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 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 Galois Matrices, eigenvalues Error correcting codes

Mathematicians invented the computer! Kelvin Tidal predictor US Tidal predictor

An astonishing discovery!!!!!!! Key idea …. Write down the equations describing a physical system Solve the equations Predict the future An astonishing discovery!!!!!!!

Navier-Stokes equations Weather forecasting

Mathematicians 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

Radon 1917 Also used to X-ray mummies Detect land mines

Mathematicians are good for music! Some musical notes sound better when played together than others The octave C to C The notes C and G (a perfect 5th) The notes C and E (a perfect 3rd)

Reason was discovered by Pythagaros Length of strings giving C and G, and C and E, were in simple fractional proportions C:C … 2/1 C:G … 3/2 C:E … 4/3

Pythagoras invented the Just Scale 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 a geometric progression 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!

A C E Mathematicians organise great parties? 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 A C E Who do you invite?

Now have 200 friends and want 100 to come to a party Have a book saying who hates who Who do you invite? 900000000000000000000000000000000000000000000000000000000000000000 Parties to check Takes a high speed computer 6000000000000000000000000000000000000000 Years to check them

Using maths we can solve it in seconds Simulated annealing Works for a party and many other problems SATNAV devices!

Conclusion …. your Life Music Party Future Are safe in the hands of a mathematician