__Mathematics__

__Page last modified 1/9/2020__

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**Appendix 1 -Calculations of Pi**

**Appendix 2 – Prime Numbers**

**James Joyce
on eternity, infinity. ***Imagine a
huge block of sand a million miles high, a million miles wide, a million miles
long. Once every million years a bird comes along and pecks off one grain of
sand. Eventually the entire block disappears, only to instantly reappear once
more. By the time that cube of sand has reappeared for the millionth time, not
one instant of Eternity has passed*.

__2010__, Japanese systems engineer **Shigeru Kondo**
computed the **value
of e** to 1,000,000,000,000 decimal places.

__14/10/2010__, **French**-**American** mathematician who developed **fractal** **geometry**, **Benoit
Mandelbrot**, died aged 85.

__3/5/1995__, **Fermat’s Last Theorem** was finally proved in generality, for all
values of n. It was proposed by Pierre de Fermat (ca. 1607 – 1665) in 1637,
that a^{n} + b^{n} = c^{n} had no solution for any
value of n greater than 2.

__2/8/1957__, **John von Neumann**, Hungarian-US
mathematician, died in Washington DC.

__27/4/1936__, English mathematician **Karl Pearson**
died in Coldharbour, Surrey.

__6/1/1922__, **Jakob Rosanes**, Ukrainian-German
mathematician, died.

__26/4/1920__, Mathematician **Srinivasa
Ramanujan** died.

__12/2/1916__, **Julius Wilhelm Richard Dedekind**,
German mathematician, died in Braunschweig.

__28/4/1906__, Austrian-US mathematician **Kurt Godel**
was born in Brno, Czechoslovakia.

__106/1903__, **Luigi Cremona**, Italian
mathematician, died (born 7/12/1830).

__28/4/1903__, **Josiah Gibbs**, US mathematician,
died (born 11/2/1839).

__2/2/1903__, **Bartel Leendert van der Waerden**,
Dutch mathematician, was born in Amsterdam (died 1996)

__24/1/1902__, **Oskar Morgenstern**, German-US
mathematician, was born in Silesia (Poland).

__27/1/1895__, **Sir James Cockle**, English
mathematician, died (born 14/1/1819).

__26/1/1895__, **Arthur Cayley**, British
mathematician, died in Cambridge.

__1894__, The New York Mathematical Society was
formed, later to become the **American
Mathematical Society**.

__1888__, **Vector
Space** was defined by Guiseppe Peano (1858 – 1932) in his work, *Geometrical Calculation According to the
Ausdehnungslhere of H Grossman*. Vectors such as (3,1) and (1,5) could be
added to form a quadrilateral (0,0, 3,1,1,5, 6,4); vectors could also be scaled
and added together. In physics they are useful for when different forces act on
a particle.

__14/4/1883__, **William Farr**, English
statistician, died (born 30/11/1807).

__5/11/1879__, **James Clerk Maxwell**, Scottish
mathematician and physicist, died in Cambridge, **England**.

__3/3/1879__, **William Clifford**, English
mathematician, died (born 4/5/1845).

__31/3/1877__, **Antoine Cournot**, French
mathematician, died (born 28/8/1801).

__1874__, German mathematician **Georg Cantor** (1845 v- 1918)
started the science of **Set Theory**
with his paper, ‘On a Characteristic Property of All Real Agebriac Numbers’.

__18/10/1871__, **Charles Babbage** was born in
Teignmouth, Devon died in London (born 26/12/1792 in Teignmouth, Devon).

__22/5/1868__, **Julius Plucker**, German
mathematician, died in Bonn, Germany.

__15/10/1867__, Jacques Inaudi, Italian
child calculating prodigy, was born.

__1865__, The **London
Mathematical Society** was founded and began to issue its journal, *Proceedings*.

__1865__, German mathematician **August Ferdinand Mobius** (born
Schulpforte 17/11/1790) presented his discovery of a figure that had only one
side and one edge, now known as the **Mobius
Strip**.

__2/9/1865__, **Sir William Hamilton**, Scottish
mathematician, died (born 4/8/1805).

__8/11/1858__, **George Peacock**, mathematician,
died in Ely, England.

__23/5/1857__, **Augustin Cauchy**, mathematician,
died (born 21/8/1789)

__23/2/1855__**, Johann Karl Friedrich Gauss**, mathematician, died in
Gottingen, **Germany**.

__29/4/1854__, **Jules Henri Poincare**, French
mathematician, was born in Nantes. In 1895 he effectively founded the science
of topology, although some of its principles were already known.

