power beyond the square into like powers; of this I have found a remarkable demonstration. This margin is too narrow to contain it.

1607-12 january 1665

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Born 1601 Beaumont-de-Lomagne, FranceDied 1665 (age 63) Castres, FranceLaw and MathematicsKnown for Number theory ( little theorem, great theorem, perfect numbers, and amicable numbers) Analytical geometry Probability Influences François Viète

Fermat's little theorem: p is a prime number and a is an integer that is not a multiple of p, then ap-1 ≡ 1(mod p), or ” p divide (ap -a) ”Fermat's great theorem is:The equation xn + yn = zn has no integer solutions other than zero, for n greater than 2. Complicated? Not at all. But this must be demonstrated. This is where things change radically. With the advent of computers, the theorem was solved up to n = 10,000, then up to n = 25,000, so that by 1980 all cases with n <4,000,000 were elucidated. In the last years before finding the complete proof for any n> 2, mathematicians were convinced that nothing new could be brought by elementary methods.Andrew Wiles closed the last chapter in 1995, more than 300 years after the theorem.

The perfect number is an integer equal to the sum of its divisors, from which the number itself is excluded. Example: 6 = 1 + 2 + 3 , 28 = 1 + 2 + 4 + 7 + 14Friendly numbers are pairs of numbers in which each number is the sum of the divisors (all proper divisors and 1) of the other number. The first sets of friendly numbers are (220, 284), (1184, 1210). It is said that Pythagoras when asked who is the Friend? he replied, "The one who is a different self, like numbers 220 and 284."Fermat's theorem in mathematical analysis gives a method for finding the maximum and minimum points of a derivable function. The value of the derivative at these points is 0.

Newton

" Was an English mathematician, physicist, astronomer, theologian, and author (described in his own day as a 'natural philosopher') who is widely recognised as one of the most influential scientists of all time and as a key figure in the scientific revolution."

1642 – 1726 A.D.

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Isaac Newton was born (according to theJulian calendar, in use in England at the time) on Christmas Day, 25 December 1642 (NS4 January 1643) "an hour or two after midnight"atWoolsthorpe ManorinWoolsthorpe-by-Colsterworth, ahamletin the county of Lincolnshire.The disc of Newton:

Most modern historians believe that Newton and Leibniz developed calculus independently, although with very differentmathematical notations. Occasionally it has been suggested that Newton published almost nothing about it until 1693, and did not give a full account until 1704, while Leibniz began publishing a full account of his methods in 1684.

His work extensively uses calculus in geometric form based on limiting values of the ratios of vanishingly small quantities: inPrincipiaitself, Newton gave demonstration of this under the name of "the method of first and last ratios"and explained why he put his expositions in this form,remarking also that "hereby the same thing is performed as by the method of indivisibles."

In 1666, Newton observed that the spectrum of colours exiting aprismin the position ofminimum deviationis oblong, even when the light ray entering the prism is circular, which is to say, the prism refracts different colours by different angles.This led him to conclude that colour is a property intrinsic to light – a point which had, until then, been a matter of debate.

Harezmi

"He was one of the first classics of Islam and the first scholar of the school in Baghdad, a pioneer in mathematics. Thus, he is often quoted as "the father of algebra"

780-850 A.D.

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Muhammad ibn Musa al-Khwarizmi was a Persian mathematician, astronomer, astrologer geographer and a scholar in the House of Wisdom in Baghdad. He was born in Persia of that time around 780. Al-Khwarizmi was one of the learned men who worked in the House of Wisdom. Al-Khwarizmi flourished while working as a member of the House of Wisdom in Baghdad under the leadership of Kalif al-Mamun, the son of the Khalif Harun al-Rashid, who was made famous in the Arabian Nights. The House of Wisdom was a scientific research and teaching center.Picture of his work:

Al-Khwarizmi’s algebra is regarded as the foundation and cornerstone of the sciences. To al-Khwarizmi we owe the world “algebra,” from the title of his greatest mathematical work, Hisab al-Jabr wa-al-Muqabala. The book, which was twice translated into Latin, by both Gerard of Cremona and Robert of Chester in the 12th century, works out several hundred simple quadratic equations by analysis as well as by geometrical example.

It also has substantial sections on methods of dividing up inheritances and surveying plots of land. It is largely concerned with methods for solving practical computational problems rather than algebra as the term is now understood.

His most recognized work as mentioned above and one that is so named after him is the mathematical concept Algorithm. The modern meaning of the word relates to a specific practice for solving a particular problem. Today, people use algorithms to do addition and long division, principles that are found in Al-Khwarizmi’s text written about 1200 years ago.

