## Saturday, January 1, 2011

### The Math Timeline, Part 1 (Up To and Including Algebra)

Mathematics is SO rich, to the point of being intimidating.

But it's not, not if you approach it properly.

And the PROPER way to approach it, is to split it into parts.

Many parts, but so what? If you have to split the splits into more splits, then so be it.

This is what I'm attempting to do, to help the intimidated feel ... not intimidated.

The best way to learn Math IMO, is to look at the 3 global splits, those being:

1) Math up to and including ... Algebra. (Part 1 of 3 ... the timeline of THIS post)
2) Math post-Algebra up to including ... Calculus
3) Math post-Calculus

For reference, I will use the beautiful book by Tony Crilly, which I spoke of lovingly: here.

And that link is important, because the numbers of those chapters refer to the numbers in parentheses at the end of each historical item that you are about to read.

And so we begin:

30,000 BC - Paleolithic peoples in Europe make number marks on bones   (2)

2000 BC - The Babylonians use symbols for numbers   (2)

2000 BC - The Babylonians observe pi is roughly 3   (5)

1950 BC - The Babylonians work with quadratic equations   (14)

1800 BC - Fractions are used in Babylonian cultures   (3)

1750 BC - The Babylonians compile tables of square roots   (4)

1650 BC - The Egyptians make use of unit fractions   (3)

700 BC - The Babylonians use zero as a placeholder in their number system  (1)

525 BC - The Pythagoreans study geometrically arranged square numbers  (4)

525 BC -  The Pythagoreans are associated with both perfect and abundant numbers (10)

c. 500 BC - Fragmentary evidence exists for Pascal's triangle in Sanskrit   (13)

350 BC  - Aristotle rejects an actual infinite  (7)

c. 300 BC - The theory of the irrational numbers by Eudoxus is published in Book 5 of Euclid's Elements  (4)

300 BC - Euclid's Elements gives a proof that there are infinitely many prime numbers (9)

300 BC - Book 9 of Euclid's Elements discusses perfect numbers (10)

c 300 BC - The extreme and mean ratio is published in Euclid's Elements  (12)

250 BC - Archimedes gives the close approximation of pi of 22/7   (5)

230 BC - Eratosthenes of Cyrene describes a method for sieving out prime numbers from the whole numbers (9)

100 - The Chinese devise a system for calculating with fractions  (3)

100 - Nicomachus of Gerasa gives a classification of numbers based on perfect numbers (10)

250 - Diophantus of Alexandria publishes Arithmetica   (14)

600 - The forerunner of our modern decimal notation is used in India  (2)

628 - Brahmagupta uses zero and states rules for its use with other numerals (1)

630 - Brahmagupta gives methods for computing square roots (4)

825 - Derived from "al-jabr" Al-Khwarizmi gives the word "algebra" to mathematics  (14)

830 - Mahavira has ideas on how zero interacts with other numerals  (1)

c. 1070 - Omar Khayyam discovers Pascal's triangle, which in some countries is named after him  (13)

1100 - Bhaskara uses zero as a symbol in algebra and attempts to show how it is manipulated  (1)

1200 - The Hindu-Arabic system of writing numerals 1,...,9, and a zero, spreads  (2)

1202 - Fibonacci uses the extra symbol 0 added to the Hindu-Arabic system of numerals 1,...,9 but not as a number on par with them  (1)

1202 - Fibonacci publishes the Liber Abaci and Fibonacci numbers (11)

1202 - Fibonacci popularizes the bar notation of fractions (3)

1303 - Zhu Shijie defines Pascal's triangle and shows how to sum certain sequences (13)

1509 - Paciola publishes The Divine Proportion  (12)

1550 - The square root symbol is introduced (4)

1572 - Rafael Bombelli calculates with imaginary numbers (8)

1585 - Simon Stevin sets out a theory of decimal fractions (3)

1591 - Francois Viete writes a mathematical text in terms of letters for knowns and unknowns  (14)