__1/11/1851__, **Thomas Galloway**, Scottish
mathematician, died (born 26/2/1796).

__4/5/1845__, **William Clifford**, English
mathematician, was born (died 3/3/1879).

__11/2/1839__, **Josiah Gibbs**, US mathematician,
was born (died 28/4/1903).

__16/3/1838__, **Nathaniel Bowditch**,
mathematician, died in Boston, USA (born in Salem, Massachusetts, 1773)

__16/1/1834__, **Jean Hachette**, French
mathematician, died (born 6/5/1769).

__31/5/1832__, **Evariste Gallois**, mathematician,
died (born 25/10/1811)

__7/12/1830__, **Luigi Cremona**, Italian
mathematician, was born (died 10/6/1903).

__16/5/1830__, **Jean Fourier**, French
mathematician, died (born 23/3/1768).

__6/4/1829__, **Neils Abel**, Norwegian
mathematician (born 1802) died inArendal.

__23/2/1826__**, Nikolai Ivanovich Lobachevski** (born near Nizhni Novgorod,
**Russia**)
gave a paper at Kazan University outlining the principles of **non-Euclidean
geometry**.

__7/4/1823__, **Jacques Charles**, mathematician,
died (born 12/11/1746)

__16/8/1821__, **Arthur Cayley**, English
mathematician, was born (died 26/1/1895).

__26/5/1821__, **Pafnutiy Chebichev**, Russian
mathematician, was born (died 8/12/1894).

__14/1/1819__, **Sir James Cockle**, English
mathematician, was born (died 27/1/1895).

__18/2/1816__, **Maurice Block**, French statistician,
was born in Berlin (died in Paris 9/1/1901).

__2/11/1815__, Mathematician **George Boole**
was born in Lincoln, **England**. In 1847 he published his paper on
symbolic logic.

__25/10/1811__, **Evariste Gallois**, mathematician,
was born (died 31/5/1832).

__30/11/1807__, **William Farr**, English
statistician, was born (died 14/4/1883).

__13/7/1807__, **Jean Bernoulli**, mathematician,
died (born 4/11/1744)

__4/8/1805__, **Sir William Hamilton**, Scottish
mathematician, was born (died 2/9/1865).

__25/8/1802__, **Neils Abel**, Norwegian
mathematician (died 1829) was born in Findoe.

__28/8/1801__, **Antoine Cournot**, French
mathematician, was born (died 31/3/1877).

__20/2/1799__, **Jean Borda**, French
mathematician, died in Paris (born in Dax 4/5/1733).

__26/2/1796__, **Thomas Galloway**, Scottish
mathematician, was born (died 1/11/1851).

__26/12/1792__, **Charles Babbage** was born in
Teignmouth, Devon (died 18/10/1871 in London).

__21/8/1789__, **Augustin Cauchy**, mathematician,
was born (died 23/5/1857).

__22/11/1784__, **Paolo Frisi**, Italian
mathematician, died (born 13/4/1728).

__29/10/1783__, **Jean Alembert**, French
mathematician, died in Paris.

__18/9/1783__, **Leonhard Euler**, **Swiss**
mathematician, died in St Petersburg, **Russia**.

__1782__, **Latin
Squares** were developed by **Euler**. These are n x n matrices with n
different symbols,where each symbol occurs once in each row and once in each
column. Sudoku puzzles are a type of Latin Square. These squares can be used in
randomised drug experiments where n groups can be given different
non-duplicated schedules of the drug.

__20/5/1782__, **William Emerson**, English
mathematician, died (born 4/5/1701).

__1777__, **Euler** first used *i* to denote the square root of minus 1. He did not publish this
until 1794, and it was **Gauss** who gained widespread acceptance for
this notation with his work *Disquisitiones
arithmeticae* in 1801.

__21/3/1768__, **Jean Fourier**, French
mathematician, was born (died 16/5/1830).

__2/2/1768__, **Charles Camus**, French
mathematician, died (born 25/8/1699).

__17/5/1765__, **Alexis Clairault**, French
mathematician, died (born 5/1713).

__1761__, Mathematician **Thomas Bayes** died (born 1701).
He developed **Bayes Theorem**, an
‘intuitive’method of calculating probabilities based on prior observations; for
example if the Sun rose yesterday morning, and the day before, it will likely
rise this morning too. If every time the Sun rises (A) a cock is heard to crow
(B), the probability that in the future the two events will occur together is
Pr(A[B) = Pr(B[A) x PrPr(A) / Pr(B). In
other words, the RHS terms are the numerical values for how often A occurs, B
occurs and A and B occur together.