Omer Khayyam

Dear, you and I are like compassesWe have two heads, one body.No matter how long I turn around,Aren't we going to give it alone sooner or later? -Omer Khayyam-

(18 June 1048 - 4 December 1131)

Biography

Binomial Theorem

Jalal Calendar

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Persian poet, philosopher, mathematician and astronomer, whose real name is Giyaseddin Ebu'l Feth Bin İbrahim El Khayyam.Ömer Khayyam, who was born on May 18, 1048 in Nisabur, Iran, was the son of a tent maker.His surname, meaning tent maker, was derived from his father's profession. But he has done things far beyond his surname.Even in his lifetime, he was regarded as the greatest scholar of the East, after Ibn-i Sina. It was said that Ömer Khayyam, who had important studies in medicine, physics, astronomy, algebra, geometry and higher mathematics, knew all the information of the time.He did not write most of his work unlike anybody else, whereas he is the anonymous hero of the theorems we hear a lot.*His greatest work is the Algebra Treatise.He studied cubic equations in four chapters of this book, which consists of ten chapters, and classified these equations.This is the first time in the history of mathematics that classifies.He defined algebra as a science aimed at determining numerical and geometric unknowns.Ömer Khayyam, whose mathematics knowledge and skills are far beyond his time, has done successful studies on equations. As a matter of fact, Khayyam has defined 13 different 3rd order equations. He solved the equations mostly using the geometric method, and these solutions are based on cleverly chosen conics.In this book, using the intersection of two cones, he states that there is a geometric plot of roots for each type of equation of the 3rd order and discusses the existence conditions of these roots.* Khayyam first introduced the concept that we call "unknown" in equations today and express with x. This concept, which is called "thing" in mathematics, has served to express and solve equations.

*Khayyam has also found the Binomial Theorem. He is thought to be the first to find the binomial theorem and the coefficients in this expansion. (What we know as Pascal's triangle is actually a Khayyam triangle).* It is said that the Pascal triangle was first discovered by Ömer Khayyam. Even the Iran Pascal Triangle is known as the "Khayyam Triangle". There is important evidence on this subject.KHAYYAM TRIANGLEPASCAL TRIANGLE

Ömer Khayyam was commissioned by Sultan Melikşah to organize the Persian calendar. Khayyam, who accepted the mission, created a calendar based on the solar year named as "Jalal Calendar". The error margin of this calendar is 1 day every 5000 years.

Some of the scientific works he wrote;*On Algebra and Geometry,*A Summary in Physical Sciences,*Entity Information Summary,*Occurrence and Opinions,*Measure of Wisdom,*The Garden of Minds.*His greatest work is the Algebra Treatise.

https://www.storyofmathematics.com/islamic.htmlhttp://matematik.dpu.edu.tr/tr/index/sayfa/3121/omer-hayyam

René Descartes

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"It seeks better to defeat you than fate and to change your desires rather than the order of the world."

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(March 31, 1596 Turaine, France - February 11, 1650, Stokholm), also known by the Latin name Cartesius, was a French philosopher, mathematician, physicist.⦁ Published works: Discourse on Method, Principles of Philosophy, Geometry

⦁ He is the creator of analytic geometry. He was the first to use Cartesian coordinates, in 1637, in two works of Discourse on Method and GeometryHe first expressed doubts about the possibility of a solution to duplicating the cube. ⦁ He deduced that the third degree equation is solved by quadratic radicals.⦁ Use the symbol of infinity. ∞⦁ He was the first to use the exponential notation, used today, although only for natural exponents.

⦁ He discovered the formula tips + faces - edges = 2 at regular polyethers although it is generally attributed to Euler.⦁ He formulated (before Galileo) the principle of inertia.⦁ In optics, he owes his corpuscular theory of light and the laws of refraction.⦁ He introduced the last letters of the alphabet for unknown quantities and the first for known ones. ( x, y, z, a,b)⦁ Create a technique to express the laws of mechanics using algebraic formulas.

⦁ It elaborates the reasons why the world should be accessible to mathematics Descartes' square1.What happens if I make this decision? 2. What happens if I do not make this decision?3. What will not happen if I make this decision? 4. What will not happens if I do not make this decision?Instead of closing:"To exist is a much more complex verb than to component of our lifeTo Exist = to live with faith, with trust, with love, with joy. When we are born WE HAVE the mission to EXIST.

ANCIENT GREECE

Thales

Plato

Pythagoras

Euclid

Archimedes

Hypatia

Pythagoras

''All things are numbers.'' -PYTHAGORAS-

Biography

PythagoreanTheorem

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ContributionstoMathematıcs

(c. 570 – c. 495 BC)

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The teaching most securely identified with Pythagoras is metempsychosis, or the "transmigration of souls", which holds that every soul is immortal and, upon death, enters into a new body.

Pythagoras of Samos was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism. Pythagoras is often known as the ‘Father of Numbers’. Pythagoras may have been killed during persecution, or escaped to Metapontum, where he eventually died.

In mathematics, the Pythagorean theorem, also known as Pythagoras's theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. This theorem can be written as an equation relating the lengths of the sides a, b and c, often called the "Pythagorean equation": a ² + b ² = c ² .