1600 - The symbols of the decimal system take their recognizable modern forms (2)

1603 - Pietro Cataldi finds the 6th and 7th perfect numbers, 2^16(2^17 -1) = 8,589,869,056 and 2^18(2^19 - 1) = 137,438,691,328    (10)

1618 - John Napier encounters a constant, e, in connection with logarithms (6)

1639 - Girard Desargues introduces the concept of infinity into geometry (7)

1655 - John Wallis is credited with being the first to use the "love knot" symbol for infinity (7)

1664 - Pascal's paper on the properties of Pascal's triangle is published posthumously  (13)

1700 - The fractional line "-" is in general use (as is %)   (3)

1706 - William Jones introduces the pi symbol (5)

1714 - Leibniz discusses the harmonic triangle  (13)

1724 - Daniel Bernoulli expresses the numbers of the Fibonacci sequence in terms of the golden ratio (11)

1727 - Euler uses the notation e in connection with the theory of logarithms; it is sometimes called Euler's number (6)

1742 - Goldbach speculates that every even number (more than 2) is a sum of two primes (9)

1748 - Euler calculates e to 23 digits; he is given the credit for the discovery of the famous formula e^i(pi) + 1 = 0 around this time  (6)

1777 - Euler first uses the symbol i to represent the square root of -1  (8)

1761 - Lambert proves that pi is irrational  (5)

1806 - Argand's diagrammatic representation leads to the name "Argand diagram"  (8)

1811 - Carl Friedrich Gauss  works with functions of complex number variables  (8)

1837 - William R. Hamilton treats complex numbers as ordered pairs of real numbers  (8)

1872 - Richard Dedekind sets out a theory of irrational numbers (4)

1874 - Cantor treats the notion of infinity rigorously, specifying different orders of infinity (7)

1876 - Fechner writes on psychological experiments to determine the proportions of the most "aesthetic" rectangle

1873 - Hermite proves e is a transcendental (6)

1882 - Lindemann proves that pi is transcendental (5)

1896 - The prime number theorem on the distribution of primes is proved (9)

1920's - Emmy Noether publishes papers in the development of modern abstract algebra  (14)

1923 - Bartok composes his "Dance Suite", believed to be inspired by the Fibonacci numbers  (11)

1930 - Bartel van der Waerden publishes his famous Moderne Algebra   (14)

1960s - Abraham Robinson devises a non-standard arithmetic based on the notion of the infinitesimal  (7)

1963 - The Fibonacci Quarterly, a journal devoted to the number theory of the Fibonacci sequence, is founded  (11)

1966 - Chen Jingrun almost confirms the Goldbach conjecture  (9)

1975 - The International Organization for Standardization (ISO) defines the A paper size  (12)

2006 - The great prime search project finds the 44th Mersenne prime (with almost ten million digits) and yet another new perfect number can be generated  (10)

2007 - e is calculated to 10^11 digits  (6)

2007 - Sculptor Peter Randall-Page creates the 70 tonne sculpture "Seed" based on the Fibonacci sequence for the Eden Project in Cornwall, UK  (11)

Phil Warnell said...

Hi Steven,

” 1761 - Lambert proves that pi is rational (5)”

Is this as test to see if your reader’s are paying attention, as pi being irrational not rational, which Lambert was the first to prove? However as the decimal representation of π expressed as 3.141592653589793238462643383279502884197 is sufficient to estimate the circumference of any circle that fits in the observable universe with precision comparable to the radius of a hydrogen atom, any further expression of it has little practical value:-) That is except when parts of the sequence are used in replacement of a random one:-)

Best,

Phil

Steven Colyer said...

Oh, Phil! You're quite right! My bad, I type too fast. Problem corrected.

That reminds me of the old math joke, where pi and the imaginary number i are greeting each other. "i" says to to pi, "Be rational!", and Pi says back to i, "Get real!"