What have mathematicians done for us? Chris Budd.

What have mathematicians done for us?

Chris Budd

A common scenario

You meet someone at a party and (foolishly)

Tell them you are a mathematician

Their immediate reaction is to …

• Panic

• Leave quickly

• Tell you that ..

Mathematics is completely useless

Mathematicians are souless geeks

All mathematicians are mad!

In response you can …

• Deny that you are a mathematician

• Not go to any more parties

• Agree that mathematicians are evil

• or …. Say that

The modern world would not exist without maths

With maths you can tell the future and save lives

Maths lies at the heart of art and music

Mathematicians organise great parties

Some ways that maths has changed the modern world

Maxwell: Electromagnetism … radio, TV, radar, mobile phones

Google

Error correcting codes

Galois

Matrices, eigenvalues

What mathematicians did to tell the future?

Where it all started ….

KeplerConic sectionAppollonius

Nature has order and pattern and follows rules

1686

In the Principia Newton showed that this order and pattern could be expressed by using mathematics (calculus)

Key idea ….

• Write down the equations describing a physical system

• Solve the equations

• Predict the future

An astonishing discovery!!!!!!!

Neptune: discovered by maths

32

2

x

GMx

dt

xd Newton’s law of gravity

Weather forecasting

0.,Re

1. 2 uuPuuut

Navier-Stokes equations

US Tidal predictorKelvin Tidal predictor

Mathematicians also invented the computer!

What mathematicians have done to save lives?

Florence Nightingale

Mathematics can look inside you

Modern CAT scanner

CAT scanners work by casting many shadows with X-rays and using maths to assemble these into a picture

Also used to

X-ray mummies

Detect land mines

Radon 1917

What have mathematicians done for music?

Was Bach a mathematician?

Music is based on the idea of the scale …

Some musical notes sound better when played together than others

The notes C and G

(a perfect 5th)

The notes C and E

(a perfect 3rd)

The octave C to C

Reason was discovered by Pythagaros

Length of strings giving C and G, and C and E, were in simple fractional proportions

C:G … 3/2 C:E … 4/3

Pythagoras invented the Just Scale .. Sequence of notes with frequencies in simple fractional proportions

Problem: Keyboard instruments could only be tuned for one key

Mathematicians invented a new Well Tempered scale with all notes in the same proportion which works well in all keys

Bach so liked the new scale that he wrote the

Well Tempered Clavier to popularise it!

It is still used today!

You have five friends, Annabel, Brian, Colin, Daphne, Edward

Want to invite three to a party

• Annabel hates Brian and Daphne

• Brian hates Colin and Edward

• Daphne hates Edward

Who do you invite? A C E

What have mathematicians done for parties?

Now have 200 friends and want 100 to come to a partyHave a book saying who hates who Who do you invite?

Parties to check

Takes a high speed computer

Years to check them

900000000000000000000000000000000000000000000000000000000000000000

6000000000000000000000000000000000000000

Works for a party and many other problems

Using maths we can solve it in seconds

SATNAV devices!

Simulated annealing

Conclusion …. your

• Future

• Life

• Music

• Party

Are safe in the hands of a mathematician