Thales

Biography

CONTRIBUTIONS TO MATHEMATICS

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Thales Theorem

" The most difficult thing in life is to know yourself.

-Thales

(624 BC-524 BC)

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Thales theorem:

SHORTLY HİS LİFE:Thales was born in 624 BC. He died in 546 BC. He is also called the forerunner of philosophy and science because he was one of the first philosophers. He is known as the initiator of the Ionian enlightenment and is the first of the Se ven Sages of Ancient Greece.

1.The diameter divides the circle into two equal parts.2.The base angles of an isosceles triangle are equal.3.Opposite angles formed by two intersecting lines are equal to each other.4.The angle whose corner is on the circle and sees the diameter is the right angle.5.A triangle with its base and two adjacent angles can be drawn.

plato

"The highest form of püre thought is in mathematichs"

( 427 BC - 347 BC )

Biography

contributionsto maths

contributions to maths

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Platonic Solids

Platonic Solids

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He was on ancient Greek philosopher and mathematician. He was born in Athens, Greece. He was born in wealthy and aristocratic family. His real name was Aristocles but his wrestling coach dubbed him "Platon" on account of his robust figure.

https://www.storyofmathematics.com/greek_plato.html

Euclid

He is a the father of geometry

Biography

Book of Elements

The GCD method

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Euclid collected his studies in geometry and mathematics until his time in the book Elements. He put forward 5 axioms in the Book of Elements. The meaning of the axiom is expressed as obvious facts that do not need proof. His 13-volume book “Elements”, which treats geometry as a system based on proofs and axioms, was the first comprehensive work in this field. Also known as the elements of Euclid, this work has been used as an important masterpiece for 2000 years. In this masterpiece, Euclid covered the subjects of plane geometry, arithmetic, number theory, rational numbers and solid body geometry. Euclidean geometry has been used for centuries and the geometry course has been taught in schools depending on Euclid's elementsWhat are Euclid's Five Axioms:1- Only one straight line passes through two points.2- A line segment can be extended in both directions without limit.3- A circle with a center and a point above it can be drawn.4- One and only one parallel can be drawn from a point taken outside a line.5- All right angles are equal to each other.

Euclid's Works:1- Elements: Eucdes Geometry - Elemental Geometry2- Verler (Dodemena)3- Geometric Places on Surfaces (Troipris Piphanea)4- Optical (Optica)5- Polysmas

B.C. The Greek mathematician who lived between 330-275 was known mostly for his geometry studies. After completing his education at the famous academy of Plato in Athens, Greek mathematician Euclid, at the request of the Greek king Ptolemy I, established a large mathematics school at the Royal Institute of Alexandria in Alexandria

https://www.matematikcozumleri.com/oklid-kimdir-kisaca-hayati/https://www.biyografi.net.tr/oklid-kimdir

The GCD method (the largest of the common divisors), which is widely used in mathematics, was found by Euclid and is called the Euclidean algorithm. If the Euclidean relation or Euclidean theorem is lowered from a right triangle to the hypotenuse, that is, to the opposite side, the equations are formed as shown in the picture belowh² = x ∙ ya² = x ∙ cb² = y ∙ cc ∙ h = b ∙ a

Archimedes

"Mathematics reveals its secrets only to those who approach it with pure love.”

( 287 BC - 212 BC )

Biography

Contributionsto maths

Contributions to maths

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Contributios to maths

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https://www.storyofmathematics.com/hellenistic_archimedes.htmlhttps://www.slideshare.net/caryl_yaun/archimedes-

hypatia

"Defend your right to think, because even thinking in a wrong way is better than not thinking."

of Alexandria (355 or 370 c. to 415)

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Discoveries

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Her most significant work is a thirteen-volume commentary on the Arithmetic of Diophantus (The Sec.), the "father of algebra", to whom the study of indeterminate equations - diophantines - and important elaborations of quadratic equations are due. In her commentary, Ipazia developed alternative solutions to old problems and formulated new ones that were later incorporated into the work of Diophantus.She also wrote an eight-volume commentary on The Conics of Apollonius of Pergamus (111 sec. a.C.), a mathematical analysis of the sections of the cone, figures that were forgotten until the 16th century when they were used to illustrate the secondary cycles and elliptical orbits of planets. In this work Ipazia included the Astronomical Corpus, a collection she compiled of astronomical tables on the motions of celestial bodies.Conics of ApolloniusThe scholar was the author with her father of a commentary on Ptolemy's Almagest, a mammoth work in thirteen books that collected all the astronomical and mathematical knowledge of the time and a revised and corrected edition of the Elements of Euclid.Hypatia and the relativity of motion

Her writings have been lost or incorporated into publications by other authors.We know however:Thirteen-volume commentary on Diophantus's Arithmetic (Il sec.)Commentary in eight volumes on The conics of Apollonius of Pergamum (111 century BC)She comments, together with her father Theon, on Ptolemy's Almagest, a work in thirteen books that collected all the astronomical and mathematical knowledge of the time.Since for Hypatia there is no clear boundary between science and philosophy, which merged with her in a single person, not even her philosophical works have reached us.

