Sunday, October 26, 2008

Hertha Marks Ayrton

Hertha Ayrton

April 28, 1854 - August 23, 1923

Phoebe Sarah Marks was born in Portsea, England in 1854. She changed her first name to Hertha when she was a teenager. After passing the Cambridge University Examination for Women with honors in English and mathematics, she attended Girton College at Cambridge University, the first residential college for women in England. Charlotte Scott also attended Girton at this time, and she and Marks helped form a mathematics club to "find problems for the club to solve and 'discuss any mathematical question that may arise'" [1]. Marks passed the Mathematical Tripos in 1880, although with a disappointing Third Class performance. Because Cambridge did not confer degrees to women at this time, just certificates, she successfully completed an external examination and received a B.Sc. degree from the University of London.

From 1881 to 1883, Marks worked as a private mathematics tutor, as well as tutoring other subjects. In 1884 she invented a draftsman's device that could be used for dividing up a line into equal parts as well as for enlarging and reducing figures. She was also active in devising and solving mathematical problems, many of which were published in the Mathematical Questions and Their Solutions from the "Educational Times". Tattersall and McMurran write that "Her many solutions indicate without a doubt that she possessed remarkable geometric insight and was quite a clever student of mathematics."

Marks began her scientific studies by attending evening classes in physics at Finsbury Technical College given by Professor William Ayrton, whom she married in 1885. She assisted her husband with his experiments in physics and electricity, becoming an acknowledged expert on the subject of the electric arc. She published several papers from her own research in electric arcs in the Proceedings of the Royal Society of London and The Electrician, and published the book The Electric Arc in 1902. According to Tattersall and McMurran,

The text included descriptions and many illustrations of her experiments, succinct chapter reviews, a comprehensive index, an extensive bibliography, and a chapter devoted to tracing the history of the electric arc. Her historical account provided detailed explanations of previous experiments and results involving the arc and concluded with the most recent research of the author and her colleagues...The book was widely accepted as tour de force on the electrical arc and received favorable reviews on the continent where a German journal enthusiastically praised if for its clear exposition and relevant conclusions.

Hertha Ayrton had been elected the first female member of the Institution of Electrical Engineers in 1899. In 1902 she became the first woman nominated a Fellow of the Royal Society of London. Because she was married, however, legal counsel advised that the charter of the Royal Society did not allow the Society to elect her to this distinction (this advice was reversed in 1923, but the first woman was still not admitted to the Royal Society until twenty years later.) However, in 1904 Ayrton did become the first woman to read her own paper before the Royal Society. This paper was on "The origin and growth of ripple-mark" [Abstract] and was later published in the Proceedings of the Royal Society. In 1906 Ayrton received the Royal Society's Hughes Medal for her experimental investigations on the electric arc, and also on sand ripples. She was the fifth recipient of this prize, award annually since 1902 in recognition of an original discovery in the physical sciences, particularly electricity and magnetism or their applications, and as of 2005, the only woman so honored.

After her husband's death in 1908, Ayrton continued her research. One set of experiments validated Lord Rayleigh's mathematical theory of vortices. She also invented a fan that could create spiral vortices to repel gas attacks. These became known as Ayrton fans, but were never widely used.

Ayrton was an active member of the Woman's Social and Political Union and participated in many suffrage rallies between 1906 and 1913. She was a founding member of the International Federation of University Women and the National Union of Scientific Workers. She served as vice-president of the British Federation of University Women and vice-president of the National Union of Women's Suffrages Societies. Two years after her death in 1923, her lifelong friend Ottilie Hancock endowed the Hertha Ayrton Research Fellowship at Girton College.

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Nobel Prize in Mathematics

A trick question! There is no Nobel prize in mathematics. Why not? That question has created numerous stories, myths, and anecdotes. The most popular is that Nobel's wife had an affair with a mathematician, usually said to be Mittag-Leffler, and in revenge Nobel refused to endow one of his prizes in mathematics. Too bad for this story that Nobel was a life-long bachelor! The other common story is that Mittag-Leffler, the leading Swedish mathematician of Nobel's time, antagonized Nobel and so Nobel gave no prize in mathematics to prevent Mittag-Leffler from becoming a winner. This story is also suspect, however, because Nobel and Mittag-Leffler had almost no contact with each other. Most likely Nobel simply never gave any thought to including mathematics among his list of prize areas.

References:

  1. Garding, Lars and Lars Hormander. "Why is there no Nobel prize in mathematics?" The Mathematical Intelligencer, 7(3)(1985), 73-74.
  2. Ross, Peter. "Why isn't there a Nobel prize in mathematics?" Math Horizons, November 1995, p9. [Reprint from the Math Forum]
  3. Why is there no Nobel Prize in Mathematics?, http://www.almaz.com/Nobel/why_no_math.html, The Nobel Prize Internet Archive

Fields Medal

The Fields Medal is considered to be the equivalent of the Nobel prize for mathematics. John Charles Fields (1863-1932), a Canadian mathematician, endowed funds in his will for an award for mathematical achievement and promise that would emphasize the international character of the mathematical endeavor. The first Fields Medal was awarded at the International Congress of Mathematics meeting in Oslo in 1936. Since 1950 the medal has been awarded every four years at the International Mathematical Congress to between 2 and 4 mathematicians. Although there is no specific age restriction in Fields' will, he did wish that the awards recognize both existing work and the promise of future achievement, so the medals have been restricted to mathematicians under the age of 40. No woman mathematician has ever won a Fields Medal.

Reference:

  1. Fields Medals and Rolf Nevalinna Prize, http://www.emis.math.ca/EMIS/mirror/IMU/medals/ [contains complete list of all winners and pictures of the front and back of the medal]
  2. Historical Introduction by Alex Lopez-Ortiz, part of his FAQ site on mathematics.

