TOK and Mathematics

Ghina Srouji

Outline Definition Axiom-theorem Structure Creative discipline Mathematical truth Applied Mathematics

Sciences

Natural Formal Human

Biology

Chemistry

Physics

Mathematics

HistoryPsy

cholo

gy

What is mathematics ?!

Science of structure, order and relation Science dealing with the logic of quantity

and shape and arrangement A science of relation Set of tools for solving practical and

technical problems A game for intellectual construction

What do thinkers say about mathematics !

“Nature is written in the language of mathematics”

Galileo“Mathematics is the music of the spheres”

Pythagoras“The world is made up of numbers” Pythagoras

Axiom-theorem Structure

The foundation of mathematics is : AXIOMS ( = collection of fundamental laws)

Formal systems of knowledge

Define Axioms Rules of Inferences

Create Theorems

Create mathematical knowledge

Mathematical truth Mathematics does not seek truth,

but it does seek coherence.

Creative Discipline !

It is a discipline that requires the least effort because it relies on little preliminary knowledge.

It is evolving: Hands on: Pythagoras theorem,

parabolas, hyperbolas, ellipses

Applied Mathematics

Tunnel of Samos

The rocket Ariane

What could be new !!!

Iteration 1) Numerical :

application : Finding Roots 2) Geometric = Fractals

* Seirpinski triangle http://math.bu.edu//DYSYS/applets/chaos-game.html

* Julia Sethttp://math.bu.edu//DYSYS/applets

Computers

Mathematics

Mathematics

Why do we ALL learn mathematics?

Why do we learn literature?

Isn’t it enough to read and write ! Why do we learn biology? history?

music? geology?

Mathematics, what for ?!

Helps researchers of all kinds and in all the domains to understand our world and how it functions

( engineers, biologists, ecologists, …)

Helps citizens in their everyday life

Mathematics offers us

another world, above our natural world.

In fact, our world is very complex whereas the mathematical world seems to be better structured.

In order to do this, we should let go of the complicated rules of our real world and join the coherent rules of the math world.

Mathemagics It is a rather fantastic and exciting

privilege of the science of mathematics that everything that was once thought of and proven still retains its worth intact.

Mathematical theories are for all time

Finally “ when the imagination is

confounded with intelligence, isn’t it mathematics?

Albert Camus

Mathematics honors the human mind

Mathematics: an introduction to

abstraction!"Let no one who is

not a geometer enter".

- Written on the door of Plato’s Academy