ESP Biography
MICHAEL TONG, ESP Teacher
Major: Computer Science, Mathematics College/Employer: Columbia University Year of Graduation: 2018 

Brief Biographical Sketch:
Not Available. Past Classes(Clicking a class title will bring you to the course's section of the corresponding course catalog)M666: Congruent Numbers and Elliptic Curves in Splash Spring 18 (Mar. 31, 2018)
In an anonymous Arab manuscript from the year 927, the following question is posed: given a squarefree integer $$n$$, does there exist a rational number $$a$$ such that $$an, a, a+n$$ are all squares of rational numbers? The examples 5 and 6 were known to the Arabs, and later Fibonacci discovered that 7 was a congruent number. In the other direction, Fermat proved that 1 was not congruent  this is equivalent to his famous Last Theorem in the special case that the exponent is 4. However, to this day, there is no algorithm for this problem in general.
Many advances on this problem were made using the theory of elliptic curves and, under the assumption that the Birch and SwinnertonDyer conjecture is true (a current Millenium Prize Problem), there is a fast algorithm to determine whether a given integer is congruent.
This class will first attack the congruent number problem using elementary methods, and then discuss how elliptic curves come in.
