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Mathematics & Reason
Mathematics & Reason
How understanding maths and reason changes your view of the World.
How understanding maths and reason changes your view of the World.
What is Mathematics?
What is Mathematics?
The search for pattern.
The search for pattern.
Betrand RussellBetrand Russell
“Mathematics, rightly viewed, possesses not only truth, but supreme beauty.”
“Mathematics, rightly viewed, possesses not only truth, but supreme beauty.”
Monty Hall ProblemMonty Hall Problem
1 2 3
Monty Hall ProblemMonty Hall Problem
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Simpson’s ParadoxSimpson’s Paradox
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Simpson’s ParadoxSimpson’s Paradox
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Bayes’s TheoremBayes’s Theorem
A patient goes to see a doctor. The doctor performs a test with 99 percent reliability--that is, 99 percent of people who are sick test positive and 99 percent of the healthy people test negative. The doctor knows that only 1 percent of the people in the country are sick. Now the question is: if the patient tests positive, what are the chances the patient is sick?
A patient goes to see a doctor. The doctor performs a test with 99 percent reliability--that is, 99 percent of people who are sick test positive and 99 percent of the healthy people test negative. The doctor knows that only 1 percent of the people in the country are sick. Now the question is: if the patient tests positive, what are the chances the patient is sick?
Bayes’s TheoremBayes’s Theorem
9900
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Penney Ante Game
Penney Ante Game
Mathematics in Gambling
Mathematics in Gambling
Penney Ante Rules
1. You pick a 3-coin sequence (e.g. H T H)
2. I pick a 3 coin sequence (e.g. T T H)
3. We toss a coin repeatedly
4. Whoever’s sequence appears first wins. T H H H H T H you win
H H H T T TH H T T T
HH T H T H
TH T T T H
H
Penny Ante is a scam ! Imagine you choose H H
H . Eventually we get the
first appearance of H H H :
. . . . . . . . . . . ? H H H
Was OJ Simpson Guilty?
Was OJ Simpson Guilty?
Mathematics & Statistics in the
Courtroom
Mathematics & Statistics in the
Courtroom
O.J. Simpson abused his wifeand she was murdered.
1 in 1,000 abused womenare killed by their
husbands. But 80% of murdered abused
womenare killed by the husbands.
3 Dice… which one would you choose?
3 Dice… which one would you choose?
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MC EsherMC Esher
Are there examples of this way of thinking in
mathematics?
Are there examples of this way of thinking in
mathematics?
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vs
BLUEBLUE beats GREENGREEN on average
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vs
GREENGREEN beats REDRED on average
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vs
REDRED beats BLUEBLUE!!
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Two blues beat two reds
Benford’s LawBenford’s Law
• Take a list of data.• Examine how many of the numbers start with a 1, 2, 3, etc
• Take a list of data.• Examine how many of the numbers start with a 1, 2, 3, etc
Benford’s LawBenford’s Law
Understanding Mathematics
Understanding Mathematics
Picasso’s GuernicaPicasso’s Guernica
Perelman’s PoincarePerelman’s Poincare
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Why do we study such old maths?
Why do we study such old maths?
