what have mathematicians done for us? chris budd
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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
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
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