Among the legacies that the ancient world left us, that of Hypatia is one of the most mysterious, and precisely for this reason among the most fascinating. What remains of her life is above all his legend. The meager news of the sources say that Hypatia was born in Alexandria around 370 AC, daughter of the mathematician Theon, and that she herself cultivated mathematics as an astronomer and was famous for knowledge, eloquence and beauty. After completing her studies in Athens, he returned to Alexandria, where she opened a school. Her much attended lectures were dedicated in particular to the commentary of Plato and Aristotle. Of her works, nothing has come down to us, if not three mathematical titles. On the basis of these and a few other reliable information, she appears as a woman immersed in the impulses and contradictions of her time, of which she ended up being a victim. Against the background of the ideological and religious disputes that accompanied the encounter-clash between Christians and pagans in the last decades of the Roman Empire, now at sunset, its horrible end which took place around 415 represents the price paid by reason to the monsters of intolerance. Absolute rigor and a will that never gave any sign of bowing to the destiny reserved for a woman of that time marked an existence dedicated to the search for truth. But the hopes, the shocks and the troubles of the heart that, between science and conscience bring closer to us a figure whose tragic destiny has become, over the centuries, the symbol of a soul that has hovered far beyond the sky of the moon in the height of the sidereal spaces close to the total light.

Euston96Donne della scienzaEnciclopedia delle donneTreccaniContini, C., Ipazia e la notte, Longanesi, Milano 1999

Ipazia also dealt with mechanics and applied technology. She is attributed three inventions:Aerometer: historically the first mention of the aerometer is connected precisely to the figure of Ipazia: Sinesius of Cyrene wrote in fact about 400 D.C. to his teacher to ask for explanations about the construction of an aerometer. As the etymology of the word itself indicates, it is an instrument that serves to determine the degrees of rarefaction or condensation of a given volume of air.Flat astrolabe: it is an ancient astronomical instrument through which it is possible to locate or calculate the position of celestial bodies such as the Sun, moon, planets and stars. The spacelabium designed by Ipazia consisted of two perforated metal discs, rotating on top of each other by means of a removable partwheel: it was used to calculate the time, to define the position of the Sun, stars, planets. It seems that through this instrument Ipazia has even solved some problems of spherical astronomy.Hydroscope: it looks like a cylindrical tube having the shape and size of a flute. In line perpendicular it has carvings, through which you can measure the weight of liquids. From one end it is clogged by a cone tightly attached to the tube, so that the base of both is unique. This is the so-called barrel. When the pipe is immersed in water, it remains erect and it is thus possible to count the carvings, which give the indication of weight.

17TH 18TH CENTURY

Riemann

Laplace

Gauss

Euler

D'alembert

Cauchy

Jean Le Rond d'Alembert

He is a French mathematician, mechanic, physicist and philosopher

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He is a famous scientist who studied pi number in his youth. It is also the inventor of the ratio test.He is the inventor of the "centrifugal" force that actually does not exist for dynamic equality. This method makes it very easy to calculate the acceleration in moving materials

http://brahms.emu.edu.tr/ersin/documents/mate

Co-founder of the theory of partial differential equations together with Daniel Bernoulli. He introduced the concept of limit. The D’Alembert paradox also shows that he was working on probability theory.

D'Alembert gave the exact solution to the problem of lengthening or shortening the days and nights. His most important work is on partial differential equations. In particular, his invention of vibrating wires is very important. He owns the d’Alembert criterion for the convergence of the series. There are many theorems that are named after him

He was born in Paris, France lived. D'Alembert is the first to examine partial differential equations.Partial differential equations and fluids With Diderot, apart from his work on mechanics and philosophical writings The mathematics of the famous 28-volume "Encyclopedie"Most of the articles were written by D'Alembert.It is one of the basic works of enlightenment.

German mathematian, generally regarded as one of the greatest mathematicians of all time for his contributions to number theory, geometry, probability theory, geodesy, planetary.

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Carl Friedrich Gauss

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"Gaussian elimination, also known as row reduction, is an algorithm in linear algebra for solving a system of linear equations. It is usually understood as a sequence of operations performed on the corresponding matrix of coefficients. This method can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square matrix. The method is named after Carl Friedrich Gauss "Suppose the goal is to find and describe the set of solutions to the following system of linear equations:

LEONHARD EULER

"Leonhard Euler (1707-1783) is the greatest mathematician of the eighteenth century.

