Somewhere around 250 AD, there lived a Greek mathematician named Diophantus. His most well-known contributions to mathematics comes from his 13 volume work Arithmetica in which he wrote and solved 189 problem and solved with with symbolic algebra.
There is not much known about his personal life but there is a fun with math problem written about him [1]. It goes as follows
‘Here lies Diophantus,’ the wonder behold. Through art algebraic, the stone tells how old: ‘God gave him his boyhood one-sixth of his life, One twelfth more as youth while whiskers grew rife; And then yet one-seventh ere marriage begun; In five years there came a bouncing new son. Alas, the dear child of master and sage After attaining half the measure of his father’s life chill fate took him. After consoling his fate by the science of numbers for four years, he ended his life.’
I study Diophantine equations, polynomial equations in one or more variable with integer coefficients. An example of such an equation is
3^x + 4^y = 5^z.
The goal in solving Diophantine equations is to determine if there are solutions in integers and if there are any, find all such solutions. The exponential Diophantine equation above was shown to have only the solution (x,y,z) = (2,2,2) by Sierpiński [2].
The families of Diophantine equations that I have worked can be found in my Research Statement.
References:
[1] Pappas, T. “Diophantus’ Riddle.” The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, pp. 123 and 232, 1989.
[2] W. Sierpiński, “On the equation $3^x + 4^y = 5^z$”, (Polish) Wiadom. Mat. (2), 1 (1955/1956), 194-195.