Milestones in Mathematics: 1803 - 2003

David E. Kullman
Miami University

1803 Ohio becomes the 17th state on March 1, the first state in the Northwest Territory.
Jared Mansfield, a graduate of Yale, begins his work as United States Surveyor General. He establishes a principal meridian, that will become the boundary between Ohio and Indiana, at the mouth of the Great Miami River and begins to lay out a grid of north-south and east-west range lines. After the War of 1812 he will become professor of natural philosophy at West Point. The city of Mansfield, Ohio, is named for him.

1804 Ohio University, founded by Manasseh Cutler and Rufus Putnam, is chartered as the first public institution of higher education in the Northwest Territory. It will be 15 years before college classes are held, with James Irvine as the first professor of mathematics.
1809 Carl Friedrich Gauss publishes a memoir on the method of least squares.
Miami University is chartered. It will be 15 years before college classes are held, with John Annan as the first professor of mathematics.
1816 Sophie Germain receives the grand prize from the French Academie des Sciences for her solution to a problem on vibrations of elastic surfaces.
1821 In his Cours d'Analyse, Augustin-Louis Cauchy defines the notions of limit and continuity in terms of an arbitrary "epsilon."
1829 Nicolai Lobachevsky publishes the first account of non-Euclidean geometry.
1832 Evariste Galois is killed in a duel on May 30.
Ohio's first normal school, the Marietta Collegiate Institute and Western Teachers' Seminary, is chartered. D. H. Allen (professor of mathematics) and Milo P. Jewett (professor in the teachers' department) are both graduates of Dartmouth College. Three years later a new charter will change the name to Marietta College.
The Western Literary Institute and College of Professional Teachers is founded at Cincinnati on October 6. Its first president, Thomas J. Matthews, will later become professor of mathematics and astronomy at Miami University.
1833 Oberlin College, the first coeducational institution of higher education, is founded.
1834 Ray's Eclectic Arithmetic, the first in a long line of popular elementary mathematics textbooks by Joseph Ray, is published in Cincinnati by Truman & Smith.
1836 Elias Loomis is chosen as the first professor of mathematics and natural philosophy by the trustees of Western Reserve College, at Hudson, Ohio. Later, he will write a very popular series of college mathematics textbooks.
1837 Ohio establishes the office of State Superintendent of Schools.
1842 Ohio Wesleyan University is chartered. Many 19th century Ohio mathematicians will receive their undergraduate education here.
1843 William Rowan Hamilton carves his famous equation for quaternions on the Brougham Bridge in Dublin on October 16.
President John Quincy Adams delivers an oration for the laying of the cornerstone of the Cincinnati Observatory, established under the leadership of Ormsby Mitchell. Mt. Adams is named after this event.
A classical course of study in Ohio colleges includes these mathematical subjects: plane and solid geometry; plane and spherical trigonometry; analytic geometry, surveying and navigation; differential and integral calculus; astronomy; and mechanics.
1847 The Ohio State Teachers' Association is organized in Akron.
1853 Georg Friedrich Bernhard Riemann defines what today is known as a Riemann integral.
Robert White McFarland is appointed professor of mathematics at Madison College in Guernsey County. He will later distinguish himself as professor of mathematics and astronomy at Miami University. As a Union officer in the Civil War, he will be instrumental in driving the Confederates out of Cumberland Gap.
1854 Joseph Ray establishes a "Mathematical Department" in The Ohio Journal of Education, devoted to the solution and discussion of mathematical problems. Many prominent Ohio mathematics teachers will contribute problems and solutions over the next six years.
1861 Karl Weierstrass discovers an example of a continuous, nowhere differentiable function.
1862 President Lincoln signs the Morrill Land Grant Act, establishing colleges of engineering, agriculture, and military science.
Aaron Schuyler, author of Ray's Surveying and Navigation, is elected to the chair of mathematics at Baldwin University (now Baldwin-Wallace College). There he will write his own series of college mathematics textbooks. He will later become Baldwin's president and, eventually, president of Kansas Wesleyan University.
Schuyler's "able assistant," Ellen Warner is one of the first females to hold the title of "Professor of Mathematics."
1863 Edward Olney, from Wood County, Ohio, is named professor of mathematics at the University of Michigan. There he will write a successful series of mathematics textbooks.
1864 A state board of examiners is established in Ohio for the purpose of certifying teachers.
1869 Eli Todd Tappan becomes president of Kenyon College. This son of Benjamin Tappan, a U.S. Senator and federal judge, was previously a professor of mathematics at Ohio University and author of Ray's Geometry.
1872 Felix Klein publishes his Erlanger Programm, showing how geometries can be classified according to the properties of figures remaining invariant under a group of transformations.
