Muḥammad ibn Mūsā al-Khwārizmī

Abū Abdallāh Muḥammad ibn Mūsā al-Khwārizmī (c. 780, Khwārizm– c. 850) was a Persian mathematician, astronomer and geographer, a scholar in the House of Wisdom in Baghdad.

In the twelfth century, Latin translations of his work on the Indian numerals, introduced the decimal positional number system to the Western world. His Compendious Book on Calculation by Completion and Balancing presented the first systematic solution of linear and quadratic equations in Arabic. In Renaissance Europe, he was considered the original inventor of algebra, although we now know that his work is based on older Indian or Greek sources. He revised Ptolemy's Geography and wrote on astronomy and astrology.

Some words reflect the importance of al-Khwarizmi's contributions to mathematics. "Algebra" is derived from al-jabr, one of the two operations he used to solve quadratic equations. Algorism and algorithm stem from Algoritmi, the Latin form of his name. His name is also the origin of guarismo and of algarismo, both meaning digit.Contents

·        Life

He was born in a Persianfamily, and his birthplace is given as Chorasmia by Ibn al-Nadim.

Few details of al-Khwārizmī's life are known with certainty. His name may indicate that he came from Khwarezm (Khiva), then in Greater Khorasan, which occupied the eastern part of the Greater Iran, now Xorazm Province in Uzbekistan. Abu Rayhan Biruni calls the people of Khwarizm "a branch of the Persian tree".

Al-Tabari gave his name as Muhammad ibn Musa al-Khwārizmī al-Majousi al-Katarbali (Arabic:( محمد بن موسى الخوارزميّ المجوسـيّ القطربّـليّ   

The epithet al-Qutrubbulli could indicate he might instead have come from Qutrubbul (Qatrabbul), a viticulture district near Baghdad. However, Rashed suggests:

Ibn al-Nadīm's Kitāb al-Fihrist includes a short biography on al-Khwārizmī, together with a list of the books he wrote. Al-Khwārizmī accomplished most of his work in the period between 813 and 833. After the Islamic conquest of Persia, Baghdad became the centre of scientific studies and trade, and many merchants and scientists from as far as China and India traveled to this city, as did Al-Khwārizmī. He worked in Baghdad as a scholar at the House of Wisdom established by Caliph al-Mamūn, where he studied the sciences and mathematics, which included the translation of Greek and Sanskrit scientific manuscripts.

·        Contributions

Al-Khwārizmī's contributions to mathematics, geography, astronomy, and cartography established the basis for innovation in algebra and trigonometry. His systematic approach to solving linear and quadratic equations led to algebra, a word derived from the title of his 830 book on the subject, "The Compendious Book on Calculation by Completion and Balancing" (al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabalaالكتاب المختصر في حساب الجبر والمقابلة   )

On the Calculation with Hindu Numerals written about 825, was principally responsible for spreading the Indian system of numeration throughout the Middle East and Europe. It was translated into Latin as Algoritmi de numero Indorum. Al-Khwārizmī, rendered as (Latin) Algoritmi, led to the term "algorithm".

Some of his work was based on Persian and Babylonian astronomy, Indian numbers, and Greek mathematics.

Al-Khwārizmī systematized and corrected Ptolemy's data for Africa and the Middle east. Another major book was Kitab surat al-ard ("The Image of the Earth"; translated as Geography), presenting the coordinates of places based on those in the Geography of Ptolemy but with improved values for the Mediterranean Sea, Asia, and Africa.

He also wrote on mechanical devices like the astrolabe and sundial.

He assisted a project to determine the circumference of the Earth and in making a world map for al-Ma'mun, the caliph, overseeing 70 geographers.

When, in the 12th century, his works spread to Europe through Latin translations, it had a profound impact on the advance of mathematics in Europe. He introduced Arabic numerals into the Latin West, based on a place-value decimal system developed from Indian sources.

