Zero

Zero is the point when reckoning begins. In mathematics it is a number meaning nothing.

Records show that the ancient Greeks seemed unsure about the status of zero as a number. They asked themselves, "If you don't have anything, why do you need a number?", leading to philosophical  arguments about the nature and existence of zero.

The Mayan civilisation constructed quite early a very sophisticated number system, possibly more advanced than any other in the world at the time. It included one of the earliest instances of the explicit zero in the world, which they represented as a shell shape.

The concept of zero as a digit in the decimal place value notation was developed in India, The earliest text to use a decimal place-value system, including a zero, was the Lokavibhāga, a Jain text from the mid fifth century.

The number 605 in Khmer numerals, from a 683 AD inscription. Early use of zero as a decimal figure

In the Medieval period there were religious arguments about the nature and existence of zero. Zero and negative numbers were banned in Florence in the 13th century because they were considered a thing of the devil.

Although mathematicians have used zero since at least the 8th century, the word 'zero' was first recorded in English only in 1604.

When he published his equations of general relativity Albert Einstein failed to notice that his theory predicted an expanding universe. Alexander Friedmann, a Russian mathematician, found to his amazement Einstein had made an elementary algebraic error that caused him to overlook a solution to his own equations. Einstein had divided by zero at one point in his calculations, a mathematical impossibility.

Humans are unable to burp in zero gravity environments.

Honeybees, despite having the brain size of a sesame seed, can understand the concept of zero.

In English, zero quantities are plural by default. Therefore you shall write "0 results found", "I have found no results".

Originally written for Songfacts

Science

Science (from Latin scientia, meaning "knowledge") is a systematic enterprise that builds and organizes understanding about the natural world. in the form of testable explanations and predictions about the universe.

Facts about the natural world have been described since classical antiquity. Aristotle wrote that the truth can be found through observation and induction. This was his scientific method. Socrates' example of applying philosophy to the study of human things, including human knowledge itself was a turning point in the history of early philosophical science.

The School of Athens by Raphael. Aristotle is pictured in blue in the centre arch

Scientific methods have been used since the Middle Ages. The English philosopher and Franciscan friar Roger Bacon, for instance, placed considerable emphasis on the study of nature through empirical methods.

The dawn of modern science is often traced back to the early modern period and in particular to the scientific revolution that took place in 17th-century Europe. During this period centuries scientists began to formulate knowledge in terms of laws of nature such as Sir Isaac Newton's laws of motion.

Robert Boyle, John Wilkins, Christopher Wren and other leading scientists founded a learned society now known as the Royal Society at London's Gresham College on November 28, 1660.

Not surprisingly, active Christians, with their interest in God's creation, brought the society into existence. In fact, its membership was overwhelmingly Puritan in makeup. It grew out of the meetings of the "Invisible College" who gathered in the late 1640s at the home of the chemist Robert Boyle's favorite sister, Katherine. She supported the Parliamentarians (and Puritans) in the revolt against Charles I. Of deep intelligence herself, Boyle welcomed the group into her house so that she might share the new findings.

When the Royal Society was chartered by King Charles II of England on July 15, 1662, it was the first scientific society in history.

The first joint Secretary of the Royal Society, Henry Oldenburg, published the first issue of Philosophical Transactions of the Royal Society, the world's longest-running scientific journal on March 6, 1665.

Title page of 1st edition of the Philosophical Transactions of the Royal Society, by Henry Oldenburg

Over the course of the 19th century, the word "science" became increasingly associated with the scientific method itself, as a way to study the natural world, including physics, chemistry, geology and biology.

The term `biology' was coined around 1800, by, amongst others, Gottfried Reinhold Treviranus, a professor at Bremen, and the French naturalist Jean-Baptiste Lamarck.

The term scientist was first used by theologian, philosopher and historian of science William Whewell in 1840. He meant it to distinguish those who sought knowledge on nature from those who sought other types of knowledge. Previously, people investigating nature called themselves "natural philosophers".

"Zohnerism", the use of true fact(s) to lead a scientifically ignorant public to a false conclusion, was coined in 1997 after 14-yr-old Nathan Zohner gathered petitions to ban the ''dangerous chemical dihydrogen monoxide'' (water) from school as the basis of his science project, titled "How Gullible Are We?"

Modern science is usually divided into separate areas of study, such as astronomy, biology, chemistry, geology, mathematics and physics.

Scientists in a laboratory of the University of La Rioja.