Richard Dedekind defines real numbers in terms of "cuts."
Enoch Beery Seitz, of Lancaster, Ohio, accepts a position as mathematics teacher at Greenville High School. Over the next 11 years he will solve more than 500 mathematical problems in six different periodicals.
1873 The Ohio Agricultural and Mechanical College opens its doors, with Robert White McFarland as professor of mathematics. The institution will soon change its name to The Ohio State University. McFarland will become president of Miami University in 1885.
1874 Georg Cantor publishes a paper showing that the set of real numbers is uncountable.
Sonia Kovalevsky becomes the first woman to earn a doctorate in mathematics.
1875 Ormond Stone assumes the directorship of the Cincinnati Observatory.
E. W. Hyde, a civil engineer from Cornell, is appointed professor of mathematics at the University of Cincinnati. He will later serve as president of the university, but will be forced to resign from the faculty during an "academic bloodbath" in 1900.
1876 J. J. Sylvester becomes the first professor of mathematics at Johns Hopkins University.
1883 William Hoover (not the Hoover of vacuum cleaner fame) is appointed professor of mathematics at Ohio University. He will become a prolific contributor to the problems section of The American Mathematical Monthly for more than 40 years.
1887 R. D. Bohannan is appointed professor of mathematics and astronomy at The Ohio State University. He will serve on the OSU faculty for 40 years, becoming department head and a founding member of the MAA.
1888 The New York Mathematical Society is founded. In 1894 its name will be changed to the American Mathematical Society.
1892 The University of Chicago opens, with E.H. Moore as acting head of the mathematics department. Moore was born in Marietta, Ohio, in 1862, and graduated from Woodward High School in Cincinnati.
1893 An international Congress of Mathematicians is held at the World's Columbian Exposition in Chicago, August 21-26. Felix Klein and E.H. Moore occupy enter stage.
The Committee of Ten on Secondary School Studies recommends a year of algebra, followed by two years of plane and solid geometry to be taught side by side with more algebra. The first year's course in algebra is recommended for all students.
1894 Benjamin Finkel , a native of Fairfield County, Ohio, and graduate of the North West Ohio Normal School, begins publishing The American Mathematical Monthly. This will later become the official journal of the MAA. The college at Ada will later be named Ohio Northern University, following Finkel's suggestion.
1900 David Hilbert poses a set of 23 problems, encompassing nearly all the branches of mathematics, to the International congress of Mathematicians, meeting in Paris. Some of these will occupy mathematicians for most of the 20th century.
Harris Hancock leaves the University of Chicago to become a professor of mathematics at the University of Cincinnati. In 1920 he will be influential in the founding of Walnut Hills High School that was, and still is a public, college-prepatory high school in Cincinnati.
1902 Samuel Rasor begins a teaching career at The Ohio State University that will last for nearly 50 years. He will chair the local organizing committee for the founding of MAA.
AMS retiring president, E. H. Moore, in an address "On the Foundations of Mathematics," calls for an inquiry approach to teaching and learning.
1904 Cassius Jackson Keyser is appointed Adrain Professor of Mathematics at Columbia University. This native of Ohio and graduate of the North West Ohio Normal School (now Ohio Northern) will become renowned in the area of mathematical philosophy.
1905 Albert Einstein publishes a paper on the special theory of relativity.
1906 Grace Chisholm Young and her husband, William Henry Young, publish The Theory of Sets of Points, the first systematic exposition of point set topology.
1909 Grace Bareis, a native of Canal Winchester with an A. B. from Heidelberg College, is the first person to receive a Ph.D. in mathematics from The Ohio State University.
1910 State normal schools are established at Bowling Green and Kent.
1915 The Mathematical Association of America is founded on The Ohio State University campus in Columbus, on December 30-31. The Ohio Section becomes the first section of the MAA and will receive its charter on March 1, 1916.
1920 The National Council of Teachers of Mathematics holds its organizational meeting in Cleveland on February 24. Charles M. Austin, who was born near Waynesville, Ohio, graduated from Ohio Wesleyan, and taught at Milford High School before moving to Oak Park, Illinois, is elected as its first president.
1921 Emmy Noether publishes a seminal paper on the theory of rings and ideals.
The state of Ohio eliminates mathematics as a compulsory subject in its high schools.
The use of slide rules is permitted on the New York State Regents' Examinations in trigonometry and intermediate algebra.
1923 The National Committee on Mathematical Requirements, chaired by Ohio native, J. W. Young, issues its report, The Reorganization of Mathematics in Secondary Education, recommending "functions" as a central concept in the high school math curriculum.
1927 Elisha Scott Loomis publishes a collection of more than 370 proofs of The Pythagorean Proposition. In 1968 it will be re-published by NCTM as a "classic in math education."