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The most elegant equation in the field of mathematics is known as Euler's formula by the name of Leonhard Euler. Euler, new to mathematics; He introduced many new concepts such as Euler Angles, Euler Circle, Euler Invariant, Euler's Line, Euler's Formulas, Euler's Function, Euler shapes

Bernoulli discovered the number e in 1683 while examining the compound interest problem and calculated the approximate value of this number. The Swiss mathematician Leonhard Euler gave the name of the constant e. Euler first referred to this constant as the "number e" in a letter he wrote to Christian Goldbach in 1731. Although the letters b and c were also used for this constant before and after Euler, the accepted name was e in the end. e=2,718281828459…

Theorie des Isoperimetres Theroie du Mouvement des Planetes et des Cometes Theroie de L' Aimantation İntroduction in Analysis İnfinitrom İntotuones Calculi Differeniolis İnstitutiones Calculi İntegralis

Leonhard Euler is a Swiss mathematician and physicist. He was born on April 15, 1707 in Basel, Switzerland. Died on September 18, 1783 in Petersburg (Leningrad) Though originally slated for a career as a rural clergyman, Euler showed an early aptitude and propensity for mathematics, and thus, after studying with Johan Bernoulli, he attended the University of Basel and earned his master's during his teens. Moving to Russia in 1727, Euler served in the navy before joining the St. Petersburg Academy as a professor of physics and later heading its mathematics division. In 1736, he published his first book of many, Mechanica. By the end of the decade, having suffered from fevers and overexertion due to cartography work, Euler was severely hampered in the ability to see from his right eye. In the mid-1740s, Euler was appointed the mathematics director of the newly created Berlin Academy of Science and Beaux Arts, taking on a variety of management roles as well becoming head of the organization itself for a time starting in 1759. He has 886 articles.All of Euler's work fill around 90 volumes. Remarkably, most of this output dates back to the last two decades of his life when he was completely blind.

http://matematik.dpu.edu.tr/ https://www.biography.com/scientist/leonhard-euler

Pierre-Simon Laplace

Biography

Laplace expansion

In linear algebra, the Laplace expansion, named after Pierre-Simon Laplace, also called cofactor expansion, is an expression for the determinant |B| of an n × n matrix B that is a weighted sum of the determinants of n sub-matrices (or minors) of B, each of size (n − 1) × (n − 1).Calculation of the determinant by Laplace expansion utilizes the cofactor and the minor. The i, j cofactor of the matrix B is the scalar Cij defined by{\displaystyle C_{ij}\ =(-1)^{i+j}M_{ij}\,,}where Mij is the i, j minor of B, that is, the determinant of the (n − 1) × (n − 1) matrix that results from deleting the i-th row and the j-th column of B.Example

Probability

Laplace's rule is extremely important because it allows us to compute the probability of an event, always that the elementary events are equiprobable, that is, that all possible outcomes have the same probability. Under these conditions, we have:The probability of an event AA is obtained by dividing the number of results that form the event A A by the number of possible outcomes.If we say that the events of AA are the favorable cases of A A, then we can write the Laplace's rule as:Example

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He was a French mathematician and scientist. He is sometimes called the “Newton of France”, because of his wide range of interests, and the enormous impact of his work.

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Laplace’s scientific contributions are numerous. In the field of astronomy, he published a work titledTraité de Mécanique Céleste, a collected work of all scientific approaches afterNewton. In the book series he also demonstrated the mathematical prove for the stability of planetary orbits – due to irregularities in the orbit curves, it was believed at the time that the solar system could collapse – and hypothesized about the possibility ofblack holes.Laplace’s second major field of research wasprobability theory. For Laplace, it was a way out to achieve certain results despite a lack of knowledge. In his two-volume workThéorie Analytique des Probabilités(1812).Laplace gave a definition of probability and dealt with dependent and independent events, especially in connection with gambling. He also dealt in the book with the expected value, mortality and life expectancy. The work refuted the thesis that a strict mathematical treatment of probability was not possible. Laplace has always been more a physicist than a mathematician. Mathematics served him only as a means to an end. Today, however, the mathematical methods that Laplace developed and used are much more important than the actual work itself, like theLaplace operator, or theLaplace transform.

-https://en.wikipedia.org/wiki/Laplace_expansion-Pierre Simon de Laplace and his true love for Astronomy and Mathematics - SciHi BlogOn March 28, 1749, French mathematician and astronomer Pierre Simon marquis de Laplace was born, whose work was pivotal to the development of...SciHi Bloghttps://mathigon.org/timeline/laplacePierre-Simon Laplace - Timeline of Mathematics - MathigonMaryam Mirzakhani (مریم میرزاخانی, 1977 - 2017) was an Iranian mathematician and professor at Stanford University. She is the only woman to have...Mathigonhttp://scihi.org/laplace-astronomy-mathematics/?fbclid=IwAR0ytUN5zRNyStlUaFPn27G2FTyqmEIdMwIEONsIpNOK8k4Qwt-cxnnMadQ-https://www.britannica.com/biography/Pierre-Simon-marquis-de-LaplacePierre-Simon, marquis de Laplace | Biography & FactsPierre-Simon, marquis de Laplace, French mathematician, astronomer, and physicist who was best known for his investigations into the stability of the...Encyclopedia Britannica

