Math 404: History of Math. Stories, Teasers, and General Information

Transcription

1 Math 404 History of Math: Stories,, and 4/19/2012

2 Italians Feud Over Cubics Scipione del Ferro Solved x 3 nx = m

3 Italians Feud Over Cubics Scipione del Ferro Solved x 3 nx = m Antonio Fior Student under Ferro

4 Italians Feud Over Cubics Scipione del Ferro Solved x 3 nx = m Antonio Fior Student under Ferro Nicholo Tartaglia Fontana Solved x 3 nx 2 = m Beat Fior in math competition

5 Italians Feud Over Cubics Girolamo Cardano Tricks Fontana to get solution to x 3 nx 2 = m Writes Ars Magna and takes on Lodovicio Ferrarri

6 Italians Feud Over Cubics Girolamo Cardano Tricks Fontana to get solution to x 3 nx 2 = m Writes Ars Magna and takes on Lodovicio Ferrarri Lodovicio Ferrarri Manages to solve the quartic Beats Fontana in competition defending Cardano

7 Nicolaus Has 3 sons, 2 do math: Jacob and Johann Jacob Theory of probability, Bernoulli trial, and Bernoulli numbers Credited for law of large numbers and the constant e Discovered the isochrone Johann Taught Euler and L Hopital Posed and solved the problem of the brachistochrone Extremely jealous of brother Jacob Has 3 sons, 1 is famous: Daniel

8 Daniel Worked on fluid dynamics The Bernoulli from your Physics class Hired by Peter the Great and works with Euler Dispute with father Johann over work

9 Daniel Worked on fluid dynamics The Bernoulli from your Physics class Hired by Peter the Great and works with Euler Dispute with father Johann over work Johann vs. Daniel Tie in a science contest at the University of Paris Johann bans Daniel from house Johann plagiarizes from Daniel, then tries to backdate book Johann stays mad until death

10 Term used to describe the connection between the monster group M and modular functions Monster group is group of finite order: Arose while trying to classify all finite simple groups Ogg and group of mathematicians see numbers arise in work: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71

11 Term used to describe the connection between the monster group M and modular functions Monster group is group of finite order: Arose while trying to classify all finite simple groups Ogg and group of mathematicians see numbers arise in work: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71 Ogg notes that the prime factors of the size of M are the same as his numbers

12 Term used to describe the connection between the monster group M and modular functions Monster group is group of finite order: Arose while trying to classify all finite simple groups Ogg and group of mathematicians see numbers arise in work: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71 Ogg notes that the prime factors of the size of M are the same as his numbers Ogg publishes a paper offering a bottle of Jack Daniel s whiskey to anyone who could explain the connection

13 Euclid and Elements Axioms, Postulates, and Books Anthyphairesis Deals with ratios and proportions Archimedes/Erastosthenes Infinitisemal calculus? Erastosthene s sieve for locating primes One of them was called Beta

14 Brahmagupta Greatest Indian mathematician of antiquity Quad. gen. of Heron s Formula and The Pulverizer Islamic Mathematicians Al-kitab al-mukhtasar fi hisab al-jabr wa l-mucabala Comprehensive Trigonometry history Recent History Replacing Euclid s 5th Postulate Square Root of Negative Numbers The camps of the Logicists, Formalists, and Intuitionists

15 Class held Monday/Wednesday Time: 4:00-5:15 PM Room: Social Sciences, Rm 222 Dr. Madden Three tests and a Final Free Response, Matching, Short Answer, Short Essay Essay: Possibly?

16 Questions?