·        Algebra

Main article: The Compendious Book on Calculation by Completion and Balancing

 A page from al-Khwārizmī's Algebra

Al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa-l-muqābala (Arabic: الكتاب المختصر في حساب الجبر والمقابلة‎, 'The Compendious Book on Calculation by Completion and Balancing') is a mathematical book written approximately 830 CE. The book was written with the encouragement of the Caliph al-Ma'mun as a popular work on calculation and is replete with examples and applications to a wide range of problems in trade, surveying and legal inheritance. The term algebra is derived from the name of one of the basic operations with equations (al-jabr, meaning completion, or, subtracting a number from both sides of the equation) described in this book. The book was translated in Latin as Liber algebrae et almucabala by Robert of Chester (Segovia, 1145) hence "algebra", and also by Gerard of Cremona. A unique Arabic copy is kept at Oxford and was translated in 1831 by F. Rosen. A Latin translation is kept in Cambridge.

It provided an exhaustive account of solving polynomial equations up to the second degree, and discussed the fundamental methods of "reduction" and "balancing", referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation.

Al-Khwārizmī's method of solving linear and quadratic equations worked by first reducing the equation to one of six standard forms (where b and c are positive integers)

·         squares equal roots ( ax2 = bx (

·         squares equal number ( ax2 = c (

·         roots equal number ( bx = c (

·         squares and roots equal number ( ax2 + bx = c (

·         squares and number equal roots ( ax2 + c = bx )

·         roots and number equal squares ( bx + c = ax2 )

by dividing out the coefficient of the square and using the two operations al-jabr (Arabic: الجبر‎ “restoring” or “completion”) and al-muqābala ("balancing"). Al-jabr is the process of removing negative units, roots and squares from the equation by adding the same quantity to each side.

The above discussion uses modern mathematical notation for the types of problems which the book discusses. However, in al-Khwārizmī's day, most of this notation had not yet been invented, so he had to use ordinary text to present problems and their solutions. For example, for one problem he writes, (from an 1831 translation)

"If some one say: "You divide ten into two parts: multiply the one by itself; it will be equal to the other taken eighty-one times." Computation: You say, ten less thing, multiplied by itself, is a hundred plus a square less twenty things, and this is equal to eighty-one things. Separate the twenty things from a hundred and a square, and add them to eighty-one. It will then be a hundred plus a square, which is equal to a hundred and one roots. Halve the roots; the moiety is fifty and a half. Multiply this by itself, it is two thousand five hundred and fifty and a quarter. Subtract from this one hundred; the remainder is two thousand four hundred and fifty and a quarter. Extract the root from this; it is forty-nine and a half. Subtract this from the moiety of the roots, which is fifty and a half. There remains one, and this is one of the two parts."

In modern notation this process, with 'x' the "thing" (shay') or "root", is given by the steps,

·        Arithmetic

Al-Khwārizmī's second major work was on the subject of arithmetic, which survived in a Latin translation but was lost in the original Arabic. The translation was most likely done in the twelfth century by Adelard of Bath, who had also translated the astronomical tables in 1126.

The Latin manuscripts are untitled, but are commonly referred to by the first two words with which they start: Dixit algorizmi ("So said al-Khwārizmī"), or Algoritmi de numero Indorum ("al-Khwārizmī on the Hindu Art of Reckoning"), a name given to the work by Baldassarre Boncompagni in 1857. The original Arabic title was possibly Kitāb al-Jam wa-l-tafrīq bi-isāb al-Hind ("The Book of Addition and Subtraction According to the Hindu Calculation")

Al-Khwarizmi's work on arithmetic was responsible for introducing the Arabic numerals, based on the Hindu-Arabic numeral system developed in Indian mathematics, to the Western world. The term "algorithm" is derived from the algorism, the technique of performing arithmetic with Hindu-Arabic numerals developed by al-Khwarizmi. Both "algorithm" and "algorism" are derived from the Latinized forms of al-Khwarizmi's name, Algoritmi and Algorismi, respectively.

·        Astronomy

 Page from Corpus Christi College MS 283. A Latin translation of al-Khwārizmī's Zīj.

Al-Khwārizmī's Zīj al-Sindhind (Arabic: زيج "astronomical tables of Sind and Hind") is a work consisting of approximately 37 chapters on calendrical and astronomical calculations and 116 tables with calendrical, astronomical and astrological data, as well as a table of sine values. This is the first of many Arabic Zijes based on the Indian astronomical methods known as the sindhind. The work contains tables for the movements of the sun, the moon and the five planets known at the time. This work marked the turning point in Islamic astronomy. Hitherto, Muslim astronomers had adopted a primarily research approach to the field, translating works of others and learning already discovered knowledge.

