( Circa 200/ 214 - 284/ 298 AD. ) The Greek (possibly a Hellenized Banylonian) mathematician, Diophantus of Alexandria (circa 200/214-284/298 A.D.) , has been called "The Father of Algebra". But, as some one said about another subject, "Algebra has many fathers". al-Khwarizmi (cited in another file) could be called "The Islamic Father of Algebra", so we'll call Diophantus "The Greek Father of Algebra".
Diophantus of Alexandria was an Egypt mathematician living in Alexandria. He was one of the first mathematicians to study equations where variables were restricted to integral values. In honor of him, these equations are commonly called Diophantine equations. One of the most famous Diophantine equation is xn + yn = zn. Fermat suggested that for n > 2, there are no solutions with positive integral values for x, y and z. A proof of this theorem (called Fermat’s last theorem) was found only recently by Andrew Wiles.
Consider the following Diophantine equation: (1)
Diophantus is interested in the following question: for a given n, how many distinct solutions (i. e., solutions satisfying x ≤ y) does equation (1) have? For example, for n = 4, there are exactly three distinct solutions:
HYPATIA OF ALEXANDRIA Hypatia , the daughter of Theon of Alexandria, was born in about 370 AD. she is the earliest woman scientist whose works have been documented. As a young woman, she traveled to Athens and Italy. Upon her return to Alexandria, she became a philosopher and mathematician. She was appointed to expound the doctrines of Plato and Aristotle and was a noted lecturer on the subjects of mathematics, astronomy, philosophy, and mechanics.
Most of her writings dealt with mathematics, especially algebra. Her most noted work, called Arithmetica, was a commentary on the writings of Diophantus. Hypatia also wrote an explanation of the geometry works of Apollonius of Perga, which was titled, On the Conics of Apollonius. Later in her career she worked with Theon and coauthored a work on Euclid's geometry which is titled Elements.
In addition to her mathematical works, Hypatia also developed an apparatus for distilling water, an instrument for measuring the level of water, a plane astrolabe (for measuring the positions of the stars, planets, and sun) and a graduated brass hydrometer for determining the specific gravity of a liquid. Hypatia's philosophical beliefs were in conflict with the views of the Christian rulers of the city of Alexandria. When Cyril, a fanatical Christian, became Partiarch of Alexadria in 412 AD he began a persecution of scholars in the city. In 415 AD Hypatia was arrested, tortured and killed in the church called Caesarium.
Hypatia of Alexandria (Greek: Υπατία; born between 350 and 370 AD – 415 AD) was a Greek or Egyptian Neoplatonist philosopher, the first notable woman in mathematics, and who also taught in the fields of astronomy and astrology. She lived in Alexandria in Roman Egypt at the turn of the 5th century, at a time when paganism was actively suppressed. Her fame stems principally from her murder in 415 AD at the hands of a Christian mob.
Letters written to Hypatia by her pupil Synesius give an idea of her intellectual milieu. She was of the Platonic school, although her adherence was to the writings of Plotinus, the 3rd century follower of Plato and principal of the neo-Platonic school.
Later sources attribute several works to Hypatia, including commentaries on Diophantus's Arithmetica, on Apollonius's Conics, and on Ptolemy's works, but none have survived. Her contributions to science are reputed (on scant evidence) to include the invention, working with her father Theon, of the astrolabe and the hydrometer.
ABOUT 150 BC : HYPSICLES writes On the Ascension of Stars. In this work he is the first to divide the Zodiac into 360 degrees
127 BC : HIPPARCHUS discovers the precession of the equinoxes and calculates the length of the year to within 6.5 minutes of the correct value. His astronomical work uses an early form of trigonometry.
ABOUT 100BC : CHINESE mathematicians are the first to introduce negative numbers
ABOUT 1AD : CHINESE mathematiccians LIU HSIN uses decimal fractions
ABOUT 60 : HERON of ALEXANDRIA writes Metrica ( Measurements) It contains formulas for calculating areas and volumes
ABOUT 100 : The Classical CHINESE Mathematics text JIUZHANG SUANSHU ( Nine Chapters on the Mathematical Art ) begins to be assembled
An early Chinese derivation of the volume of a pyramid:
Liu Hui, third century A.D. In the field of astronomy, the Chinese were one of the earliest peoples to keep systematic record of their observations of the heavens. Sitings and records of these sitings go back over forty centuries. The Chinese observed sunspots, meteorites, eclipses and comets which they called "guest stars." They also observed rare events such as the splitting of comets as the record of 896 CE from the Tang Dynasty indicates, and meteorite showers. The earliest account of the latter exists in The Chronicles of Zuo Ming regarding such a shower in 687 BCE.