Ruth Lyttle Satter Prize in Mathematics

[Description from the Notices of the American Mathematical Society]
The Ruth Lyttle Satter Prize in Mathematics was established in 1990 using funds donated to the American Mathematical Society by Joan S. Birman of Columbia University in memory of her sister, Ruth Lyttle Satter. Professor Satter earned a bachelor's degree in mathematics and then joined the research staff at AT&T Bell Laboratories during World War II. After raising a family, she received a Ph.D. in botany at the age of forty-three from the University of Connecticut at Storrs, where she later became a faculty member. Her research on the biological clocks in plants earned her recognition in the U.S. and abroad. Professor Birman requested that the prize be established to homor her sister's commitment to research and to encouraging women in science. The prize is awarded every two years to recognize an outstanding contribution to mathematics research by a woman in the previous five years. The winners have been:

Louise Hay Award for Contributions to Mathematics Education

[Description from the Notices of the American Mathematical Society]
The Executive Committee of the Association for Women in Mathematics established the annual Louise Hay Award for Contributions to Mathematics Education. The purpose of this award is to recognize outstanding achievements in any area of mathematics education, to be interpreted in the broadest possible sense. While Louise Hay was widely recognized for her contributions to mathematical logic and for her strong leadership as head of the Department of Mathematics, Statistics, and Computer Science at the University of Illinois at Chicago, her devotion to students and her lifelong commitment to nurturing the talent of young women and men secure her reputation as a consummate educator. The annual presentation of this award is intended to highlight the importance of mathematical education and to evoke the memory of all that Hay exemplified as a teacher, scholar, administrator, and human being.

The winners have been:

For more information about the award and the recipients, visit Louise Hay Award at the Association for Women in Mathematics web site.

Leroy P. Steele Prize for Seminal Contributions to Research

The Steele Prizes were established in 1970. In 1993, the AMS formalized three categories for the prizes. The prize for "seminal contributions to research" is awarded for a paper, whether recent or not, that has proved to be of fundamental or lasting importance in its field, or a model of important research.

Women mathematicians who have won the prize are:

  • 2007 Karen Uhlenbeck, "Removable singularities in Yang-Mills fields," Comm. Math. Phys. 83 (1982), 11-29; and "Connections with Lp bounds on curvature," Comm. Math. Phys. 83 (1982), 31-42.

Chauvenet Prize

The Chauvenet Prize is awarded annually by the Mathematical Association of America to the author of an outstanding expository article on a mathematical topic by a member of the association. First awarded in 1925, the Prize is named for William Chauvenet, a professor of mathematics at the United States Naval Academy. It was established through a gift in 1925 from J.L. Coolidge, then MAA President. Winners of the Chauvent Prize are among the most distinguished of mathematical expositors.

Women mathematicians who have won the prize are:

  • 1996 Joan Birman, "New Points of View in Knot Theory," AMS Bulletin, 28(1993).
  • 2001 Carolyn S. Gordon (with David L. Webb), "You can't hear the shape of a drum", American Scientist 84 (1996), 46-55.
  • 2002 Ellen Gethner (with Stan Wagon and Brian Wick), "A Stroll through the Gaussian Primes", American Mathematical Monthly, vol 105, no. 4 (1998), 327-337.

MacArthur Fellowships

MacArthur fellowships, popularly known as the "genius awards," cannot be applied for; rather, candidates are drawn from a pool of initial nominations by an anonymous group of 100 people. The John D. and Catherine T. MacArthur Foundation aims to recognize people whose achievements in the arts, humanities, sciences, social sciences, and public affairs show the promise of even greater accomplishments in the future. There are no strings attached. Recipients can spend the money, usually anywhere from $150,000 to $375,000 over a period of five years, anyway they want. The fellowships were established in 1981.

Women mathematicians who have received MacArthur Fellowships are:

Alice T. Schafer Prize

The Schafer Prize is awarded to an undergraduate woman in recognition of excellence in mathematics and is sponsored by the Association for Women in Mathematics The Schafer Prize was established in 1990 by the executive committee of the AWM and is named for former AWM president and one of its founding members, Alice T. Schafer, who has contributed a great deal to women in mathematics throughout her career. The criteria for selection includes, but is not limited to, the quality of the nominees' performance in mathematics courses and special programs, exhibition of real interest in mathematics, ability to do independent work, and if applicable, performance in mathematical competitions.

The winners of the Schafer Prize have been:

  • 1991 Linda Green (University of Chicago) and Elizabeth Wilmer (Harvard University)
  • 1992 Jeanne Nielsen (Duke University)
  • 1993 Zvezdelina E. Stankova (Bryn Mawr College)
  • 1994 Catherine O'Neil (University of California) and Dana Pascovici (Dartmouth College)
  • 1995 Jing Rebecca Li (University of Michigan)
  • 1996 Ruth Britto-Pacumio (Massachusetts Institute of Technology)
  • 1997 Ioana Dumitriu (New York University's Courant Institute of Mathematical Sciences)
  • 1998 Sharon Ann Lozano (University of Texas at Austin) and Jessica A. Shepherd (University of Utah)
  • 1999 Caroline J. Klivans (Cornell University)
  • 2000 Mariana E. Campbell (University of California, San Diego)
  • 2001 Jaclyn (Kohles) Anderson (University of Nebraska at Lincoln)
  • 2002 Kay Kickpatrick (Montana State University) and Melanie Wood (Duke University)
  • 2003 Kate Gruher (University of Chicago)
  • 2004 Kimberley Spears (University of California)
  • 2005 Melody Chan (Yale University)
  • 2006 Alexandra Ovetsky (Princeton University)
  • 2007 Ana Caraiani (Princeton University)

For more information about the Alice T. Schafer Prize for Excellence in Mathematics by an Undergraduate Woman, see Alice T. Schafer Prize at the Association for Women in Mathematics web site.

