Each day we note a mathematician whose contributions bear on the subject matter
of the day's material. Below is a listing of previous winners of the coveted
*Mathematician of the Day* award.

**DATE****8/27:***Rene Descartes (1596-1650).*- Introduced current notation for symbolically describing the connections between equations and graphs.
**8/29:***Pythagoras (ca.580 BC-ca.520 BC) and Euclid (ca.365 BC-ca.300 BC).*-
Pythagoras is considered the first ``real" mathematician. He and his followers
proved many of the fundamental results of geometry. Euclid is best known for his
treatise on geometry,
*The Elements*. Here, he assimilated for the first time the known results of geometry from antiquity. **9/3:***John Napier (1550-1617).*- Scottish part-time mathematician who developed logarithms.
**9/5:***Leonhard Euler (1707-1783).*- The first to use the concept of
``function" consistently in analysis, and the first to formulate the ideas of
calculus in terms of functions. Euler also introduced much of the notation that
we use today, including the Greek letter
*pi*for the ratio of the circumference to the diameter of a circle,*i*for the imaginary unit, and*e*for the base of the natural logarithm. **9/10:***Charles Babbage (1792-1871).*- Invented the principle of the analytical engine, the forerunner of the modern digital computer.
**9/12:***Johann Bernoulli (1667-1748).*- Bernoulli was the mathematician behind the first calculus textbook, ``Analyse des infiniment petits" (``Analysis of the Infinitely Small"), by l'Hopital.
**9/19:***Pierre de Fermat (1601-1665).*- French lawyer and city councilman who studied mathematics as a hobby. Fermat proposed the idea of attaching tangent lines to graphs, and approximating the slope of a tangent line via secant lines, although his approach was not given in terms of limits, as we use now. Fermat also used tangent lines to determine local maximum and minimum values of graphs; his method was essentially the same that we use today.
**9/24:***Sir Isaac Newton (1642-1727).*- Co-developer of calculus.
**9/26:***Augustin Louis Cauchy (1789-1857).*- First mathematician to make consistent use of limits to describe the ideas of calculus.
**10/1:***Joseph Louis Lagrange (1736-1813).*- First stated and proved the Mean Value Theorem.
**10/3:***Gottfried Wilhelm von Leibniz (1646-1716).*- Co-developer of calculus. During a visit to France, Leibniz became aquainted with the work of Descartes, Fermat, and others. He developed these ideas, independently of Newton, into calculus. Leibniz thought of calculus in terms of analysis, whereas Newton subscribed to a more geometrical perspective. For example, Leibniz described the definite integral in terms of sums, while Newton interpreted the definite integral as the area of a plane region. Leibniz is also responsible for introducing much of the modern calculus notation.
**10/8:***Georg Friedrich Bernhard Riemann (1826-1866).*- Clarified the
notion of a definite integral by defining it precisely as a limit of sums,
which have come to be called
*Riemann sums.* **10/10:***Archimedes (287 BC-212 BC) and Hippocrates (ca. 470 BC-ca. 410 BC).*- Archimedes is considered by many to be the greatest mathematician of ancient times. Both he and Hippocrates worked (independently, of course, since they lived about 200 years apart!) on the problem of determining the areas of nonstandard geometric regions by relating them to geometric shapes, such as triangles or rectangles, of known area.
**10/17:***Sir Isaac Barrow (1630-1677).*- Newton's teacher at Cambridge, Barrow was the first to recognize differentiation and integration as inverse operations. It was on Barrow's ideas that Newton (and probably Leibniz also) based the Fundamental Theorem of Calculus.
**10/22:***Nicole Oresme (1323-1382).*- Had some notion of functional relationship between quantities (e.g. velocity as a function of time), and proposed graphing such relationships. (This was done more than 200 years before Descartes was even born!) Oresme described a conceptual process of integration, or ``continuous summation,'' to calculate distance traveled as area under the velocity-time graph.
**10/29:***Johann Hudde (1628-1704).*- Discovered Hudde's Rule, which essentially gives formula for the derivative of a polynomial. Hudde did this algebraically, with no notion of limits or infinitely small quantities.
**10/31:***Bhaskara (1114-1185).*- Hindu mathematician and astronomer, who was interested in the concept of instantaneous motion of planets. In the course of his studies, he discovered what came to be known as the formula for the derivative of the sine function.
**11/5:***Al'Khwarizmi (ca. 790-ca. 850) and Omar Khayyam (1048-1122).*- Two
prominent mathematicians of the medieval and pre-medieval period in the
Middle East. During this time, the geometric ideas of the ancient Greek
mathematicians were preserved and blended with the more algebraic ideas of
the mathematicians of ancient India. It is from Al'Khwarizmi's name that
the term
*algorithm*was derived, and the title of one of his books includes the word*al-jabr,*from which the term*algebra*arose. Khayyam was a poet as well as a scientist, and authored the well-known book of four-line poems known as the*Rubaiyat*. **11/7:***Karl Weierstrass (1815-1897).*- Among many other achievements, proved that a continuous function on a closed and bounded interval always has maximum and minimum values.
**11/12:***Francois Viete (1540-1603).*- Introduced the first systematic algebraic notation, and was a major influence on Descartes. Viete used vowels to represent variables and consonants to represent constants. The current practice of using letters at the end of the alphabet for variables and letters at the beginning of the alphabet for constants was introduced by Descartes. Also, Viete was one of the first to recognize the formula for an antiderivative of x^n.
**11/14:***Alan Turing (1912-1954).***11/19:***George Berkeley (1685-1753).*- An Irish theologian who criticized the logical foundation of Newton's calculus. This motivated a number of mathematicians (including some former "Mathematicians of the Day") to attempt to develop the concepts of calculus in a more rigorous way.
**11/26:***Carl Friedrich Gauss (1777-1855).*- Generally considered the greatest mathematical genius who ever lived.
**12/3:***Bonaventura Cavalieri (1598-1647).*- Developed a method of "indivisibles", which was a way of calculating the area of geometric figures using lots of tiny simple geometric shapes. This was a major influence on Leibniz and the development of integral calculus.
**12/5:***Charles Lutwidge Dodgson (1832-1898).*- Wrote some mathematics books, including "Euclid and His Modern Rivals."
Best known, however, for books written under his pseudonym, "Lewis Carroll".