He was born in Beaumont-en-Auge, Normandy, France on April 23, 1749.In 1765 he went to the school of the Duke of Orleans in Beaumont and later to study theology in Caen where he studied for five years.Laplace never graduated in theology, he went to Paris with recommendations for the than, already famous mathematician Jean le Rond d'Alembert. Laplace could now devote himself to original research and in the next 17 years, from about 1771. to 1787, he wrote most of his works in the field of astronomy. In the late thirties, he started a family and had two children. At the time of the restoration of the Bourbon government he was awarded the title of Marquis. He died in Paris on April 5, 1827.

Augustin Louis Cauchy

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French mathematician and physicist. He has contributed to many areas of mathematics, he has dozens of theorems bearing his own last name.

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He wrote more than 500 works in all branches of mathematics, mechanics, physics and astronomy, most of them very thick.In his book Cours d'analyse, published in 1821, he reviewed the main principles of analysis and criticized them constructively.Cauchy - Riemann equations, Cauchy theorem, Cauchy integral formula and Cauchy fundamental value discoveries can be listed

https://www.matematikciler.com/cauchy-1789-1857/http://matematik.dpu.edu.tr/index/sayfa/3128/augustin-louis-cauchyhttps://tr.wikipedia.org/wiki/Cauchy_integral_teoremi

In 1814, he developed the theory of complex functions. Today, he proved by expressing the famous theorem known as the Cauchy theorem. In this field, integrals and their calculation methods were also given by Cauchy. His work on this field was published in 1827.Cauchy's Theorem: It is an important theorem about line integrals of holomorphic functions in the complex plane. Essentially, what the theorem states is this: If two separate paths connect two same points and a function is holomorphic in the inner region between these two separate paths, then these two path integrals of the function are equal.

He gave his work on polyhedral geometric shapes, symmetric functions and them.He brought the measure of convergence to the analysis. This was one of his most important breakthroughs. The second is to establish probability analysis and group theory. The third is complex functions theory.

Cauchy is a French mathematician. He was born on August 21, 1789 in Paris. He died of bronchitis on May 23, 1857Cauchy was educated alongside his father until the age of thirteen. Then he started studying at the Ecole Centrale du Panthéon. After leaving this school, he studied mathematics with a good teacher for ten months. At the age of sixteen, he entered the Polytechnique school in second place. In 1807 he transferred to the engineering school. He finished this school in 1810. He worked for three years in Napoleon's army as a military engineer at Cherbourg. In his spare time he started with arithmetic and finished astronomy. He reviewed all topics of mathematics by simplifying some proofs.

LEONHARD EULER

"Leonhard Euler (1707-1783) is the greatest mathematician of the eighteenth century.

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The most elegant equation in the field of mathematics is known as Euler's formula by the name of Leonhard Euler. Euler, new to mathematics; He introduced many new concepts such as Euler Angles, Euler Circle, Euler Invariant, Euler's Line, Euler's Formulas, Euler's Function, Euler shapes

Bernoulli discovered the number e in 1683 while examining the compound interest problem and calculated the approximate value of this number. The Swiss mathematician Leonhard Euler gave the name of the constant e. Euler first referred to this constant as the "number e" in a letter he wrote to Christian Goldbach in 1731. Although the letters b and c were also used for this constant before and after Euler, the accepted name was e in the end. e=2,718281828459…

Theorie des Isoperimetres Theroie du Mouvement des Planetes et des Cometes Theroie de L' Aimantation İntroduction in Analysis İnfinitrom İntotuones Calculi Differeniolis İnstitutiones Calculi İntegralis

Leonhard Euler is a Swiss mathematician and physicist. He was born on April 15, 1707 in Basel, Switzerland. Died on September 18, 1783 in Petersburg (Leningrad) Though originally slated for a career as a rural clergyman, Euler showed an early aptitude and propensity for mathematics, and thus, after studying with Johan Bernoulli, he attended the University of Basel and earned his master's during his teens. Moving to Russia in 1727, Euler served in the navy before joining the St. Petersburg Academy as a professor of physics and later heading its mathematics division. In 1736, he published his first book of many, Mechanica. By the end of the decade, having suffered from fevers and overexertion due to cartography work, Euler was severely hampered in the ability to see from his right eye. In the mid-1740s, Euler was appointed the mathematics director of the newly created Berlin Academy of Science and Beaux Arts, taking on a variety of management roles as well becoming head of the organization itself for a time starting in 1759. He has 886 articles.All of Euler's work fill around 90 volumes. Remarkably, most of this output dates back to the last two decades of his life when he was completely blind.

