__Mathematics__

__Page last modified 3/1/2020__

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

__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.

__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.

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

__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.

__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.

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

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

__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.

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

__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.

__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**.

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

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

__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.

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

__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**.

__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.

__25/1/1812__, 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.

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

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

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

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

__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.

__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.

__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 trhe 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).

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

__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).

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

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

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

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

__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.

__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.

__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..

__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.

__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’.

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

__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.

1588, Italian mathematician Pietro
Cataldi discovedred the **largest known prime number, 524,287**. It remained the
largest-known prime for almost two centuries.

__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).

__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.

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

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

__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.