Germany · 1815-1897

Karl Weierstrass

Karl Weierstrass was mathematician and teacher. He strengthened the foundations of analysis with precise definitions of limits, continuity, and convergence.

Documented historical record

Biographical and historical reference works document Karl Weierstrass’s role and the mathematical work summarized on this page.

Historical eraIndustrial & Scientific Age
Math subjects
Grade bands

6-8, 9-12, College

Profession trails

The person and the work

Biography

Karl Weierstrass was mathematician and teacher associated with Germany. He strengthened the foundations of analysis with precise definitions of limits, continuity, and convergence.

A function bearing his name is continuous everywhere but differentiable nowhere. Together, these contributions connect algebra and functions and calculus and change to the working problems, tools, and questions of the period.

Mathematical contribution

What this hero added or preserved

Core mathematical work

He strengthened the foundations of analysis with precise definitions of limits, continuity, and convergence.

Method, teaching, or application

A function bearing his name is continuous everywhere but differentiable nowhere.

Why this matters

The larger lesson

Karl Weierstrass shows that mathematics grows through proof, calculation, observation, design, teaching, or careful records. The lasting lesson is that algebra and functions and calculus and change can turn a difficult question into a method another person can inspect and reuse.

Place the work in time

Timeline

  1. 1815

    Life and working period

    Karl Weierstrass worked as mathematician and teacher in Germany.

  2. Legacy

    Lasting mathematical connection

    A function bearing his name is continuous everywhere but differentiable nowhere.

Key idea

An equation balances two descriptions

Karl Weierstrass’s work shows how symbols can represent an unknown quantity while preserving equality.

Example

In 4x + 10 = 54, subtracting 10 and dividing by 4 gives x = 11.

Try it yourself

Solve the equation

Solve 4x + 10 = 54.

  1. Subtract 10 from both sides.
  2. Divide both sides by 4.
  3. Substitute the result to check.
Show the answer

x = 11.

Math at work

Scientists and astronomers use the same habits

Scientists and astronomers use algebra and functions to plan, compare, test, or communicate decisions. Karl Weierstrass’s work provides a historical example of that connection.

Keep curiosity alive

A little-known fact

A function bearing his name is continuous everywhere but differentiable nowhere.

Common misconception

Karl Weierstrass matters because of only one famous formula or anecdote.

What the evidence supports

The documented record is broader: He strengthened the foundations of analysis with precise definitions of limits, continuity, and convergence.

Keep exploring

Connected learning paths