# Departmental Seminar : Let there be numbers

**Event location:** 070250

**Event date and time:** 23/04/2019 13:00:00

Departmental Seminar titled "Let there be numbers" presented by Stefan Veldsman on the 23rd of April at 13:00 in 070250.

Abstract: The Prussian mathematician Leopold Kronecker (1823 - 1891) said:

"Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk”

(God made the integers, all the rest is the work of man).

How true is this as we guide first year students through the number systems. We take the natural numbers (counting numbers) as a given. Then we give the integers which is a necessity when we want to solve equations like x + 4 = 2. Following this, using suitable equations, we can justify the need for and existence of the rationals, irrationals and hence the real numbers. And then suddenly we are confronted with finding a solution to an equation like x2 + 1 = 0. What to do now? No problem, we just tell them: “let i be a number [sic] for which i2 = -1”. Then we have a solution and the problem is solved! From here we develop the complex number system as numbers of the form a + bi and we give the rules for doing arithmetic with such numbers. This is not natural; in fact very artificial. There is a better way. If you want to know how and you know what a 2 X 2 matrix is, come and listen to this talk.