http://matematik.dpu.edu.tr/ https://www.biography.com/scientist/leonhard-euler

Bernhard Riemann

A genius mathematician who gave meaning to the theory of many scientists and fit many formulas in his short life of 40 years

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His work on multivalued functions provided an introduction to topology. To make the multivalued functions monovalent, Riemann took the famous n-leaf surfaces and combined this n-leaf plane into a single plane. The surface of these leaves is called the famous Riemann surface.In 1856, he revealed an original work on Abelian functions, a classic work on hypergeometric series and a work on differential equations.

https://tr.wikipedia.org/wiki/Riemann_toplam%C4%B1http://matematikvideodersler.blogspot.com/2014/11/george-friedrich-bernhard-riemann-hayat.html

His claim that the Zeta function, which he claims in his most impressive theory, "Riemann Hypothesis, shows the distribution of prime numbers, has not been proven right or wrong since 1857, when it was published."16 Recall that Riemann's zeta function isform,Here u and v are real numbers, s = u + iv and i ^ 2 = - 1. I wonder for which values of the variable s z (s) = 0? Riemann's hypothesis is this. Values of u with 0 <u <l would be z (s) = O for all values of the form s = l / 2 + iv where u = l / 2, for example.

Jacobi taught him mechanics and higher algebra, Dirichlet analysis and number theory, Stenier modern geometry, and Eisenstein elliptic functions. Riemann wanted to use complex variables and to derive his theory in as few calculations as possible, based on a small number of general and simple principles. Riemann's most important service to mathematics is his work on complex functions theory. The definition of the modern analytic function with complex variables as we know it today belongs entirely to Riemann.His work on multivalued functions provided an introduction to topology. To make the multivalued functions monovalent, Riemann took the famous n-leaf surfaces and combined this n-leaf plane into a single plane. The surface of these leaves is called the famous Riemann surface.

George Friedrich Bernhard Riemann (17 September 1826 - 20 July 1866) was a German mathematician who made significant contributions in the field of analysis and differential geometryIn 846, at the age of 19, he began studying philology and theology at the University of Göttingen. He attended the lectures of the mathematician Gauss, who explained the method of least squares. In 1847 Riemann's father gave him permission to quit theology and study mathematics.He went to Berlin in 1847. Jacobi, Dirichlet or Steiner was teaching here. The mathematician, who stayed in Berlin for two years, returned to Göttingen in 1849.Riemann gave his first lecture in 1854, and with this lecture he not only laid the foundations of Riemannian geometry, but also laid the foundations for the structures that Einstein would later use in the theory of relativity. He was promoted to the position of private professor at Götingen University in 1857 and became professor in 1859.

David Hilbert

"Wir müssen wissen, wir werden wissen. (We need to know, we will.)"

(1862 -1943 )

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Hilbert space (infinite-dimensional Euclidean space), Hilbert curves, Hilbert and Hilbert's inequality and various classification theorems, including many mathematical term that bears his name, and slowly formed himself as the most famous mathematician of his time. His pithy enumeration of the 23 most important open mathematical questions at the 1900 Paris conference of the International Congress of Mathematicians at the Sorbonne set the stage for almost the whole of 20th Century mathematics. The details of some of these individual problems are highly technical; some are very precise, while some are quite vague and subject to interpretation; several problems have now already been solved, or at least partially solved, while some may be forever unresolvable as stated.

Hilbert’s AlgorithmAs early as 1899, he proposed a whole new formal set of geometrical axioms, known as Hilbert’s axioms, to substitute the traditional axioms of eEuclid.He showed that although there were an infinite number of possible equations, it was nevertheless possible to split them up into a finite number of types of equations which could then be used, almost like a set of building blocks, to produce all the other equations.Interestingly, though, Hilbert could not actually construct this finite set of equations, just prove that it must exist (sometimes referred to as an existence proof, rather than constructive proof).Hilbert SpaceThe Hilbert space is a generalization of the concept of Euclidean space.Hilbert space provided the basis for important contributions to the mathematics of physics over the following decades, and may still offer one of the best mathematical formulations of quantum mechanics.Hilbert was unfailingly optimistic about the future of mathematics, never doubting that his 23 problems would soon be solved. In fact, he went so far as to claim that there are absolutely no unsolvable problems –a famous quote of his (dating from 1930, and also engraved on his tombstone) proclaimed, “We must know! We will know!”– and he was convinced that the whole of mathematics could, and ultimately would, be put on unshakable logical foundations.