The Chinese were also one of the earliest people to make star maps:Shi Shen, an astronomer, catalgied an eight-volume series of his observations of the heavens in the 4th century BCE. The earliest known western star maps were made by the Greek astronomer Hiparchus in 2 BCE.
In addition to their observations and records of the heavens, the Chinese also developed highly sophisticated navigational systems based on the stars. Chinese sailors in the third century BCE were already able tofind their bearings using the Great Dipper and the North Pole. In conjunction with their observations of the heavens the Chinese also built planetariums, and various instruments including armillaries for measuring the celestial coordinates. Scientists reading the records estimate that the Chinese were probably using an armillary to map the heavens by the 4th century BCE.
In Chinese history, the study of astronomy was inseparable from mathematics. From the earliest times, the Chinese, according to Joseph Needham, were far in advance of of contemporary civilizations such as those of Egypt, Babylon, Greece and Rome. There is evidence for instance, that the Chinese had mastered the decimal system since the dawn of history. The earliest treatise on mathematics, Zhoubi suanjing was proably written during the Zhou Dynasty between 1030-1022 BCE. During the Han Dynasty (221BCE-220CE) several mathematical treatises were compiled by distinguished mathemeticians such as Liu Hui whose Haidao suanjing (The Sea and Island Mathematical Manual) appeared sometime around 220CE.
In the following Tang and Song dynasties several outstanding astronomer cum mathematicians would leave their mark on the Chinese scientific scene.The so-called "Golden Age" of Chinese mathematics, however, would not be reached till the last half, and early parts of the thirteenth and fourteenth centuries.
The dual studies in astronomy and mathematics would result in the some of the most remarkable inventions including the astronomical clock by the astronomer Su Song over nine hundred years ago. In the second century CE the famous astronomer Shang Heng devised a mobile water-driven globe which revolved in correspondence with the movements of the heavenly bodies.
About 150: PTOLEMY produces many important geometrical results with applications in astronomy. His version of asstronomy will be the accepted one for well over one thousand years
About 250 : DIOPHANTUS of ALEXANDRIA rites Arithmetica, a study of number theory problems in which only rational numbers are allowed as solutions
About 250 : The MAYA civilization of Central America uses an almost place-value number system to base 20
About 263 : By using a regular polygon with 192 sides LIU HUI calculates the value of "pi" as 3.14159 which is correct to five decimal places
(14 tháng 3 năm 1879 – 18 tháng 4 năm 1955) ALBERT EINSTEIN là nhà vật lý người Mỹ gốc Đức – Do Thái. Ông nổi tiếng với tư cách là cha đẻ của thuyết tương đối. Ngoài thuyết tương đối, ông cũng có nhiều đóng góp lớn trong việc xây dựng cơ học lượng tử và cơ học thống kê.
Ông đã công bố hơn 300 công trình khoa học và 150 công trình phi khoa học. Ông được giới vật lý học hết sức ngưỡng mộ và năm 1999 ông được tạp chí Times phong là "Người đàn ông của thế kỷ".
Albert Einstein sinh ra trong một gia đình người Do Thái tại thành phố Ulm, bang Baden-Württemberg nước Đức. Ông sinh ngày 14 tháng 3 năm 1879. Cha ông, Hermann Einstein, là một kỹ sư đồng thời cũng là người bán hàng. Mẹ ông tên là Pauline Einstein. Năm 1880, gia đình Einstein chuyển về sống tại Munich - nơi cha và chú ông thành lập nên một công ty cung cấp thiết bị điện.
Gia đình ông không theo đạo của người Do Thái. Albert Einstein được theo học tại trường tiểu học Catholic. Mặc dù ông gặp một chút trở ngại trong ngôn ngữ, ông là một trong những học sinh giỏi nhất của trường.