MAA Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service to Mathematics

The Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service to Mathematics is the most prestigious award made by the Mathematical Association of America. This award, first given in 1990, is the successor to the Award for Distinguished Service to Mathematics, awarded since 1962.

Women mathematicians who have won this award or the previous Distinguished Service Award are:

Sylvester Medal of the Royal Society of London

The Sylvester Medal has been awarded by the Royal Society of London every three years since 1901 for the encouragement of mathematical research without regard to nationality. It is given in honor of Professor J. J. Sylvester.

Women mathematicians who have won the Sylvester Medal are:

Complete list of winners of the Sylvester Medal

De Morgan Medal of the London Mathematical Society

The De Morgan Medal, the London Mathematical Society's premier award, is awarded every third year in memory of Professor A. De Morgan, the Society's first President. The only criteria for the award is the candidate's contributions to mathematics. The medal was first awarded in 1884.

Women mathematicians who have won the De Morgan Medal are:

Complete list of winners of the De Morgan Medal

Adams Prize

The Adams Prize, given annually by the University of Cambridge to a British mathematician under the age of 40, commemorates the discovery by John Couch Adams of the planet Neptune through calculation of the discrepancies in the orbit of Uranus. It was enowed by members of St John's College, Cambridge, and approved by the Senate of the University in 1848. Each year applications are invited from mathematicians who have worked in a specific area of mathematics.

Women mathematicians who have won the Adams Prize are:

  • 2002 Susan Howson, University of Nottingham (Number Theory)

CRM-Fields-PIMS Prize

The CRM-Fields-PIMS prize is intended to be the premier mathematics prize in Canada. The prize recognizes exceptional achievement in the mathematical sciences. The winner's research should have been conducted primarily in Canada or in affiliation with a Canadian university. The main selection criterion is outstanding contribution to the advancement of research. The prize was established by the Centre de recherches mathematiques and the Fields Institute as the CRM-Fields prize in 1994. In 2005, Pacific Institute for the Mathematical Sciences (PIMS) became an equal partner.

Women mathematicians who have won the CRM-Fields-PIMS prize are:

AWM Emmy Noether Lecturers

The Association for Women in Mathematics established the Emmy Noether Lectures to honor women who have made fundamental and sustained contributions to the mathematical sciences. These one-hour expository lectures are presented at the Joint Mathematics Meetings each January. The Emmy Noether Lecturers have been:

AWM web site about the Emmy Noether Lectures.

Emmy Noether Lecturers, International Congress of Mathematicians

The Emmy Noether Lectures at the International Congress of Mathematicians, held every four years, is jointly organized by European Women in Mathematics, the Committee on Women of the Canadian Mathematical Society, and the Association for Women in Mathematics.

AWM/MAA Falconer Lecturers

The Association for Women in Mathematics and the Mathematical Association of America annually present the Etta Z. Falconer Lectures to honor women who have made distinguished contributions to the mathematical sciences or mathematics education. These one-hour expository lectures are presented at Mathfest each summer. While the lectures began with Mathfest 1996, the title "Etta Z. Falconer Lecture" was established in 2004 in memory of Falconer's profound vision and accomplishments in enhancing the movement of minorities and women into scientific careers. The Falconer Lecturers have been:

  • 1996 Karen E. Smith, MIT, "Calculus mod p"
  • 1997 Suzanne M. Lenhart, University of Tennessee, "Applications of Optimal Control to Various Population Models"
  • 1998 Margaret H. Wright, Bell Labs, "The Interior-Point Revolution in Constrained Optimization"
  • 1999 Chuu-Lian Terng, Northeastern University, "Geometry and Visualization of Surfaces"
  • 2000 Audrey Terras, University of California at San Diego, "Finite Quantum Chaos"
  • 2001 Pat Shure, University of Michigan, "The Scholarship of Learning and Teaching: A Look Back and a Look Ahead"
  • 2002 Annie Selden, Tennessee Technological University, "Two Research Traditions Separated by a Common Subject: Mathematics and Mathematics Education"
  • 2003 Katherine P. Layton, Beverly Hills High School, "What I Learned in Forty Years in Beverly Hills 90212"
  • 2004 Bozenna Pasik-Duncan, University of Kansas "Mathematics Education of Tomorrow"
  • 2005 Fern Hunt, National Institute of Standards and Technology, "Techniques for Visualizing Frequency Patterns in DNA"
  • 2006 Trachette Jackson, University of Michigan, "Cancer Modeling: From the Classical to the Contemporary"
  • 2007 Katherine St. John, City University of New York, "Polygenetic Trees"

AWM web site about the Falconer Lectures.

AWM-SIAM Sonia Kovalevsky Lecturers

The Assocation for Women in Mathematics in cooperation with the Society for Industrial and Applied Mathematics (SIAM) sponsers the AWM-SIAM Sonia Kovalevksy Lecture Series. The lecture is given annually at the SIAM Annual Meeting by a woman who has made distinguished contributions in applied or computational mathematics. The lectureship may be awarded to any woman in the scientific or engineering community. The Kovalevsky Lecturers have been:

  • 2003 Linda R. Petzold, University of California, Santa Barbara, "Towards the Multiscale Simulation of Biochemical Networks"
  • 2004 Joyce R. McLaughlin, Rensselaer Polytechnic Institute, "Interior Elastodynamics Inverse Problems: Creating Shear Wave Speed Images of Tissue"
  • 2005 Ingrid Daubechies, Princeton University, "Superfast and (Super)sparse Algorithms"
  • 2006 Irene Fonseca, Carnegie-Mellon University, "New Challenges in the Calculus of Variations"
  • 2007 Lai-Sang Young, Courant Institute of Mathematical Sciences

AWM web site about the Sonia Kovalevsky Lecturers.