DAVID HILBERT(January 23, 1862 - February 14, 1943 )He is a famous German mathematician. The German mathematician David Hilbert, who reduced geometry to a set of axioms and made an important contribution to the creation of formal foundations of mathematics, is the 20th president of functional analysis with his work on Integral Equations. He pioneered its development in the century.

https://www.storyofmathematics.com/20th_hilbert.htmlhttp://matematik.dpu.edu.tr/index/sayfa/3116/david-hilbert

Avoiding reference to concrete images, Hilbert introduced the "system of three objects" into mathematics, which he called points, lines, and planes. These objects, which are not definitively shown what they are, reveal some Relations described by 21 axioms grouped in 5 groups.The axiom of belonging, order, equality or equivalence, parallelism and continuity are among them. Thereafter, he established geometries in which one or the other of the axioms was not verified.

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Cahit Arf

David Hilbert

George Cantor

CAHİT ARF

"I dedicated my life to mathematics, in return it gave me my life back."

(1910-1997)

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Cahit Arf ‘s Qutoes About Maths:• "Mathematics is an art just like painting, music and sculpture."• "I dedicated my life to mathematics, in return it gave me my life back."• “Do not let others do your work. Because they do as they want.”• “Mathematics is essentially a matter of patience. It is necessary to understand by discovering, not by memory. "• "I believe in Allah when I take the Quran in my hand, and in myself when I take the pen."

• Cahit Arf ( 1910 – 1997 ) was best known as a mathematician who came up with the “Arf invariant of a quadratic form”. However, he was more than the mathematical problems that he inevitably solved. He was thought of as the greatest Turkish mathematician of the 20th century.• Cahit Arf was born in 1910 in the Selanik part of the Ottoman Empire. His family eventually had to move when the Balkan War of 1912 forced them to consider Istanbul as their home. Cahit would be educated in Izmir where he would go on to receive a scholarship from the Turkish Ministry of Education.• Cahit Arf was a mathematical genius. He was able to study in Paris before returning to Turkey where he taught mathematics at the elite Galatasaray Lisesi. An honor few experience, Arf Cahit would remain there briefly before joining the math program at Istanbul University in 1933.• In 1937, Cahit Arf went to the University of Gottingen where he would be able to secure his Ph.D. He later broadened his horizons by going to the states to work diligently from 1964 until 1966 at the Institute for Advanced Study in Princeton, New Jersey.• Cahit Arf spent a year at Berkeley following his research in Princeton. After he returned to Turkey, he continued to work in research. His continued dedication to mathematics would be profoundly noticed when he joined the Middle East Technical University where he remained until he reached his retirement in 1980. He died on 1997.

George Cantor

Τhe matician who managed to measure infinity and ... ended up in a psychiatric hospital.

Biography

Diagonal Argument

Cantor's Axiom

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Cantor's work

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"Cantor diagonal argument"The number of the actual numbers of the space (0,1) is bigger than the number of the set N of the natural numbers.

Cantormanagedto create the Theory of Sets, which became a basic theory in Mathematics,to establish the 1-to-1 correspondence between the members of elements of two sets,to define infinitive setsof ... infinitive elements,to prove thatreal numbers are more than natural numbers,to introduce fundamental concepts such as dynamo set,to talk about the Hypothesis of Continuοus,and much more..........

Georg Cantor has gone down in the history of mathematics as one of the most famous pioneers in science. Born in St. Petersburg, Russia in 1845, Cantor moved from Germany to Germany where he grew up, studied and worked hard, giving to mathematics a great deal. Until 1918, when he died, after a long period of poverty, he managed to create the Theory of Sets, which became a basic theory in Mathematics, to establish the 1-to-1 correspondence between the members of two sets, to define infinitive sets of ... infinitive evidence, to prove that real numbers are more than natural numbers, to introduce fundamental concepts such as dynamo set, to talk about the Hypothesis of Continuous and much more.Cantor managed to move first in mathematical ... paths that had not been discovered. He used concepts that were considered "forbidden" in the mathematical community at that time, provoking several reactions. The stimulation that led him to his incredible discoveries came from the field of philosophy. The concept of infinity, when referring to the words of a philosopher, sounded much more friendly to the ears of the Russian mathematician.The theoretical words he heard and read in books about the concept of infinity, gave him the impetus for the beginning of his research. However, his devotion to such a delicate issue led him, fortunately after his discoveries, to the psychiatric hospital. The Russian mathematician began to lose his mind, fell into a very deep depression and lost all contact with the outside world when he was admitted to hospital, where he spent the last years of his life.The case of the famous Russian mathematician comes to prove once again that mathematics is not ... a completely safe occupation. The mysterious world of mathematics can turn into a trap for anyone who chooses to go deep into it. What remains to be seen is when the next one will be found ... the bold one who will try to give infinity an additional characterization.

1. Cantor Georg-Contributions in the fundamental theory of the transcendental numbers.2. R. Xenikakts - Real Analysis3. K. Kalfa - Elements of Set Theory4. Wikipedia

"Cantor's axiom"The set A has a smaller number of elements than the set B, when A has the same number of elelments as a subset of B, but B does not have the same number of elements as anyone of the subsets of A.