__17/10/1759__, **Jacques Bernoulli**,
mathematician, was born (died 7/1789).

__27/11/1754__, **Abraham Demoivre**, English
mathematician, died (born 26/5/1667).

__15/4/1754__, **Jacopo Riccati**, mathematician, died
in Treviso, Italy.

__12/11/1746__, **Jacques Charles**, mathematician,
was born (died 7/4/1823).

__4/11/1744__, **Jean Bernoulli**, mathematician,
was born (died 13/7/1807).

__1736__, The symbol e for natural logarithms,
devised by **Leonhard
Euler** in 1727, first appeared
in print.

__1736__, **Graph
Theory** was originated by **Leonhard Euler**. It had topological origins,
dealing with networks of points connected by lines (the Konigsberg Bridge
problem), and does not deal with graphs such as bar charts or pie charts.

__1734__, Swiss mathematician **Leonhardt Euler** introduced the
term f(x) to denote a mathematical function.

__1733__, The **Bell
Curve**, showing that valuers for random processes couldcluster around a mean
with values further off becoming less likely,was invented by Abraham de Moivre
(1667 - 1754). This was developed in 1833 by German mathematician Friedrich
Gauss (1777 – 1855).

__4/5/1733__, **Jean Borda**, French
mathematician, was born in Dax (died in Paris 20/2/1799).

__13/4/1728__, **Paolo Frisi**, Italian
mathematician, was born (died 22/11/1784).

__27/6/1726__, **Nicolas Bernoulli**,
mathematician, died (born 27/1/1695).

__16/5/1718__, **Maria Agnesi**, **Italian** mathematician, was born (died
9/1/1799).

__5/6/1716__, **Roger Cotes**, English mathematician, died (born
10/7/1682).

__15/10/1715__, **Humphry Ditton**, English mathematician, died
(born 29/5/1675).

__15/4/1707__, **Leonhard Euler**, Swiss mathematician, was born
(died 18/9/1783).

__20/3/1707__, **Jedediah Buxton**, English arithmetician, was
born (died 1772).

__16/8/1705__, **Jacques Bernoulli**, mathematician, died (born
in Basel 27/12/1654).

__4/5/1701__, **William Emerson**, English mathematician, was
born (died 20/5/1782).

__27/1/1695__, **Nicolas Bernoulli**, mathematician, was born
(died 26/7/1726).

__1691__, **Leibniz** first used the
mathematical terms **coordinate**, **ordinate** and **abscissa**. He also introduced the term ‘**function’** to describe a mathematical equation where every unique
input produces one unique output, for example if the function is x^{2},
then input 4 produces output 16.

__11/11/1688__, **Louis Castel**, mathematician, was born (died
1757).

__10/7/1682__, **Roger Cotes**, English mathematician, was born
(died 5/6/1716).

__4/5/1677__, **Isaac Barrow**, English mathematician, died
(born 1630).

__21/11/1675__, **Leibniz** became the first mathematician to use
the modern notation of f[x] dx for integration/differentiation.

__29/5/1675__, **Humphry Ditton**, English mathematician, was
born (died 15/10/1715).

__26/5/1667__, **Abraham Demoivre**, English mathematician, was
born (died 27/11/1754).

__1665__, **Isaac Newton** worked out a system of ‘fluxions’
– precursor of modern **calculus**. He also began work on a theory of **gravity**.

__12/1/1665__, French
mathematician **Pierre
de Fermat** (born 1601) died.

__1659__, First publication of the (division) sign, in *Teutsche Algebra*, written by **Johann Heinrich**
and published long after his death in 1588.

__27/12/1654__, **Jacques
Bernoulli**, mathematician, was born in Basel (died 16/8/1705).

__1653__, Mathematician **Blaise Pascal** (1623-1662) wrote his treatise,
On the Arithmetical Traingle (published posthumously in 1665). His Triangle
consisted of rows of numbers where each term is the sum of the two above, e.g.
1 – 1,1 – 1,2,1 – 1,3,3,1, ….This triangle is important in Probability Theory
and for polynomial equations and fractals.