The original Arabic version (written c. 820) is lost, but a version by the Spanish astronomer Maslamah Ibn Ahmad al-Majriti (c. 1000) has survived in a Latin translation, presumably by Adelard of Bath (January 26, 1126).[25] The four surviving manuscripts of the Latin translation are kept at the Bibliothèque publique (Chartres), the Bibliothèque Mazarine (Paris), the Bibliotheca Nacional (Madrid) and the Bodleian Library (Oxford).

·        Trigonometry

Al-Khwārizmī's Zīj al-Sindhind also contained tables for the trigonometric functions of sines and cosine. A related treatise on spherical trigonometry is also attributed to him.

·        Geography

  Hubert Daunicht's reconstruction of al-Khwārizmī's planisphere.

Al-Khwārizmī's third major work is his Kitāb ṣūrat al-Arḍ (Arabic: كتاب صورة الأرض "Book on the appearance of the Earth" or "The image of the Earth" translated as Geography), which was finished in 833. It is a revised and completed version of Ptolemy's Geography, consisting of a list of 2402 coordinates of cities and other geographical features following a general introduction.

There is only one surviving copy of Kitāb ṣūrat al-Arḍ, which is kept at the Strasbourg University Library. A Latin translation is kept at the Biblioteca Nacional de España in Madrid. The complete title translates as Book of the appearance of the Earth, with its cities, mountains, seas, all the islands and rivers, written by Abu Ja'far Muhammad ibn Musa al-Khwārizmī, according to the geographical treatise written by Ptolemy the Claudian.

The book opens with the list of latitudes and longitudes, in order of "weather zones", that is to say in blocks of latitudes and, in each weather zone, by order of longitude. As Paul Gallez[dubious – discuss] points out, this excellent system allows the deduction of many latitudes and longitudes where the only extant document is in such a bad condition as to make it practically illegible.

Neither the Arabic copy nor the Latin translation include the map of the world itself; however, Hubert Daunicht was able to reconstruct the missing map from the list of coordinates. Daunicht read the latitudes and longitudes of the coastal points in the manuscript, or deduces them from the context where they were not legible. He transferred the points onto graph paper and connected them with straight lines, obtaining an approximation of the coastline as it was on the original map. He then does the same for the rivers and towns.

Al-Khwārizmī corrected Ptolemy's gross overestimate for the length of the Mediterranean Sea from the Canary Islands to the eastern shores of the Mediterranean; Ptolemy overestimated it at 63 degrees of longitude, while al-Khwarizmi almost correctly estimated it at nearly 50 degrees of longitude. He "also depicted the Atlantic and Indian Oceans as open bodies of water, not land-locked seas as Ptolemy had done." Al-Khwarizmi thus set the Prime Meridian of the Old World at the eastern shore of the Mediterranean, 10–13 degrees to the east of Alexandria (the prime meridian previously set by Ptolemy) and 70 degrees to the west of Baghdad. Most medieval Muslim geographers continued to use al-Khwarizmi's prime meridian.

·        Jewish calendar

Al-Khwārizmī wrote several other works including a treatise on the Hebrew calendar (Risāla fi istikhrāj tarīkh al-yahūd "Extraction of the Jewish Era"). It describes the 19-year intercalation cycle, the rules for determining on what day of the week the first day of the month Tishrī shall fall; calculates the interval between the Jewish era (creation of Adam) and the Seleucid era; and gives rules for determining the mean longitude of the sun and the moon using the Jewish calendar. Similar material is found in the works of al-Bīrūnī and Maimonides.

·        Other works

Several Arabic manuscripts in Berlin, Istanbul, Tashkent, Cairo and Paris contain further material that surely or with some probability comes from al-Khwārizmī. The Istanbul manuscript contains a paper on sundials, which is mentioned in the Fihrist. Other papers, such as one on the determination of the direction of Mecca, are on the spherical astronomy.

