Imaginary Numbers Mathematicians

Luca Pacioli

Leonardo da Vinci's math teacher, publisher of "Summa de Arithmetica",

Omar Khayyam

11th century Persian mathematician , identified 19 different solutions for the cubic - kept all coefficients positive, fell short of his goal - a general solution to the cubic, "Maybe one of those who will come after us will succeed in finding it"

Scipione Del Ferro

Mathematics professor at the University of Bologna, found a method to reliably solve the depressed cubic, hid the solution until his death in 1526

Antonio Fior

Student of Scipione , not a talented mathematician, young and ambitious, boasts about his ability to solve the cubic, challenges mathematician Niccolo Fontana Tartaglia, gave 30 depressed cubic equations to Tartaglia, received 30 equations from Tartaglia and could not solve 1, lost the duel.

Niccolo Fontana Tartaglia

Known as Tartaglia because of his stutter, self taught, gave 30 math equations to Fior, received 30 depressed cubic equations to solve and answered all 30 correctly in 2 hours, won the duel, "I did not deem him capable of finding such a rule on his own", created an algorithm to solve the depressed cubic- a math poem, said "Pitiful. A man of no substance. A very stupid man. An ignoramus in Mathematical matters."

Gerolamo Cardano

A polymath based in Milan, swore a solemn oath to not reveal Tartaglia's method of solving the depressed cubic, discovered a solution to the full cubic equation, did not care to keep the solution a secret - was a physician and famous intellectual - the credit was more valuable, found Ferro's original solution and therefore was able to publish his findings despite the oath, published "Ars Magna" - "written in five years, may it last for five hundred", acknowledges contributions made by Tartaglia, del Ferro, and Fior, says the idea of negatives is "As subtle as it is useless."

Rafael Bombelli

picked up where Cardano left off, said the square root of a negative "cannot be called either positive or negative", figured out that Cardano's method did work but you have to abandon geometric proof - negatives which make no sense in reality they are an intermediate step to the solution,

Francois Viete

introduces the modern symbolic notation for algebra

Rene Descartes

makes heavy use of the square roots of negatives - calls them imaginary numbers

Leonhard Euler

introduces the letter i to represent the square root of negative 1

Erwin Schrodinger

creator of one of the most important and famous equations in physics, "What is unpleasant here, and indeed directly to be objected to, is the use of complex numbers. ( The wave function) is surely fundamentally a real function."

Freeman Dyson

Physicist, "Schrodinger put the square root of mines into the equation, and suddenly it made sense. Suddenly it became a wave equation instead of a heat conduction equation. And Schrodinger found to his delight that the equation has solutions corresponding to the quantized orbits in the Bohr model of the atom. It turns out that Schrodinger equation describes correctly everything we know about the behavior of atoms. It is the basis of all chemistry and most of physics. And that square root of minus one means that nature works with complex numbers and not with real numbers. That discovery came as a complete surprise to Schrodinger as well as to everybody else."