The Bible described many scientific truths in the Old Testament, thousands of years before man discovered them. Here are some examples:

Scientific Fact or Principle Bible reference Date of discovery by man

Life originated in the sea Genesis 1 19th Century
Man was the last animal created Genesis 1 15th Century
The Earth is held in place by invisible forces Job 26:7 1650
The Earth is round Isaiah 40:22 15th Century

"The Blue Marble" is a famous photograph of the Earth 

Certain animals carry diseases harmful to man Leviticus 11 16th Century
Quarantine for disease control Leviticus 13 17th Century
Blood is necessary for life Leviticus 17:11 19th Century
Oceans have natural paths in them Psalms 8:8 1854
Mountain ranges on ocean floor Job 2 1950s
Light is a particle and has mass (a photon) Job 38:19 1932
Radio astronomy (stars give off signals) Job 38:7 1945
Infinite number of stars exist Genesis 15:5 1940
Stars move through space Job 38:32 19th Century
Plants use sunlight to manufacture food Job 8:16 1920.

Here is a list of songs about science.

Source Christianity

Pi

Pi is a mathematical constant, the ratio of a circle's circumference to its diameter, which is commonly approximated as 3.14159.

The circumference of a circle is slightly more than three times as long as its diameter.

HISTORY

Until 1706 the ratio of a circle's perimeter to its diameter was known as “the quantity which, when the diameter is multiplied by it, yields the circumference." The Greek letter pi was introduced as a simpler definition by the Welsh mathematician William Jones (1675- July 3, 1749) in his 1706 work Synopsis Palmariorum Matheseos; or, a New Introduction to the Mathematics. He chose π the Greek for p as it was the first letter of “periphery” or “perimeter” which were the words then used for circumference.

William Jones by William Hogarth

A bill before the State Legislature of Indiana in 1897 tried to set the value of pi at 3.2. It was approved by the House, but not the Senate.

The publisher and writer John Taylor first proposed the idea that Egypt's Great Pyramid at Giza, built around 2589 to 2566 B.C., was designed based on pi. Taylor found that the vertical height of the pyramid has the same relationship to the perimeter of its base as the radius of a circle has to its circumference. Other people have since made the link between the Great Pyramid and pi as well, although it may not have been intentional

DIGITS

Pi is an irrational number: its decimal value goes on for ever, never stopping or repeating.

British mathematician William Shanks famously took 15 years between 1858 and 1873 to calculate π to 707 digits, but made a mistake in the 528th digit, rendering all subsequent digits incorrect.

The value of pi was calculated to a world record 50 trillion digits by Timothy Mullican in Huntsville, Alabama, USA on January 29, 2020. Using a 2012-era computer (Ivy Bridge) along with a very large array of 48 modern hard drives. it took 10 months to complete the computation. 

The value of pi was calculated to a world record 62,831,853,071,796 digits by the University of Applied Sciences of the Grisons in Chur, Switzerland, on August 19, 2021. Using a computer with one terabyte of RAM and 510 terabytes of disk space, they completed the calculation within 108 days. 

The value of pi was calculated to a world record 100 trillion digits on March 21, 2022 by Emma Haruka Iwao on Google Cloud. Iwao used the y-cruncher program to calculate the digits of pi. The program uses the Chudnovsky algorithm, which is a fast and accurate way to calculate pi. The calculation took 157 days to complete and used 515 terabytes of storage.

A pi pie. 

In an episode of Star Trek: The Original Series, Spock commands an evil super computer to compute pi to the last digit (which, you no doubt realize is highly illogical …).

The first 144 digits of pi add up to 666 (which many scholars say is “the mark of the Beast”). And 144 = (6+6) x (6+6).

If you list the first 360 digits of PI, the last 3 digits will be "360". PI comes from a circle which has 360 degrees.

You have to go to the 606th and 607th digits in the decimal expansion of pi (3.14159265…) before you see the number 68. Every other two-digit number occurs earlier in the value of pi.

According to two mathematicians, 39 digits of π are sufficient to perform most cosmological calculations, since that is the accuracy necessary to calculate the circumference of the observable universe with a precision of one atom.

The world record for memorizing the value of pi was set by Rajveer Meena at the VIT University, Vellore, India, on March 21, 2015. Rajveer, a resident of Mohocha village in Swaimodhapur district of Rajasthan, correctly recited from memory its first 70,000 digits. He wore a blindfold throughout the entire recall, which took him 9 hours 27 minutes.

FUN PI FACTS

Pi Day is celebrated around the world on March 14 or 3.14 and officially kicks off at 1:59 pm. When combined the date and time results in 3.14159, the approximate numerical value of pi.

A mosaic outside the Mathematics Building at the Technical University of Berlin. By Holger Motzkau - 

March 14 may be Pi Day but the ultimate Pi Day was March 14, 1592, or 3.14.1592 as the Americans write it, which has the first seven digits of pi.