Two texts deserve special interest on the morning width (Maʿrifat saʿat al-mashriq fī kull balad) and the determination of the azimuth from a height (Marifat al-samt min qibal al-irtifā).

He also wrote two books on using and constructing astrolabes. Ibn al-Nadim in his Kitab al-Fihrist (an index of Arabic books) also mentions Kitāb ar-Rukhāma(t) (the book on sundials) and Kitab al-Tarikh (the book of history) but the two have been lost.

Ghiyāth al-Dīn Jamshīd Masoūd al-Kāshī (or al-Kāshānī)

 (c. 1380 Kashan, Iran – 22 June 1429 Samarkand, Transoxania) was a  Persian  astronomer  and  mathematician.

Biography

Al-Kashi was one of the best mathematicians in the Islamic world. He was born in 1380, in Kashan, in central Iran. This region was controlled by Tamurlane, better known as Timur. Al-Kashi lived in poverty during his childhood and the beginning years of his adulthood.

The situation changed for the better when Timur died in 1405, and his son, Shah Rokh, ascended into power. Shah Rokh and his wife, Goharshad, a Persian princess, were very interested in the sciences, and they encouraged their court to study the various fields in great depth. Their son, Ulugh Beg, was enthusiastic about science as well, and made some noted contributions in mathematics and astronomy himself. Consequently, the period of their power became one of many scholarly accomplishments. This was the perfect environment for al-Kashi to begin his career as one of the world’s greatest mathematicians.

Eight years after he came into power in 1409, Ulugh Beg founded an institute in Samarkand which soon became a prominent university. Students from all over the Middle East, and beyond, flocked to this academy in the capital city of Ulugh Beg’s empire. Consequently, Ulugh Beg harvested many great mathematicians and scientists of the Muslim world. In 1414, al-Kashi took this opportunity to contribute vast amounts of knowledge to his people. His best work was done in the court of Ulugh Beg, and it is said that he was the king’s favourite student.

Al-Kashi was still working on his book, called “Risala al-watar wa’l-jaib” meaning “The Treatise on the Chord and Sine”, when he died in 1429. Some scholars believe that Ulugh Beg may have ordered his murder, while others say he died a natural death. The details are unclear.

Astronomy

Khaqani Zij

Al-Kashi produced a Zij entitled the Khaqani Zij, which was based on Nasir al-Din al-Tusi's earlier Zij-i Ilkhani. In his Khaqani Zij, al-Kashi thanks the Timurid sultan and mathematician-astronomer Ulugh Beg, who invited al-Kashi to work at his observatory (see Islamic astronomy) and his  university  (see  Madrasah) which taught Islamic theology as well as Islamic science. Al-Kashi produced sine tables to four sexagesimal digits (equivalent to eight decimal places) of accuracy for each degree and includes differences for each minute. He also produced tables dealing with transformations between coordinate systems on the celestial sphere, such as the transformation from the ecliptic coordinate system to the equatorial coordinate system.

Astronomical Treatise on the size and distance of heavenly bodies

He wrote the book Sullam al-Sama on the resolution of difficulties met by predecessors in the determination of distances and sizes of heavenly bodies such as the Earth , the Moon , the Sun and the Stars.

Treatise on Astronomical Observational Instruments

In 1416, al-Kashi wrote the Treatise on Astronomical Observational Instruments, which described a variety of different instruments, including the triquetrum and armillary sphere, the equinoctial armillary and solsticial armillary of Mo'ayyeduddin Urdi, the sine and versine instrument of Urdi, the sextant  of  al-Khujandi, the Fakhri sextant at the Samarqand observatory, a double quadrant Azimuth-altitude instrument he invented, and a small armillary sphere incorporating an alhidade which he invented.

Plate of Conjunctions

Al-Kashi invented the Plate of Conjunctions, an analog computing instrument used to determine the time of day at which planetary conjunctions will occur, and for performing linear interpolation.

Planetary computer

Al-Kashi also invented a mechanical planetary computer which he called the Plate of Zones, which could graphically solve a number of planetary problems, including the prediction of the true positions in longitude of the Sun and Moon, and the planets in terms of elliptical orbits; the latitudes of the Sun, Moon, and planets; and the ecliptic of the Sun. The instrument also incorporated an alhidade and ruler.