__8/10/1652__, **John Greaves**,
English mathematician, died (born 1602).

__30/9/1632__, **Thomas Allen**,
English mathematician, died at Gloucester Hall (born 21/12/1542 at Gloucester
Hall).

__1631__, First recorded used of the
multiplication sign, by **William Oughtred**. First use of the signs <
and > to mean ‘less than’ and ‘more than’.

__26/1/1630__, **Henry Briggs**, mathematician, died.

__1629__, Brackets were first used
in mathematics by the Dutch mathematician, **Albert Gerard**.

__10/12/1626__, **Edmund Gunter**, English mathematician, died
(born 1581).

__2/7/1621__, **Thomas Harriot**, English mathematician, died
(born 1560).

__1614__, **Logarithms** were invented by the Scottish
mathematician, **John
Napier** (1550-1617), who in that year published a 97-page work
entitled ‘*Mirifici Logarithmorum Canonia
Descriptio’*. He coined the word ‘logarithm from two Greek words meaning
‘ratio’ and ‘number’.

__1603__, **Pietro A Cataldi** discovered the 6^{th}
and 7^{th} **Perfect Numbers**,
which are 8,859,869,056 and 137,438,691,328.

__17/8/1601__, **Pierre de
Fermat**, mathematician, was born (died 12/1/1665).

__5/3/1574__, **William
Oughtred** was born in Eton. Around 1621 he invented the slide rule.

__1572__, **Complex** / **imaginary** numbers were applied to solve
equations in **Rafael
Bombelli’s** work, *Algebra*. **Imaginary** numbers are those with a
negative square root,and **complex**
numbers are those with a real and imaginary element, such as 3 + 4i, which are
expressed on a 2-d grid.

__1556__, The = sign was created by **Robert Recorde**, on the basis
that nothing can be more equal than a pair of parallel lines.

__21/12/1542__, **Thomas Allen**,
English mathematician, was born in Uttoxeter, Staffordshire (died 30/9/1632 at
Gloucester Hall).

__13/7/1527__, **John Dee**,
English mathematician, was born (died 1608).

__1525__, The first manual of geometry was compiled by the German
engraver, **Albrecht
Durer**.

__1524__, First recorded usage of the modern **square root symbol**, in Die Coss, by Christoff Rudolff.

__1513__, The fifth **Perfect
Number** was discovered, 33,350,336. A **Perfect
Number** is one whose factors add up to the number itself, like 6 is the sum
of 1, 2 and 3.

__1489__, The first recorded use of
the mathematical symbols + and -, in the book Mental Arithmetic by **Johann Wildmann**,
published in Leipzig. They were used for ‘excess’ and ‘deficiency’, and by the
1500s came to mean ‘add’ and ‘subtract’.

__1434__, **Leone Battista**, born in Genoa,
Italy, 14/2/1404, published a nook on the geometrical laws of perspective in
drawing.

__1299__, In Florence, Italy, the
use of Arabic numerals was banned.

__1240__, Death of Italian
mathematician **Leonardo
Pisano Bigollo** (or, **Fibonacci**) (born ca. 1170). He developed the **Fibonacci Series**,
1,1,2,3,5,8,13,21,34….where each term is the sum of the two previous ones. This
series governs how biological systems reproduce.

__1055__, The **Arabs** introduced decimal notation to **Spain**.

__15/5/1048__, The **Persian** mathematician and poet **Omar Khayyam**
was born at Nisipar. He was the first to solve cubic equations (those
containing terms to the power of three).

__830__, The Arabic text *Hisab al jabr w’al muqabalah* (The
Science of Reunion and Opposition) became the basis of **algebra** in the West. Renaissance scholars sometimes preferred the
Latin term ‘analysis’.

__665__, Death of Indian mathematician **Brahmagupta**
(ca. 598-665). He drew up formal rules for the use of **zero** in
mathematics, as a number not just as a placeholder.

__462__, Birth of **Aryabhata**, **Indian** mathematician who wrote on
the **powers and roots of numbers**.

__17/4/485__, Proclus, Greek mathematician, died in Athens.

__250__, **Diophantes of Alexandria** wrote
the first known book on **algebra**.

__200__, Chinese mathematicians used powers
of 10 to express numbers.

__120__, Death of **Nichomachus**,mathematician who
first formulated the concept of **Perfect
Numbers**. These are numbers whose factors, including 1, add to the number
itself; 6 = 3+2+1, and 28 = 14+7+4+2+1. 496 and 98,128 are the next two **Perfect Numbers**. By 2007, just 44 such
numbers were known.

