Karl Theodor Wilhelm Weierstrass was born in Germany, from a liberal Catholic family. Weierstrass did not like music but did very well in his studies. Encouraged by his father, he went to Bonn University to study law. Then he became adept at drinking and fencing instead of law and mathematics, leaving without graduating.
In Münster, he prepared for secondary education, where he was protected by Gudermann, who initiated Weierstrass into function theory, following in the footsteps of Abel.
He obtained his diploma as a teacher at age 26, teaching at various high schools and later at the University of Berlin, where in his lectures he emphasized the "static variable theory", with no recourse of moving points or lines, no abandonment of infinitely large quantities. small, dealing only with the real numbers, the addition and its inverse operation, and the "less than" ratio.
The symbolism of Weierstrass and his student Heine expelled the notion of variability from Calculus, and it is unnecessary to use fixed infinitesimals. He was thus trying to replace intuitive concepts with logical precision and rigorous demonstrations.
Weierstrass tried to separate the Calculus from Geometry based on the concept of numbers only. For this it was necessary to define irrational number regardless of limit. He came to the conclusion that there was a boundary of a convergent sequence taking the sequence itself as the number or boundary and defined irrational number as the ordered sequence of a rational aggregate, contributing not only to the definition of real number but also to a better concept of limits, which is in essence what we have today.
Weierstrass made his first discoveries at the age of forty and was recognized as the world's leading analyst, a notable exception to the commonly accepted idea that a mathematician should reveal himself early.
Source: Fundamentals of Elementary Mathematics, Gelson Iezzi - Current Publisher