Krieger-Nelson Prize Lectureship for Distinguished Research by Women in Mathematics

The Canadian Mathematical Society inaugurated the The Krieger-Nelson Prize to recognize outstanding research by a female mathematician. The first prize was awarded in 1995. The winners have been:

As part of its celebrations of the World Mathematical Year in 2000, the Canadian Mathematical Society sponsored the creation of a poster on women in mathematics. The poster features the six outstanding women mathematicians who were awarded the Krieger-Nelson prize from 1995 to 2000.

American Mathematical Society Colloquium Lecturers

The American Mathematical Society Colloquium Lectures have been presented since 1896. Women mathematicians who have presented lectures are:

Complete list of the AMS Colloquium Lecturers.

Josiah Willard Gibbs Lecturers

To commemorate the name of Professor Gibbs, the American Mathematical Society established an honarary lectureship in 1923 to be known as the Josiah Willard Gibbs Lectureship. The lectures are of a semipopular nature and are given by invitation. They are usually devoted to mathematics or its applications. It is hoped that these lectures will enable the public and the academic community to become aware of the contribution that mathematics is making to present-day thinking and to modern civilization.

Women mathematicians who have presented the Josiah Willard Gibbs Lectures have been:

Earle Raymond Hedrick Lecturers

The Earle Raymond Hedrick Lectures were established by the Mathematical Association of America in 1952 to present to the Association a lecturer of known skill as an expositor of mathematics "who will present a series of at most three lectures accessible to a large fraction of those who teach college mathematics."

Women mathematicians who have presented the Earle Raymond Hedrick Lectures have been:

J. Sutherland Frame Lectures

The J. Sutherland Frame Lectures were established by Pi Mu Epsilon to honor James Sutherland Frame who was instrumental in founding the Pi Mul Epsilon Journal and in creating the Pi Mu Epsilon Summer Student Paper Conferences in conjunction with the American Mathematical Society and the Mathematical Association of America. The lectures are presented at the summer meeting of the Mathematical Association of America.

Women mathematicians who have presented the J. Sutherland Frame Lectures have been:

  • 1988 Doris Schattschneider, "You Too Can Tile the Conway Way"
  • 1989 Jame Cronin Scanlon, "Entrainment of Frequency
  • 1995 Marjorie Senechal, "Tilings as Differntial Games"
  • 2004 Joan P. Hutchinson, "When Five Colors Suffice"

Complete List of J. Sutherland Frame Lecturers.

Presidents of the Association for Women in Mathematics

The Association for Women in Mathematics was established in 1971 to encourage women to enter careers in mathematics and related areas, and to promote equal opportunity and equal treatment of women in the mathematical community. The Presidents of the AWM have been:

Presidents of the Mathematical Association of America

In December 1915, ten women and 96 men met at The Ohio State University to established the organization that became the Mathematical Association of America. Women who have served as President of the MAA have been

Presidents of the American Mathematical Society

The American Mathematical Society was founded in 1889. Since then, women who have served as President of the AMS have been

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Maria Gaetana Agnesi

Maria Agnesi

May 16, 1718 - January 9, 1799

Written by Elif Unlu, Class of 1995 (Agnes Scott College)

Even though her contribution to mathematics are very important, Maria Gaetana Agnesi was not a typical famous mathematician. She led a quite simple life and she gave up mathematics very early. At first glance her life may seem to be boring, however, considering the circumstances in which she was raised, her accomplishments to mathematics are glorious. Enjoy!

During the Middle Ages, under the influence of Christendom, many European countries were opposed to any form of higher education for females. Women were mostly deprived from the fundamental elements of education, such as reading and writing, claiming that these were a source of temptation and sin. For the most part, learning was confined to monasteries and nunneries which constituted the only opportunity for education open to girls during the Middle Ages. After the fall of Constantinople (today Istanbul), many scholars migrated to Rome, bringing Europe knowledge and critical thinking, which in turn gave rise to the Renaissance. However, except in Italy, the status of women throughout Europe changed very slowly.

In Italy, however, where the Renaissance had its origin, women made their mark on the academic world. Intellectual women were admired by men, they were never ridiculed for being intellectual and educated. This attitude enabled Italian women to participate in arts, medicine, literature, and mathematics. Among many others, Maria Gaetana Agnesi was by far the most important and extraordinary figure in mathematics during the 18th century.

"Maria Gaetana Agnesi was born in Milan on May 16, 1718, to a wealthy and literate family" [Osen, 39]. She was the oldest of 21 children. Her father was a professor of mathematics and provided her a profound education. "She was recognized as a child prodigy very early; spoke French by the age of five; and had mastered Latin, Greek, Hebrew, and several modern languages by the age of nine. At her teens, Maria mastered mathematics" [Osen, 40]. The Agnesi home was a gathering place of the most distinguished intellectuals of the day. Maria participated in most of the seminars, engaging with the guests in abstract philosophical and mathematical discussions. Maria was very shy in nature and did not like these meetings. She continued participating in the home gatherings to please her father until the death of her mother. Her mothers death provided her the excuse to retire from public life. She took over management of the household. Her father did not oppose this, because it was difficult and expensive to find a housekeeper to take care of 21 children and a lonely man. It is possible that this heavy duty job was one of the reasons why she never married.