Mathematics

Law of cosines

In French, the law of cosines is named Théorème d'Al-Kashi (Theorem of Al-Kashi), as al-Kashi was the first to provide an explicit statement of the law of cosines in a form suitable for triangulation.

The Treatise on the Chord and Sine

In The Treatise on the Chord and Sine, al-Kashi computed sin 1° to nearly as much accuracy as his value for π, which was the most accurate approximation of sin 1° in his time and was not surpassed until Taqi al-Din in the 16th century. In algebra and numerical analysis, he developed an iterative method for solving cubic equations, which was not discovered in Europe until centuries later.

A method algebraically equivalent to Newton's method was known to his predecessor Sharaf al-Dīn al-Tūsī. Al-Kāshī improved on this by using a form of Newton's method to solve xP − N = 0 to find roots of N. In western Europe, a similar method was later described by Henry Biggs in his Trigonometria Britannica, published in 1633.

In order to determine sin 1°, al-Kashi discovered the following formula often attributed to François Viète in the 16th century:

he discovered the math term pi

The Key to Arithmetic

Computation of π

In one of his numerical approximations of π, he correctly computed 2π to 9 sexagesimal digits. This approximation of 2π is equivalent to 16 decimal places of accuracy. This was far more accurate than the estimates earlier given in Greek mathematics (3 decimal places by Archimedes), Chinese mathematics (7 decimal places by Zu Chongzhi) or Indian mathematics (11 decimal places by Madhava of Sangamagrama). The accuracy of al-Kashi's estimate was not surpassed until Ludolph van Ceulen computed 20 decimal places of π nearly 200 years later.

Decimal fractions

In discussing decimal fractions, Struik states that (p. 7):

"The introduction of decimal fractions as a common computational practice can be dated back to the Flemish pamphlet De Thiende, published at Leyden in 1585, together with a French translation, La Disme, by the Flemish mathematician Simon Stevin (1548-1620), then settled in the Northern Netherlands. It is true that decimal fractions were used by the Chinese many centuries before Stevin and that the Persian astronomer Al-Kāshī used both decimal and sexagesimal fractions with great ease in his Key to arithmetic (Samarkand, early fifteenth century). "

Khayyam's triangle

In considering Pascal's triangle, known in Persia as "Khayyam's triangle" (named after Omar Khayyám), Struik notes that (p. 21):

"The Pascal triangle appears for the first time (so far as we know at present) in a book of 1261 written by Yang Hui, one of the mathematicians of the Sung dynasty in China. The properties of binomial coefficients were discussed by the Persian mathematician Jamshid Al-Kāshī in his Key to arithmetic of c. 1425. Both in China and Persia the knowledge of these properties may be much older. This knowledge was shared by some of the Renaissance mathematicians, and we see Pascal's triangle on the title page of Peter Apian's German arithmetic of 1527. After this we find the triangle and the properties of binomial coefficients in several other authors. "

Biographical film

In 2009 IRIB produced and broadcast (through Channel 1 of IRIB) a biographical-historical film series on the life and times of Jamshid Al-Kāshi, with the title The Ladder of the Sky  (Nardebām-e Āsmān). The series, which consists of 15 parts of each 45 minutes duration, is directed by Mohammad-Hossein Latifi and produced by Mohsen Ali-Akbari. In this production, the role of the adult Jamshid Al-Kāshi is played by Vahid Jalilvand.

Vahid Jalilvand

Marie Curie

 Marie Skłodowska Curie (7 November 1867 – 4 July 1934)

was a Polish–French physicist–chemist famous for her pioneering research on radioactivity. She was the first person honored with two Nobel Prizes in physics and chemistry. She was the first female professor at the University of Paris. She was the first woman to be entombed on her own merits (in 1995) in the Paris Panthéon.

She was born Maria Salomea Skłodowska in Warsaw, in Russian Poland, and lived there to age twenty-four. In 1891 she followed her older sister Bronisława to study in Paris, where she earned her higher degrees and conducted her subsequent scientific work. She shared her Nobel Prize in Physics (1903) with her husband Pierre Curie (and with Henri Becquerel). Her daughter Irène Joliot-Curie and son-in-law, Frédéric Joliot-Curie, would similarly share a Nobel Prize. She was the sole winner of the 1911 Nobel Prize in Chemistry. Curie was the first woman to win a Nobel Prize, and is the only woman to win in two fields, and the only person to win in multiple sciences.