__95 BCE__, First use of **negative numbers**, in China.

__323 BCE__, **Euclid**
published his work ‘*Elements’*, the
standard text on **geometry**. He proved
that there must be infinitely many **prime numbers**.

__395 BCE__, **Theodorus of Cyrene** demonstrated
that the square roots of 3,5,6,7,8,10, 12,13,14, 15 and 17 were **irrational**.

__445 BCE__, The earliest concept of **irrational numbers** (numbers like the square root of 2, or Pi, that have infinite decimal
places). **Hippacos
of Metapontium** discovered that some magnitudes are ‘not
commensurable’, such as the diagonal and sode of a square; they have no common
unit. Also at this time **Zeno of Elea** formulated paradoxes **contrasting continuity with discreteness**,
such as the notion that a faster runner cannot ever catch a tortoise that has a
headstart. These questions are still not fully answered today.

__465 BCE__, The dodecahedron, a solid with 12
faces, was described by **Hippasus** of Greece.

__545 BCE__, Death of **Thales of
Miletus**. He derived the ‘Thales Proposition’; that triangles over
the diameter of a circle are always right-angled.

__628 CE__, The Indian astronomer amd mathematician **Brahmagupta**
first described the concept of ‘**zero’** as a true number. By 300 BCE use of the
number zero was common in Babylonian mathematical texts. The name’zero’cpomes
from the Sanskrit ‘sunya’, meaning ‘nothing’; it became ‘sifr’ in Arabic, and
was latinised by **Leonardo Fibonacci** into ‘zephirum’

__876 BCE__, First known use of a
symbol for **zero**, in **India**. The actual concept of **zero** may have been known earlier than this.

__1300 BCE__, **Decimal numerals** in use in China.

__1725 BCE__, **Egyptian** geometrical uinderstanding was
advanced, with formulae for the volume of a truncated pyramid.

__1875 BCE__, The **Pythagorean Theorem** was known in Mesopotamia.

__1975 BCE__, **Quadratic equations**, where symbols up to the power of two are used,
were known and could be solved in Mesopotamia.

__2000 BCE__, **Decimal notation** first used in Mesopotamia.

__3000 BCE__, **Numerology** was being practised in Egypt. The art of numerology
helped develop the science of mathematics, along with the need to keep accounts
of trading and payments.

__3400 BCE__, In Sumeria, clay counting tokens and **written mathematical
symbols** first used.

**Appendix 1 – Calculations of Pi**

__1988__, **Japanese** **computer** scientist **Yasumasa Kanada** **calculated Pi to 201,326,000 decimal places**.

__12/4/1852__, **Ferdinand Lindemann** was born in
Hannover, Germany. In 1882 he proved that Pi is a transcendental number.

__25/1/1812__, Mathematician **William Shanks**
was born in Corsenside, England. He attempted a calculation of **Pi to 707 places in 1853**. However in
1944 it was discovered he had made an error at **place 528**, causing all digits thereafter to be erroneous.

__1717__, **Abraham Sharp** calculated **the value of Pi to 72 places**.

__605__, Use of decimal notation in India.
In China, **Pi was calculated to be
between 3.1415926 and 3.1415927**.

__200__, In China, a polygon of 3072 sides
was used to calculate **the value of Pi as
3.14159**.

**Appendix 2 – Prime Numbers**

__2018__, The largest **prime number**
so far known was calculated by Patrick Laroche. It had **24,862,048 digits**.

__1985__, The number composed of 1,031 ones in a row
was found to be** prime**.

__1985__, The largest-then-known **prime number**,(2
to the power 216,065) minus 1, with 66,050 digits,was discovered.

__1896__, **Jacques Hadamard** proved that, for large values
of a, the number of **primes** less than a approximates to a / log a.

__1859__, **Bernhardt Reimann** (1826-66) introduced the **Reimann Hypothesis**, which predicted the
frequency of **prime numbers** amongst all integers.

__1648__, Death of French monk **Marin Mersenne** (born 1588), who first
identified what are now know as **Mersenne Prime Numbers**; those whose formula is 2^{n}
– 1.

__1588__, Italian mathematician Pietro Cataldi discovedred the **largest known prime number, 524,287**. It
remained the largest-known prime for almost two centuries.