Khi Einstein 5 tuổi, ông được cha tặng một chiếc la bàn và ông đã để ý và nhận ra rằng trong không gian phải có một cái gì đó làm chuyển động cây kim chỉ hướng. Việc này đã để lại cho ông một ấn tượng sâu sắc với khoa học. Sau đó, ông bắt đầu dựng các mô hình và máy đơn giản, chứng tỏ tài năng thiên bẩm của mình.
Đến năm 1894, công ty của cha ông phá sản. Gia đình ông phải chuyển đến sống ở Ý, đầu tiên là ở Milan rồi mới chuyển đến Pavia sau đó vài tháng. Trong thời gian này, Einstein đã viết công trình khoa học đầu tiên của mình về từ trường. Thật ra ông được ở lại Munich để học hết trung học phổ thông nhưng mùa xuân năm 1895 ông đã rời khỏi đây về Pavia sống với gia đình.
Sau đó Einstein quyết định không học hết trung học mà xin học tại Học viện công nghệ liên bang Thụy Sĩ tại Zürich (ETH). Ông đã trượt kỳ kiểm tra đầu vào mặc dù điểm thi môn Toán và Vật Lý rất cao. Do đó ông đã được gửi tới Aarau (Thụy Sĩ) để hoàn thành chương trình học phổ thông. Đến năm 17 tuổi, ông tốt nghiệp và từ bỏ quốc tịch Đức để tránh phải đi nghĩa vụ quân sự và đến học tại khoa toán của trường ETH. Tại đây ông đã gặp người vợ đầu tiên của mình là Mileva Marić, người phụ nữ duy nhất học toán ( hai người cưới nhau vào ngày 6 tháng 1 năm 1903 ). Năm 1900, Albert Einstein tốt nghiệp và sau đó một năm ông đã gia nhập quốc tịch Thụy Sĩ.
April 15 - 1452 / May 2 - 1529Birth name Leonardo di Ser Piero
Born April 15, 1452(1452-04-15)
Vinci, Florence, in present-day Italy
Died May 2, 1519 (aged 67)
Amboise, Touraine (in present-day Indre-et-Loire, France)
Nationality Italian
Field Many and diverse fields of arts and sciences
Movement High Renaissance
Works Mona Lisa, The Last Supper, The Vitruvian Man
Born 30 March 1853 (1853-03-30)
Zundert, The Netherlands
Died 29 July 1890 (1890-07-30) (aged 37)
Auvers-sur-Oise, France
Nationality Dutch
Field Painter
Movement Post-Impressionism
Works The Potato Eaters, Sunflowers, the starry night. Irises,
potrait of Dr. gachet
Vincent Willem van Gogh vɪnˈsɛnt ʋɪlˈɛm vɑnˈxɔx (30 March 1853 – 29 July 1890) was a Dutch Post-Impressionist artist.[1] Some of his paintings are now among the world's best known, most popular and expensive works of art.
Van Gogh spent his early adult life working for a firm of art dealers. After a brief spell as a teacher, he became a missionary worker in a very poor mining region. He did not embark upon a career as an artist until 1880.
He produced more than 2,000 works, including around 900 paintings and 1,100 drawings and sketches, during the last ten years of his life. Most of his best-known works were produced in the final two years of his life, during which time he cut off part of his left ear following a breakdown in his friendship with Paul Gauguin. After this he suffered recurrent bouts of mental illness, which led to his suicide.
Sigmund Freud was born on 6 May 1856 to Galician Jewish parents in Příbor (German: Freiberg in Mähren), Moravia, Austrian Empire, now Czech Republic. His father Jakob was 41, a wool merchant, and had two children by a previous marriage. His mother Amalié was 21. Owing to his intellect, which was obvious from an early stage of his childhood, his parents favoured him over his siblings, and even though they were poor they offered everything to give him a proper education. Due to the economic crisis of 1857, father Freud lost his business, and the family moved first to Leipzig, Germany before settling in Vienna, Austria. In 1865, Sigmund entered the Leopoldstädter Communal-Realgymnasium, a prominent high school. Freud was an outstanding pupil and graduated the Matura in 1873 with honors.