However, she did not give up mathematics yet. In 1738 she published a collection of complex essays on natural science and philosophy called Propositiones Philosophicae, based on the discussions of the intellectuals who gathered at her father's home. In many of these essays, she expressed her conviction that women should be educated.

By the age of twenty, she began working on her most important work, Analytical Institutions, dealing with differential and integral calculus. "It is said that she started writing Analytical Institutions as a textbook for her brothers, which then grew into a more serious effort" [Osen, 41]. When her work was published in 1748, it caused a sensation in the academic world. It was one of the first and most complete works on finite and infinitesimal analysis. Maria's great contribution to mathematics with this book was that it brought the works of various mathematicians together in a very systematic way with her own interpretations. The book became a model of clarity, it was widely translated and used as a textbook.

Analytical Institutions gave a clear summary of the state of knowledge in mathematical analysis. The first section of Analytical Institutions deals with the analysis of finite quantities. It also deals with elementary problems of maxima, minima, tangents, and inflection points. The second section discusses the analysis of infinitely small quantities. The third section is about integral calculus and gives a general discussion of the state of the knowledge. The last section deals with the inverse method of tangents and differential equations.

Agnesi's original drawing Maria Gaetana Agnesi is best known from the curve called the "Witch of Agnesi" (see illustration from her text Analytical Institutions). Agnesi wrote the equation of this curve in the form y = a*sqrt(a*x-x*x)/x because she considered the x-axis to be the vertical axis and the y-axis to be the horizontal axis [Kennedy]. Reference frames today use x horizontal and y vertical, so the modern form of the curve is given by the Cartesian equation yx2=a2(a-y) or y = a3/(x2 + a2). It is a versed sine curve, originally studied by Fermat. "It was called a versiera, a word derived from the Latin vertere, meaning 'to turn', but it was also an abbreviation for the Italian word avversiera, meaning 'the wife of the devil'" [Osen, 45]. However, when Maria's text was translated into English the word versiera was confused with "witch", and the curve came to be known as the witch of Agnesi.

After the success of her book, Maria was elected to the Bologna Academy of Sciences. The university sent her a diploma and her name was added to the faculty. However, there is a debate over whether or not Maria accepted this appointment. The consensus is that she accepted the position and served at the university until the death of her father. It seems that her father was the inspiration for her interest in mathematics. When he died, Maria gave up any further work in mathematics. "When, in 1762, the University of Turin asked her for her opinion of the young Lagrange's recent articles on the calculus of variations, her response was that she was no longer concerned with such interests" [Osen, 47].

Maria was a very religious woman. She devoted the rest of her life to the poor and homeless sick people, especially women. When the Pio Instituto Trivulzo, a home for the ill and infirm, was opened, Maria was given an appointment as the director of the institute. She took care of ill and dying women until her own death.

It seems to me that even though she was a genius, mathematics was only a temporary hobby of hers. It may be that she was only dealing with mathematics to please her father who apparently was expecting his prodigy child to be involved in mathematics. Of course, this is only a personal observation. However, her behavior implies that she was not dedicated to mathematics which I think explains why she gave up mathematics altogether as soon as her father died. She was a very shy and decent person. She was not ambitious to become a well-known mathematician. Her most famous work, Analytical Institutions, was intended to be a textbook for her brothers. Her intelligence and talent made it possible to integrate all the state of the art knowledge about calculus in a very clear way. Religious life and helping the needy seem to have interested her more than mathematics.

April 1995

Notes by Larry Riddle

Maria Gaetana Agnesi's younger sister, Maria Teresa Agnesi, was a composer, harpsichordist, singer and librettist. She was born on October 17, 1720. While still a teenager, she would perform in her home while her older sister lectured and debated in Latin. Her first theatrical work, Il ristoro d'Arcadia, was successfully presented in Milan in 1747. She wrote seven operas of which three were based on her own librettos. The Empress Maria Theresia was known to sing from a collection of arias that Maria Teresa Agnesi had composed for her. In 1752 she married Pier Antonio Pinottini but had no children. She died on January 19, 1795. Her portrait hangs today in the theatre museum of La Scala.

Here are three of the keyboard pieces composed by Maria Teresa Agnesi. To listen to these pieces you will need to configure your browser to play midi files.

Sonata per il Clavicembalo (Allegro and Menuet)
Sonata in G Major
Allegro ou Presto in A Major

The Canadian composer Elma Miller has written a work called "The Witch of Agnesi" for B flat clarinet, bass clarinet, horn, 2 percussion, viola and double bass. The work was commissioned by the Alliance for Canadian New Music Projects and was first performed in late October 1989 in Toronto. Despite its premier performance so near Halloween, the inspiration for the piece was the curve of Maria Agnesi!

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International Year of Astronomy (IYA)
...and Kepler


 Kepler Portrait

(Picture courtesy of Sternwarte Kremsmünster, Upper-Austria)
A Short Biography

Johannes Kepler was born at 2:30 PM on December 27, 1571, in Weil der Stadt, Württemburg, in the Holy Roman Empire of German Nationality. He was a sickly child and his parents were poor. But his evident intelligence earned him a scholarship to the University of Tübingen to study for the Lutheran ministry. There he was introduced to the ideas of Copernicus and delighted in them. In 1596, while a mathematics teacher in Graz, he wrote the first outspoken defense of the Copernican system, the Mysterium Cosmographicum.