Her achievements include a theory of radioactivity (a term that she coined), techniques for isolating radioactive isotopes, and the discovery of two elements, polonium and radium. Under her direction, the world's first studies were conducted into the treatment of neoplasms, using radioactive isotopes. She founded the Curie Institutes: the Curie Institute (Paris) and the Curie Institute (Warsaw).

While an actively loyal French citizen, Skłodowska–Curie (as she styled herself) never lost her sense of Polish identity. She taught her daughters the Polish language and took them on visits to Poland. She named the first chemical element that she discovered "polonium" (1898) for her native country. During World War I she became a member of the Committee for a Free Poland (Komitet Wolnej Polski).[4] In 1932 she founded a Radium Institute (now the Maria Skłodowska–Curie Institute of Oncology) in her home town, Warsaw, headed by her physician-sister Bronisława.

Early life

Władysław Skłodowski with daughters (from left) Maria, Bronisława, Helena

Maria Skłodowska was born in Warsaw, Poland, on 7 November 1867, the fifth and youngest child of well-known teachers Bronisława and Władysław Skłodowski. Maria's older siblings were Zofia (born 1862), Józef (1863), Bronisława (1865) and Helena (1866).

Maria's father was an atheist; her mother—a devout Catholic. Two years earlier Maria's oldest sibling, Zofia, had died of typhus. The deaths of her mother and sister, according to Robert William Reid, caused Maria to give up Catholicism and become agnostic.

When she was ten years old, Maria began attending the boarding school that her mother had operated while she was well; next Maria attended a gymnasium for girls, from which she graduated on 12 June 1883. She spent the following year in the countryside with relatives of her father's, and the next with her father in Warsaw, where she did some tutoring.

On both the paternal and maternal sides, the family had lost their property and fortunes through patriotic involvements in Polish national uprisings. This condemned each subsequent generation, including that of Maria, her elder sisters and her brother, to a difficult struggle to get ahead in life.

In October 1891, at her sister's insistence and after receiving a letter from Żorawski, in which he definitively broke his relationship with her, she decided to go to France after all.

Maria's loss of the relationship with Żorawski was tragic for both. He soon earned a doctorate and pursued an academic career as a mathematician, becoming a professor and rector of Kraków University and president of the Warsaw Society of Learning. Still, as an old man and a mathematics professor at the Warsaw Polytechnic, he would sit contemplatively before the statue of Maria Skłodowska which had been erected in 1935 before the Radium Institute that she had founded in 1932.

In Paris, Maria briefly found shelter with her sister and brother-in-law before renting a primitive garret and proceeding with her studies of physics, chemistry, and mathematics at the Sorbonne (the University of Paris).

Sorbonne

Pierre Curie

Skłodowska studied during the day and tutored evenings, barely earning her keep. In 1893, she was awarded a degree in physics and began work in an industrial laboratory at Lippman's. Meanwhile she continued studying at the Sorbonne, and in 1894, earned a degree in mathematics.

That same year, Pierre Curie entered her life. He was an instructor at the School of Physics and Chemistry, the École supérieure de physique et de chimie industrielles de la ville de Paris (ESPCI). Skłodowska had begun her scientific career in Paris with an investigation of the magnetic properties of various steels; it was their mutual interest in magnetism that drew Skłodowska and Curie together.

Her departure for the summer to Warsaw only enhanced their mutual feelings for each other. She still was laboring under the illusion that she would be able to return to Poland and work in her chosen field of study. When she was denied a place at Kraków University merely because she was a woman, however, she returned to Paris. Almost a year later, in July 1895, she and Pierre Curie married, and thereafter the two physicists hardly ever left their laboratory. They shared two hobbies, long bicycle trips and journeys abroad, which brought them even closer. Maria had found a new love, a partner, and a scientific collaborator upon whom she could depend.

