Transcript Slide 1
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 Matrices, eigenvalues Galois Error correcting codes Where it all started …. What mathematicians did to tell the future? Appollonius Conic section Kepler 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!!!!!!! d 2x 2 dt GMx x 3 Newton’s law of gravity Neptune: discovered by maths 1 2 ut u.u P u, .u 0 Re Navier-Stokes equations Weather forecasting Mathematicians also invented the computer! Kelvin Tidal predictor US Tidal predictor 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 Radon 1917 Also used to X-ray mummies Detect land mines 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 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: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! What have mathematicians done for 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 Who do you invite? ACE Now have 200 friends and want 100 to come to a party Have a book saying who hates who Who do you invite? 9000000000000000000000000000000000000000000 00000000000000000000000 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 • Future • Life • Music • Party Are safe in the hands of a mathematician