Kepler's family was Lutheran and he adhered to the Augsburg Confession a defining document for Lutheranism. However, he did not adhere to the Lutheran position on the real presence and refused to sign the Formula of Concord. Because of his refusal he was excluded from the sacrament in the Lutheran church. This and his refusal to convert to Catholicism left him alienated by both the Lutherans and the Catholics. Thus he had no refuge during the Thirty-Years War.

Map of Holy Roman Empire
The Holy Roman Empire of German Nationality at the Time of Kepler

Kepler was forced to leave his teaching post at Graz due to the counter Reformation because he was Lutheran and moved to Prague to work with the renowned Danish astronomer, Tycho Brahe. He inherited Tycho's post as Imperial Mathematician when Tycho died in 1601. Using the precise data that Tycho had collected, Kepler discovered that the orbit of Mars was an ellipse. In 1609 he published Astronomia Nova, delineating his discoveries, which are now called Kepler's first two laws of planetary motion. And what is just as important about this work, "it is the first published account wherein a scientist documents how he has coped with the multitude of imperfect data to forge a theory of surpassing accuracy" (O. Gingerich in forward to Johannes Kepler New Astronomy translated by W. Donahue, Cambridge Univ Press, 1992), a fundamental law of nature. Today we call this the scientific method.

In 1612 Lutherans were forced out of Prague, so Kepler moved on to Linz. His wife and two sons had recently died. He remarried happily, but had many personal and financial troubles. Two infant daughters died and Kepler had to return to Württemburg where he successfully defended his mother against charges of witchcraft. In 1619 he published Harmonices Mundi, in which he describes his "third law."

In spite of more forced relocations, Kepler published the seven-volume Epitome Astronomiae in 1621. This was his most influential work and discussed all of heliocentric astronomy in a systematic way. He then went on to complete the Rudolphine Tables that Tycho had started long ago. These included calculations using logarithms, which he developed, and provided perpetual tables for calculating planetary positions for any past or future date. Kepler used the tables to predict a pair of transits by Mercury and Venus of the Sun, although he did not live to witness the events.

Johannes Kepler died in Regensburg in 1630, while on a journey from his home in Sagan to collect a debt. His grave was demolished within two years because of the Thirty Years War. Frail of body, but robust in mind and spirit, Kepler was scrupulously honest to the data.

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Antony van Leeuwenhoek (1632-1723)

. . . my work, which I've done for a long time, was not pursued in order to gain the praise I now enjoy, but chiefly from a craving after knowledge, which I notice resides in me more than in most other men. And therewithal, whenever I found out anything remarkable, I have thought it my duty to put down my discovery on paper, so that all ingenious people might be informed thereof.

Antony van Leeuwenhoek. Letter of June 12, 1716

Antony van Leeuwenhoek was an unlikely scientist. A tradesman of Delft, Holland, he came from a family of tradesmen, had no fortune, received no higher education or university degrees, and knew no languages other than his native Dutch. This would have been enough to exclude him from the scientific community of his time completely. Yet with skill, diligence, an endless curiosity, and an open mind free of the scientific dogma of his day, Leeuwenhoek succeeded in making some of the most important discoveries in the history of biology. It was he who discovered bacteria, free-living and parasitic microscopic protists, sperm cells, blood cells, microscopic nematodes and rotifers, and much more. His researches, which were widely circulated, opened up an entire world of microscopic life to the awareness of scientists.

Leeuwenhoek was born in Delft on October 24, 1632. (His last name, incidentally, often is quite troublesome to non-Dutch speakers: "layu-wen-hook" is a passable English approximation.) His father was a basket-maker, while his mother's family were brewers. Antony was educated as a child in a school in the town of Warmond, then lived with his uncle at Benthuizen; in 1648 he was apprenticed in a linen-draper's shop. Around 1654 he returned to Delft, where he spent the rest of his life. He set himself up in business as a draper (a fabric merchant); he is also known to have worked as a surveyor, a wine assayer, and as a minor city official. In 1676 he served as the trustee of the estate of the deceased and bankrupt Jan Vermeer, the famous painter, who had had been born in the same year as Leeuwenhoek and is thought to have been a friend of his. And at some time before 1668, Antony van Leeuwenhoek learned to grind lenses, made simple microscopes, and began observing with them. He seems to have been inspired to take up microscopy by having seen a copy of Robert Hooke's illustrated book Micrographia, which depicted Hooke's own observations with the microscope and was very popular.

microscope Leeuwenhoek is known to have made over 500 "microscopes," of which fewer than ten have survived to the present day. In basic design, probably all of Leeuwenhoek's instruments -- certainly all the ones that are known -- were simply powerful magnifying glasses, not compound microscopes of the type used today. A drawing of one of Leeuwenhoek's "microscopes" is shown at the left. Compared to modern microscopes, it is an extremely simple device, using only one lens, mounted in a tiny hole in the brass plate that makes up the body of the instrument. The specimen was mounted on the sharp point that sticks up in front of the lens, and its position and focus could be adjusted by turning the two screws. The entire instrument was only 3-4 inches long, and had to be held up close to the eye; it required good lighting and great patience to use.

Compound microscopes (that is, microscopes using more than one lens) had been invented around 1595, nearly forty years before Leeuwenhoek was born. Several of Leeuwenhoek's predecessors and contemporaries, notably Robert Hooke in England and Jan Swammerdam in the Netherlands, had built compound microscopes and were making important discoveries with them. These were much more similar to the microscopes in use today. Thus, although Leeuwenhoek is sometimes called "the inventor of the microscope," he was no such thing.

