Objective: To understand the nature of maths; especially the distinction with science and possible links to art

Hillbilly Maths and Nature by Numbers

– a provocation

Objective: To understand the nature of maths; especially the distinction with science and possible links to art

Hillbilly Maths and Nature by Numbers

– a provocation

The most certain

academic discipline?

Objective: To understand the nature of maths; especially the distinction with science and possible links to art

Hillbilly Maths and Nature by Numbers

– a provocation

Objective: To understand the nature of maths; especially the distinction with science and possible links to art

Hillbilly Maths and Nature by Numbers

– a provocation

Objective: To understand the nature of maths; especially the distinction with science and possible links to art

Hillbilly Maths and Nature by Numbers

– a provocation

What is it?

The most certain

academic discipline?

Maths is the subject where we never know what we are talking about, nor whether what we are saying is true.

Bertrand Russell (mathematician, philosopher)

detail

What do the angles

in a triangle add up to?

How do you know?

Maths is not science; the role of experiment is not decisive, and mathematicians look for proofs.

A proof is a set of mathematical steps which support a conclusion; it’s a (very good?) reason to believe something.

ba

c

ba

c

ba

c

ba

ca b

Axiomatic deductive reasoning

If the angles on a straight line add up to 180 degrees

If the alternate angles on parallel lines are equal(These are called AXIOMS)

then the angles in a triangle add up to 180 degrees

This is deductive reasoning. Is the conclusion certain? Is it true?

Truth of axioms? System under consideration

Axiomatic deductive reasoning

If the angles on a straight line add up to 180 degrees

If the alternate angles on parallel lines are equal(These are called AXIOMS)

then the angles in a triangle add up to 180 degrees

This is deductive reasoning. Is the conclusion certain? Is it true?

Truth of axioms? System under consideration

Axiomatic deductive reasoning

If the angles on a straight line add up to 180 degrees

If the alternate angles on parallel lines are equal(These are called AXIOMS)

then the angles in a triangle add up to 180 degrees

This is deductive reasoning. Is the conclusion certain? Is it true?

Truth of axioms? System under consideration

6

5

3

1

2

1

5

2

3

1

2

1

Maths is the subject where we never know what we are talking about, nor whether what we are saying is true.

Bertrand Russell (mathematician, philosopher)

But is it all about axioms?

There are 1000 lockers numbered 1-1000. Suppose you open all of the lockers, then close every other locker. Then, for every third locker, you close each opened locker and open each closed locker. You follow the same pattern for every fourth locker, every fifth locker, and so on up to every thousandth locker. Which locker doors will be open when the process is complete?

Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. One goes into the first room, and it's dark, completely dark. One stumbles around bumping into the furniture, and gradually, you learn where each piece of furniture is, and finally, after six months or so, you find the light switch. You turn it on, and suddenly, it's all illuminated. You can see exactly where you were. At the beginning of September, I was sitting here at this desk, when suddenly, totally unexpectedly, I had this incredible revelation. It was the most -- the most important moment of my working life. Nothing I ever do again will. . .

Objective: To understand the nature of maths; especially the distinction with science and possible links to art