When performing calculations for interplanetary navigation, NASA scientists only use Pi to the 15th decimal point. When calculating the circumference of a 25 billion mile (40 billion kms) wide circle, for instance, the calculation would only be off by 1.5 inches (38.1 mm).

If you write "3.14" on a piece of paper and hold it up to a mirror, it looks like the word "PIE".

You can remember the value of Pi (3.1415926) by counting the letters of each word in the phrase "May I have a large container of coffee?"

Source Daily Express

Numerology

Traditionally Greek and Hebrew numbers all applied to a letter (Alpha =1, Beta =2 etc). Many numbers in the Bible contain symbolic meaning. The best known is 666 the Number of the Beast. 6 symbolises man and 7 spiritual perfection. In the scriptures the sentences are made up of an abnormally high amount of combinations of 7s.

8 is the number that symbolizes Resurrection. There are eight examples of resurrection in the Bible.

In Greek, the name of Jesus is spelled I H S O U S (iota, eta, sigma, omicron, upsilon, sigma). Substituting in the Greek numeral system the equivalent numerical values to each letter in the name of Jesus (iota, 10; eta, 8; sigma, 200; omicron, 70; upsilon, 400; sigma, 200) and adding them up, the total is 888 - the resurrection number.

In the original Hebrew, if you skip 50 letters, then another 50, then another 50 the word Torah is spelt at the beginning of Genesis and Exodus, whilst the word YHVH is spelt out in Leviticus. For example, take the final taf' , in the word BereshiT, in Genesis 1:1 and then count 49 letters. The 50th letter is a vav u. Count again 49 letters and the 50th letter is resh r. Repeating a count of 49 letters and the 50th letter is hey v. This spells the word TORAH.  Using the same skip length of 50 and applied to the last taf , in Exodus 1:1, ShemoT. The search here also spells TORAH .

Exodus 1:1-6.  Four letters, 50 letters apart, starting from the first taw on the first verse, form the word תורה (Torah).

Pythagoras and his students believed that everything was related to mathematics, and felt that everything could be predicted and measured in rhythmic cycles. In his system:
1 was Unity and represented Deity, which has no parts
2 was diversity, and therefore disorder: the principle of strife and all evil;
3 was Perfect Harmony, or the union of unity and diversity
4 was Perfection. It is the first squara (2x2 = 4).
5 was the prevailing number in Nature and Art
6 was Justice
7 was the Climatic number in all diseases.

Pythagoras, the man in the center with the book,in Raphael's The School of Athens

William Shakespeare was born on 23/4/1564 and died on 23/4/1616. If you take the day of the months when Shakespeare was born and died and add them together (23+23=46), the total of 46 which was also Shakespeare's age when the King James Bible was completed. William Shakespeare is an anagram of "I like a Psalm." The 46th word from the beginning of Psalm 46 is "Shakes" and the 46th word from the end is "Spear".

Numerologists believe that events linked to the time 11:11 appear more often than can be explained by chance or coincidence. For example, the Armistice that ended the fighting in western Europe of the First World War took effect at 11 a.m. Paris time on November 11, 1918, "the eleventh hour of the eleventh day of the eleventh month". However, skeptics say that examples of 11:11 phenomena in world events are examples of post-hoc reasoning and confirmation bias.

11-11-11 11:11:11 example. By Xantolus - Wikipedia1

Former professional baseball right fielder Larry Walker was fixated on the number 3. He wore number 33, was married on November 3 at 3:33 and his phone number had “as many threes as the phone company would allow.” In 1993, he signed a $3 million contract with the Montreal Expos.

Some Chinese assign a different set of meanings to the numbers and certain number combinations are considered luckier than others. 13 is among the luckiest of numbers. In Mandarin, when the numbers 1 and 3 are combined to make 13, the resulting spoken word can mean 'assured growth'.

Despite the long history of numerological ideas, the word "numerology" is not recorded in English before c.1907.

Source Brewer's Dictionary of Phrase and Fable

Number

HISTORY

Pythagoras and his followers considered 10 the most sacred number, as 10 = 1+2+3+4, which represented existence (1), creation (2), life (3) and the four elements, earth, air, fire and water (4).

The ancient Greeks did not consider One to be a number at all. A number, said Euclid, is an “aggregate of units”, so numbers began at Two.

In 500 AD some Indian mathematicians suggest the use of the symbol "0" meaning zero or nothing.

By 810 the Arabs had established the modern system of numerals which we use today. They'd picked it up around 750 from Hindus, who had invented it some 150 years earlier.

Westerners call our numbers "Arabic," because the notation system came to Europe via Islamic Arab mathematicians. The first written record of Arabic numbers in the West is a Spanish codex from 976.