However, because of various technical difficulties in building them, early compound microscopes were not practical for magnifying objects more than about twenty or thirty times natural size. Leeuwenhoek's skill at grinding lenses, together with his naturally acute eyesight and great care in adjusting the lighting where he worked, enabled him to build microscopes that magnified over 200 times, with clearer and brighter images than any of his colleagues could achieve. What further distinguished him was his curiosity to observe almost anything that could be placed under his lenses, and his care in describing what he saw. Although he himself could not draw well, he hired an illustrator to prepare drawings of the things he saw, to accompany his written descriptions. Most of his descriptions of microorganisms are instantly recognizable.

In 1673, Leeuwenhoek began writing letters to the newly-formed Royal Society of London, describing what he had seen with his microscopes -- his first letter contained some observations on the stings of bees. For the next fifty years he corresponded with the Royal Society; his letters, written in Dutch, were translated into English or Latin and printed in the Philosophical Transactions of the Royal Society, and often reprinted separately. To give some of the flavor of his discoveries, we present extracts from his observations, together with modern pictures of the organisms that Leeuwenhoek saw.

In a letter of September 7, 1674, Leeuwenhoek described observations on lake water, including an excellent description of the green charophyte alga Spirogyra: "Passing just lately over this lake, . . . and examining this water next day, I found floating therein divers earthy particles, and some green streaks, spirally wound serpent-wise, and orderly arranged, after the manner of the copper or tin worms, which distillers use to cool their liquors as they distil over. The whole circumference of each of these streaks was about the thickness of a hair of one's head. . . all consisted of very small green globules joined together: and there were very many small green globules as well."

A letter dated December 25, 1702, gives descriptions of many protists, including this ciliate, Vorticella: "In structure these little animals were fashioned like a bell, and at the round opening they made such a stir, that the particles in the water thereabout were set in motion thereby. . . And though I must have seen quite 20 of these little animals on their long tails alongside one another very gently moving, with outstretched bodies and straightened-out tails; yet in an instant, as it were, they pulled their bodies and their tails together, and no sooner had they contracted their bodies and tails, than they began to stick their tails out again very leisurely, and stayed thus some time continuing their gentle motion: which sight I found mightily diverting."

On September 17, 1683, Leeuwenhoek wrote to the Royal Society about his observations on the plaque between his own teeth, "a little white matter, which is as thick as if 'twere batter." He repeated these observations on two ladies (probably his own wife and daughter), and on two old men who had never cleaned their teeth in their lives. Looking at these samples with his microscope, Leeuwenhoek reported how in his own mouth: "I then most always saw, with great wonder, that in the said matter there were many very little living animalcules, very prettily a-moving. The biggest sort. . . had a very strong and swift motion, and shot through the water (or spittle) like a pike does through the water. The second sort. . . oft-times spun round like a top. . . and these were far more in number." In the mouth of one of the old men, Leeuwenhoek found "an unbelievably great company of living animalcules, a-swimming more nimbly than any I had ever seen up to this time. The biggest sort. . . bent their body into curves in going forwards. . . Moreover, the other animalcules were in such enormous numbers, that all the water. . . seemed to be alive." These were among the first observations on living bacteria ever recorded.

Leeuwenhoek looked at animal and plant tissues, at mineral crystals and at fossils. He was the first to see microscopic foraminifera, which he described as "little cockles. . . no bigger than a coarse sand-grain." He discovered blood cells, and was the first to see living sperm cells of animals. He discovered microscopic animals such as nematodes and rotifers. The list of his discoveries goes on and on. Leeuwenhoek soon became famous as his letters were published and translated. In 1680 he was elected a full member of the Royal Society, joining Robert Hooke, Henry Oldenburg, Robert Boyle, Christopher Wren, and other scientific luminaries of his day -- although he never attended a meeting. In 1698 he demonstrated circulation in the capillaries of an eel to Tsar Peter the Great of Russia, and he continued to receive visitors curious to see the strange things he was describing. He continued his observations until the last days of his life. After his death on August 30, 1723, the pastor of the New Church at Delft wrote to the Royal Society:

. . . Antony van Leeuwenhoek considered that what is true in natural philosophy can be most fruitfully investigated by the experimental method, supported by the evidence of the senses; for which reason, by diligence and tireless labour he made with his own hand certain most excellent lenses, with the aid of which he discovered many secrets of Nature, now famous throughout the whole philosophical World.
British scientist Brian J. Ford has rediscovered some of Leeuwenhoek's original specimens in the archives of the Royal Society of London. His study of these historic specimens and other material, using Leeuwenhoek's own microscopes and other single-lens microscopes, has shown how remarkably good a scientist and craftsman Leeuwenhoek really was. Here's the full story of Dr. Ford's research.

Berkeley, California resident Al Shinn manufactures replicas of Leeuwenhoek microscopes. He has also made plans and instructions available, for those who would like to make their own Leeuwenhoek-type microscopes.

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Lavoisier, Antoine (1743-1794)

French chemist who, through a conscious revolution, became the father of modern chemistry. As a student, he stated "I am young and avid for glory." He was educated in a radical tradition, a friend of Condillac and read Maquois's dictionary. He won a prize on lighting the streets of Paris, and designed a new method for preparing saltpeter. He also married a young, beautiful 13-year-old girl named Marie-Anne, who translated from English for him and illustrated his books. Lavoisier demonstrated with careful measurements that transmutation of water to earth was not possible, but that the sediment observed from boiling water came from the container. He burnt phosphorus and sulfur in air, and proved that the products weighed more than he original. Nevertheless, the weight gained was lost from the air. Thus he established the Law of Conservation of Mass.