New elements

In 1896 Henri Becquerel discovered that uranium salts emitted rays that resembled X-rays in their penetrating power. He demonstrated that this radiation, unlike phosphorescence, did not depend on an external source of energy, but seemed to arise spontaneously from uranium itself. Becquerel had, in fact, discovered radioactivity.

Skłodowska–Curie decided to look into uranium rays as a possible field of research for a thesis. She used a clever technique to investigate samples. Fifteen years earlier, her husband and his brother had invented the electrometer, a sensitive device for measuring electrical charge. Using the Curie electrometer, she discovered that uranium rays caused the air around a sample to conduct electricity. Using this technique, her first result was the finding that the activity of the uranium compounds depended only on the quantity of uranium present. She had shown that the radiation was not the outcome of some interaction of molecules, but must come from the atom itself. In scientific terms, this was the most important single piece of work that she conducted.

Skłodowska–Curie's systematic studies had included two uranium minerals, pitchblende and  torbernite (also known as chalcolite). Her electrometer showed that pitchblende was four times as active as uranium itself, and chalcolite twice as active. She concluded that, if her earlier results relating the quantity of uranium to its activity were correct, then these two minerals must contain small quantities of some other substance that was far more active than uranium itself.

The idea [writes Reid] was her own; no one helped her formulate it, and although she took it to her husband for his opinion she clearly established her ownership of it. She later recorded the fact twice in her biography of her husband to ensure there was no chance whatever of any ambiguity. It [is] likely that already at this early stage of her career [she] realized that... many scientists would find it difficult to believe that a woman could be capable of the original work in which she was involved.

In her systematic search for other substances beside uranium salts that emitted radiation, Skłodowska–Curie had found that the element thorium likewise, was radioactive.

Pierre and Marie Curie in their Paris laboratory, before 1907

She was acutely aware of the importance of promptly publishing her discoveries and thus establishing her priority. Had not Becquerel, two years earlier, presented his discovery to the Académie des Sciences  the day after he made it, credit for the discovery of radioactivity, and even a Nobel Prize, would have gone to Silvanus Thompson instead. Skłodowska–Curie chose the same rapid means of publication. Her paper, giving a brief and simple account of her work, was presented for her to the Académie on 12 April 1898 by her former professor, Gabriel Lippmann.

Even so, just as Thompson had been beaten by Becquerel, so Skłodowska–Curie was beaten in the race to tell of her discovery that thorium gives off rays in the same way as uranium. Two months earlier, Gerhard Schmidt had published his own finding in Berlin.

At that time, however, no one else in the world of physics had noticed what Skłodowska–Curie recorded in a sentence of her paper, describing how much greater were the activities of pitchblende and chalcolite compared to uranium itself: "The fact is very remarkable, and leads to the belief that these minerals may contain an element which is much more active than uranium." She later would recall how she felt "a passionate desire to verify this hypothesis as rapidly as possible."

Pierre Curie was sure that what she had discovered was not a spurious effect. He was so intrigued that he decided to drop his work on crystals temporarily and to join her. On 14 April 1898, they optimistically weighed out a 100-gram sample of pitchblende and ground it with a pestle and mortar. They did not realize at the time that what they were searching for was present in such minute quantities that they eventually would have to process tons of the ore.

As they were unaware of the deleterious effects of radiation exposure attendant on their chronic unprotected work  with radioactive substances, Skłodowska–Curie and her husband had no idea what price they would pay for the effect of their research upon their health.

Pierre, Irène, Marie Curie

In July 1898, Skłodowska–Curie and her husband published a paper together, announcing the existence of an element which they named "polonium", in honor of her native Poland, which would for another twenty years remain partitioned among three empires. On 26 December 1898, the Curies announced the existence of a second element, which they named "radium" for its intense radioactivity — a word that they coined.

Pitchblende is a complex mineral. The chemical separation of its constituents was an arduous task. The discovery of polonium had been relatively easy; chemically it resembles the element bismuth, and polonium was the only bismuth-like substance in the ore. Radium, however, was more elusive. It is closely related, chemically, to barium, and pitchblende contains bothelements. By 1898, the Curies had obtained traces of radium, but appreciable quantities, uncontaminated with barium, still were beyond reach.