After planning to study law, Freud joined the medical faculty at University of Vienna to study under Darwinist Prof. Karl Claus. At that time, Eel life history was still unknown, and due to their mysterious origins and migrations, a racist association was often made between eels and Jews and Gypsies. In search for their male sex organs, Freud spent four weeks at the Austrian zoological research station in Trieste, dissecting hundreds of eels without finding more than his predecessors such as Simon von Syrski. In 1876, he published his first paper about "the testicles of eels" in the “Mitteilungen der österreichischen Akademie der Wissenschaften”, conceding that he could not solve the matter either. Frustrated by the lack of success which would have gained him fame, and disgusted by the blood and gore, Freud chose to change his course of study. Biographers like Siegfried Bernfeld wonder if and how this early episode was significant for his later work regarding hidden sexuality and frustrations.
Medical school
In 1874, the concept of "psychodynamics" was proposed with the publication of Lectures on Physiology by German physiologist Ernst Wilhelm von Brücke who, in coordination with physicist Hermann von Helmholtz, one of the formulators of the first law of thermodynamics (conservation of energy), supposed that all living organisms are energy-systems also governed by this principle. During this year, at the University of Vienna, Brücke served as supervisor for first-year medical student Sigmund Freud who adopted this new “dynamic” physiology. In his Lectures on Physiology, Brücke set forth the radical view that the living organism is a dynamic system to which the laws of chemistry and physics apply. This was the starting point for Freud's dynamic psychology of the mind and its relation to the unconscious. The origins of Freud’s basic model, based on the fundamentals of chemistry and physics, according to John Bowlby, stems from Brücke, Meynert, Breuer, Helmholtz, and Herbart. In 1879, Freud interrupted his studies to complete his one year of obligatory military service, and in 1881 he received his Dr. med. (M.D.) with the thesis "Über das Rückenmark niederer Fischarten" (on the spinal cord of lower fish species).
- Freud married Martha Bernays in 1886, after opening his own medical practice, specializing in neurology.
- After experimenting with hypnosis on his neurotic patients, Freud abandoned this form of treatment, in favor of a treatment where the patient talked through his or her problems. This came to be known as the "talking cure". (The term was initially coined by the patient Anna O. who was treated by Freud's colleague Josef Breuer.) The "talking cure" is widely seen as the basis of psychoanalysis
Freud held the opinion (based on personal experience and observation) that sexual activity was incompatible with the accomplishing of any great work. Since he felt that the great work of creating and establishing psychotherapy was his destiny, he told his wife that they could no longer engage in sexual relations. Indeed from about the age of forty until his death Freud was absolutely celibate “in order to sublimate the libido for creative purposes,” according to his biographer Ernest Jones.
Last years
- In 1930 Freud received the Goethe Prize in appreciation of his contribution to psychology and to German literary culture.
- Three years later the Nazis took control of Germany and Freud's books featured prominently amongst those burned by the Nazis.
- In March 1938, Nazi Germany annexed Austria in the Anschluss. This led to violent outbursts of anti-Semitism in Vienna, and Freud and his family received visits from the Gestapo.
- Freud decided to go into exile "to die in freedom". He and his family left Vienna in June 1938 and traveled to London.
- A heavy cigar smoker, Freud endured more than 30 operations during his life due to mouth cancer.
- In September 1939 he prevailed on his doctor and friend Max Schur to assist him in suicide.
- After reading Balzac's La Peau de chagrin in a single sitting he said, "My dear Schur, you certainly remember our first talk. You promised me then not to forsake me when my time comes. Now it is nothing but torture and makes no sense any more."
- Schur administered three doses of morphine over many hours that resulted in Freud's death on September 23, 1939.
- Three days after his death, Freud's body was cremated at Golders Green Crematorium during a service attended by Austrian refugees, including the author Stefan Zweig. His ashes were later placed in the crematorium's columbarium.
- They rest in an ancient Greek urn which Freud had received as a present from Marie Bonaparte and which he had kept in his study in Vienna for many years.
- After Martha Freud's death in 1951, her ashes were also placed in that urn. Golders Green Crematorium has since also become the final resting place for Anna Freud and her lifelong friend Dorothy Burlingham, as well as for several other members of the Freud family.
Freud's ideas
- Freud has been influential in two related but distinct ways.
- He simultaneously developed a theory of how the human mind is organized and operates internally, and how human behavior both conditions and results from this particular theoretical understanding. This led him to favor certain clinical techniques for attempting to help cure psychopathology.
DIOPHANTUS OF ALEXANDRIA
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