Repeating the experiments of Priestley, he demonstrated that air is composed of two parts, one of which combines with metals to form calxes. However, he tried to take credit for Priestley's discovery. This tendency to use the results of others without acknowledgment then draw conclusions was characteristic of Lavoisier. In Considérations Générales sur la Nature des Acides (1778), he demonstrated that the "air" responsible for combustion was also the source of acidity. The next year, he named this portion oxygen (Greek for acid-former), and the other azote (Greek for no life). He also discovered that the inflammable air of Cavendish which he termed hydrogen (Greek for water-former), combined with oxygen to produce a dew, as Priestley had reported, which appeared to be water.

In Reflexions sur le Phlogistique (1783), Lavoisier showed the phlogiston theory to be inconsistent. In Methods of Chemical Nomenclature (1787), he invented the system of chemical nomenclature still largely in use today, including names such as sulfuric acid, sulfates, and sulfites. His Traité Élémentaire de Chimie (Elementary Treatise of Chemistry, 1789) was the first modern chemical textbook, and presented a unified view of new theories of chemistry, contained a clear statement of the Law of Conservation of Mass, and denied the existence of phlogiston. In addition, it contained a list of elements, or substances that could not be broken down further, which included oxygen, nitrogen, hydrogen, phosphorus, mercury, zinc, and sulfur. His list, however, also included light, Eric Weisstein's World of Physics and caloric, Eric Weisstein's World of Physics which he believed to be material substances. In the work, Lavoisier underscored the observational basis of his chemistry, stating "I have tried...to arrive at the truth by linking up facts; to suppress as much as possible the use of reasoning, which is often an unreliable instrument which deceives us, in order to follow as much as possible the torch of observation and of experiment." Nevertheless, he believed that the real existence of atoms was philosophically impossible. Lavoisier demonstrated that organisms disassemble and reconstitute atmospheric air in the same manner as a burning body.

With Laplace, he used a calorimeter to estimate the heat evolved per unit of carbon dioxide produced. They found the same ratio for a flame and animals, indicating that animals produced energy by a type of combustion. Lavoisier believed in the radical theory, believing that radicals, which function as a single group in a chemical reaction, would combine with oxygen in reactions. He believed all acids contained oxygen. He also discovered that diamond is a crystalline form of carbon. Lavoisier made many fundamental contributions to the science of chemistry. The revolution in chemistry which he brought about was a result of a conscious effort to fit all experiments into the framework of a single theory. He established the consistent use of chemical balance, used oxygen to overthrow the phlogiston theory, and developed a new system of chemical nomenclature. He was beheaded during the French revolution.

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Anders Celsius
Anders Celsius
1701-1744
Anders Celsius, born in Uppsala, was one of a large number of scientists (all related) originating from Ovanåker in the province of Hälsingland. The family name is a latinised version of the name of the vicarage (Högen). His grandfathers were both professors in Uppsala: Magnus Celsius the mathematician and Anders Spole the astronomer. His father, Nils Celsius, was also professor in astronomy. Celsius, who was said to have been very talented in mathematics from an early age, was appointed professor of astronomy in 1730.

He began his "grand tour", lasting for four years, in 1732, and he visited during these years almost all the notable european observatories of the day, where he worked with many of the leading 18th century astronomers.

Soon after his return to Uppsala he participated in the French astronomer Maupertuis' famous expedition 1736 to Torneå, in the most northern part of Sweden. ("The Lapland expedition.") The aim of the expedition was to measure the length of a degree along a meridian, close to the pole, and compare the result with a similar expedition to Peru (today Ecuador) near the equator. The expeditons confirmed Newton's belief that the shape of the earth is an ellipsoid flattened at the poles.

Celsius' participation in this expedition made him famous and was important in his efforts to interest the Swedish authorities in donating the resources necessary to build a modern observatory in Uppsala. He was successful, and the Celsius observatory was ready in 1741, equipped with instruments purchased during his long voyage abroad, comprising the most modern instrumental technology at that time.

In those days geographical measurements, metereological observations and other things, not considered as astronomy today, were included in the work of an astronomy professor. He carried out many geographical measurements for the Swedish General map, and was also one of the first to note that the land of the nordic countries is slowly rising above sea level, a process which has been going on since the melting of the ice from the latest ice age. He believed though, that it was the water that was evaporating.

For his metereological observations he constructed his world famous Celsius thermometer, with 0 for the boiling point of water and 100 for the freezing point. After his death in 1744 the scale was reversed to its present form.

Together with his assistant Olof Hjorter he also was the first to realize that the aurora phenomenon has magnetic causes through observing the inclination of a compass-needle and finding that the larger deviations correlated with stronger aurora activity.

In astronomy he made observations of eclipses and various astronomical objects. He published catalogues of carefully determined magnitudes for a total of 300 stars using his own photometric system (mean error=0.4 mag). The idea of his system consists of using identical transparent glass plates and viewing the ray of light from a star through them. He could then compare the magnitudes of the stars by the number of glass plates needed to extinguishe the light. (The star Sirius, the brightest star in the sky, needed 25 of his plates to be extinguished.)

Celsius published most of his work in the publications of the Royal Society of Sciences in Uppsala, which is the oldest Swedish scientific society founded in 1710, where Celsius was the secretary 1725-1744, and in the publications of the Royal Swedish Academy of Sciences, founded in 1739. He also presided at about twenty dissertations in astronomy where, as was the general rule in those days, he was the main author. His popular book Arithmetics for the Swedish Youth was typical of the spirit of his period, the Enlightenment.
Celsius was a very active supporter for introducing the Gregorian calender in Sweden but he wasn't successful until 1753, almost ten years after his death, when the Julian calender was abandoned by dropping 11 days.

Anders Celsius died of tuberculosis in april 1744, only 42 years old. His grave is next to his grandfather's, Magnus Celsius, in the church at Gamla Uppsala, about 5 km north of central Uppsala.

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