1929 Marie Gugle, of Columbus, Ohio, becomes the first female president of NCTM.
1930 Tibor Radó, a native of Hungary, is appointed professor at The Ohio State University to help establish a graduate program in mathematics. That same year he solves Plateau's problem to determine a minimal surface with specified boundary constraints.
1931 Kurt Gödel proves the incompleteness theorem. Within any sufficiently rich mathematical system there are always propositions that cannot be proved either true or false using only the axioms of that system.
1936 Otto Szász, a native of Hungary and an important figure in the field of classical analysis, joins the faculty at the University of Cincinnati after fleeing from the Nazis.
1938 H. C. Christofferson, Miami University, becomes the 10th President of NCTM.
1945 Grace Murray Hopper logs the first computer "bug" at 1545 hours on September 9.
Eugene Lukacs, a native of Hungary, joins the faculty at Our Lady of Cincinnati College (now merged into Xavier University). In the 1970's this expert in probability theory will join the faculty at Bowling Green State University.
1946 Marshall Hall joins the mathematics faculty at The Ohio State University. During his lifetime he will publish more than 120 research papers on group theory and related topics.
Henry Mann receives the Cole Prize in number theory from the American Mathematical Society. That same year he becomes an assistant professor at The Ohio State University.
1950 Twelve mathematics teachers, including Harold P. Fawcett and H. C. Christofferson, meet at the Faculty Club of The Ohio State University on November 4th to organize the Ohio Council of Teachers of Mathematics (OCTM).
1951 The first OCTM annual meeting is held on the OSU campus in Columbus on April 21. Ona Kraft, of Collinwood High School in Cleveland, is elected as the first president.
The University of Illinois Committee on School Mathematics (UICSM) is formed, marking the beginning of the "New Math" reform movement.
1958 NCTM president Harold Fawcett, MAA president G. Baley Price, and AMS president Richard Brauer appoint a committee to establish the School Mathematics Study Group.
1963 Arnold E. Ross leaves Notre Dame to become chair of the mathematics department at Ohio State. He will direct the Ross Summer Program in mathematics until 2000.
Paul J. Cohen proves that the continuum hypothesis is independent of the other standard axioms of set theory. (Kurt G̉del had proved its consistency in 1939.)
1964 Hans Zassenhaus joins the faculty of The Ohio State University. During the next 30 years he will publish nearly 150 research papers on group theory and algebra.
IBM introduces its System/360 computers, based on "solid logic technology."
1970 The first hand-held calculator, the Pocketronic, is introduced by Cannon Instruments in Japan. It was designed by Texas Instruments, whose DataMath calculator (costing $150) will appear two years later, followed by the SR-10 Slide Rule calculator in 1973.
Harold Fawcett and Kenneth B. Cummins publish The Teaching of Mathematics from Counting to Calculus.
1972 Eugene Smith, the first doctoral student of Harold Fawcett, becomes the 27th President of NCTM.
1973 The Ohio Mathematics Association of Two Year colleges (OhioMATYC) is founded in Columbus on April 28.
1976 Kenneth Appel and Wolfgang Haken publish a computer-assisted proof the Four-Color Theorem
1977 The first personal computers (Apple I, Radio Shack TRS-80, Commodore PET) appear.
Benoit Mandelbrot publishes Fractals: Form, Chance and Dimension.
1983 Paul Erdös wins the Wolfe Prize of $50,000. During his lifetime he is the author or co-author of 1,475 mathematical papers.
1984 Joe Crosswhite, Ohio State University, becomes the 33rd President of NCTM.
1989 NCTM Publishes Curriculum and Evaluation Standards for School Mathematics, and OCTM establishes a task force to implement those standards in Ohio.
1990 The TI-81 graphing calculator is introduced designed with the help of two Ohio State faculty, Frank Demana and Bert Waits. In 2003 NCTM will establish the TI-Demana-Waits Scholarship for undergraduates who are members of NCTM.
1993 James R.C. Leitzel, of The Ohio State University, initiates MAA Project NExT, designed to nurture young college mathematics faculty and prepare them for the profession.
1994 Andrew Wiles completes his corrected proof of Fermat's Last Theorem.
John Nash is awarded the Nobel Prize in economics for his work on non-cooperative game theory. A movie about his life will be titled, A Beautiful Mind.
2000 NCTM publishes Principles and Standards for School Mathematics (PSSM).
Dirk Struik, internationally known historian of mathematics, dies at age 106.
2003 Benoit B. Mandelbrot and James A. Yorke share the Japan Prize (50 million yen) for their work on fractals and chaos.
The first Abel prize (6 million Norwegian kroner) is awarded by the Norwegian Academy of Science and Letters to Jean-Pierre Serre "for playing a key role in shaping the modern form of many parts of mathematics.

The author thanks the students in his spring 2003 Great Theorems of Mathematics class for their assistance in identifying events to be included among these "milestones" in mathematics.


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