The Curies undertook the arduous task of separating out radium salt by differential crystallization. From a ton of pitchblende, one-tenth of a gram of radium chloride was separated in 1902. By 1910, Skłodowska–Curie, working on without her husband, who had been killed accidentally by a horse drawn vehicle in 1906, had isolated the pure radium metal.

In an unusual decision, Marie Skłodowska–Curie intentionally refrained from patenting the radium-isolation process, so that the scientific community could do research unhindered.

In 1903, under the supervision of  Henri Becquerel, Marie was awarded her DSc from the University of Paris.

Nobel Prizes

In 1903 the Royal Swedish Academy of Sciences awarded Pierre Curie, Marie Curie and Henri Becquerel the Nobel Prize in Physics, "in recognition of the extraordinary services they have rendered by their joint researches on the radiation phenomena discovered by Professor Henri Becquerel."

Skłodowska–Curie and her husband were unable to go to Stockholm to receive the prize in person, but they shared its financial proceeds with needy acquaintances, including students.

Pierre's death

On 19 April 1906 Pierre was killed in a street accident. Walking across the Rue Dauphine in heavy rain, he was struck by a horse-drawn vehicle and fell under its wheels; his skull was fractured. While it has been speculated that previously he may have been weakened by prolonged radiation exposure, there are no indications that this contributed to the accident.

Skłodowska–Curie was devastated by the death of her husband. She noted that, as of that moment she suddenly had become "an incurably and wretchedly lonely person". On 13 May 1906, the Sorbonne physics department decided to retain the chair that had been created for Pierre Curie and they entrusted it to Skłodowska–Curie together with full authority over the laboratory. This allowed her to emerge from Pierre's shadow. She became the first woman to become a professor at the Sorbonne, and in her exhausting work regime she sought a meaning for her life.

Recognition for her work grew to new heights, and in 1911 the Royal Swedish Academy of Sciences awarded her a second Nobel Prize, this time for Chemistry. A delegation of celebrated Polish men of learning, headed by world-famous novelist Henryk Sienkiewicz, encouraged her to return to Poland and continue her research in her native country.

In 1911 it was revealed that in 1910–11 Skłodowska–Curie had conducted an affair of about a year's duration with physicist Paul Langevin, a former student of Pierre Curie's. He was a married man who was estranged from his wife. This resulted in a press scandal that was exploited by her academic opponents. Despite her fame as a scientist working for France, the public's attitude tended toward xenophobia—the same that had led to the  Dreyfus Affair - which also fueled false speculation that Skłodowska–Curie was Jewish. She was five years older than Langevin and was portrayed in the tabloids as a home-wrecker. Later, Skłodowska–Curie's granddaughter, Hélène Joliot, married Langevin's grandson, Michel Langevin.

Skłodowska–Curie's second Nobel Prize, in 1911, enabled her to talk the French government into funding the building of a private Radium Institute (Institut du radium, now the Institut Curie), which was built in 1914 and at which research was conducted in chemistry, physics, and medicine. The Institute became a crucible of Nobel Prize winners, producing four more, including her daughter Irène Joliot-Curie and her son-in-law, Frédéric Joliot-Curie.

Death

Skłodowska–Curie visited Poland for the last time in the spring of 1934. Only a few months later, on 4 July 1934, Skłodowska-Curie died at the Sancellemoz Sanatorium in Passy, in Haute-Savoie, eastern France, from aplastic anemia contracted from exposure to radiation. The damaging effects of ionizing radiation were not then known, and much of her work had been carried out in a shed, without proper safety measures. She had carried test tubes containing radioactive isotopes in her pocket and stored them in her desk drawer, remarking on the pretty blue-green light that the substances gave off in the dark.

She was interred at the cemetery in Sceaux, alongside her husband Pierre. Sixty years later, in 1995, in honor of their achievements, the remains of both were transferred to the Panthéon, Paris. She became the first – and so far the only – woman to be honored with interrment in the Panthéon on her own merits.

Her laboratory is preserved at the Musée Curie.

Because of their levels of radioactivity, her papers from the 1890s are considered too dangerous to handle. Even her cookbook is highly radioactive. They are kept in lead-lined boxes, and those who wish to consult them must wear protective clothing.