Adoption of the Arabic numeric system crept along among the educated elite until the fourteenth century, when Italian merchants finally ditched their Roman I's and V's. Other traders wisely followed suit.

The Cistercian numerals are a forgotten number system, developed by the Cistercian monastic order in the early thirteenth century, much more compact than Arabic or Roman numerals: with a single character you could write any integer from 1 to 9999.

Although mathematicians have used zero since at least the 8th century, the word 'zero' was first recorded in English only in 1604.

American Jeremy Harper counted aloud every number up to a million, live on the Internet. He spoke for 16 hours a day, completing the marathon after 89 days on September 14, 2007.  Harper did not leave his apartment or shave until he finished.

NUMBERS AND WORDS

Until the 19th century, a "long hundred" was still a term used to mean 120, especially in the measurement of numbers of fish sold.

The word “twelve” is from the old English twelf, literally “two left” (over 10).

After a million comes--- billion, trillion, quadrillion, quintillion, sextillion, septillion, octillion, nonillion, decillion, and undecillion.

In English, every number shares at least one letter with the numbers immediately before and after: One shares an 'O' with Two, which shares a 'T' with Three, which shares a 'R' with "Four," and so on indefinitely)

Every odd number that exists has the letter "e" in it.

If you were to spell out numbers from one, you would not find the letter 'A' until you reach 'One Thousand'.

Forty is the only number which when spelled out in English has its letters in alphabetical order.

Four is the only number that has the same amount of letters as its actual value.

The highest number that can be spelled out without using any letter more than once is five thousand.
The next highest is eighty-four.

NUMBERS IN OTHER CULTURES

In China, 13 is considered to be among the luckiest of numbers and people often pay huge amounts for items that contain it.

The Andamanese language has only two words for numbers: they mean 'one' and 'more than one'.

In Old Norse, the word hundrad, from which our 'hundred' derives, originally meant 120.

In Thai, the number 5 is pronounced "ha" -- so instead of saying "hahahahaha," Thai speakers will sometimes write "55555."

FUN WITH NUMBERS

2006 111,111,111 x 111,111,111 = 12,345,678,987,654,321

Multiply 37,037 by any single number (1-9), then multiply that number by 3. Every digit in the answer will be the same as that first single number.

The smallest number that can be divided exactly by each of the numbers between one and 10 is 2,520.

1 divided by 998001 gives a complete sequence from 000 to 999 in order.

If you multiply a number with 9, and add all the digits of the resulting number, the sum would always come out to be 9.

PERFECT NUMBER

A perfect number in mathematics is an integer that is equal to the sum of the smaller numbers that divide it exactly. So 6 (=3+2+1) and 28 (=14+7+4+2+1) are perfect.

After 6 and 28, the next three perfect numbers are 496 and 8,128 and 33,550,336.

Nobody knows if there are any odd numbers that are perfect.

The ancient Greeks also thought six perfect as a man's height was six times his foot length. Plato considered the number 10 to be perfect, as there are 10 fingers on both hands and 10 toes.

Sources Christianitytoday.com, Daily Mail, Daily Express

Mathematics

Even though mathematics is used to measure and predict and model, it's debated whether math is inherent to the universe or just something we invented to describe/measure/predict natural phenomenon.

The Ancient Babylonians did mathematics in base 60, rather than base 10 as in the metric system. This gave us 60 seconds in a minute, 360 degrees in a circle, etc.

The Plimpton 322 clay tablet from ancient Babylon  confounded mathematicians when it was revealed that it’s markings were complex calculations made 2,000 years before Pythagoras tackled the problems.

Archimedes was one of the first mathematicians to study convex curves, but interest in their analysis waned until the 19th century. This was due to a lack of mathematical tools and techniques for studying these types of curves, as well as the fact that other areas of mathematics were more pressing and relevant at the time.

3rd century BC Greek mathematician Diophantus of Alexandria wrote a series of thirteen books called Arithmatica (six surviving), which are still considered crucial for defining modern algebra. The books included over 150 algebra problems that Diophantus solved.

Hypatia, an early 5th century Alexandrian, was the first woman to teach mathematics—unfortunately, a mob of Christian zealots killed her.

The word “algorithm” traces back to the 9th-century Persian mathematician Al-Khwarizmi, whose name was Latinized as Algoritmi. His step-by-step methods for arithmetic were so influential that medieval scholars began calling such procedures “algorisms,” the term that eventually evolved into “algorithm.”

The Italian mathematician Leonardo Fibonacci (c. 1170 – c. 1250) popularized the Hindu–Arabic 0-9 numeral system and place value to the Western World primarily through his composition in 1202 of Liber Abaci (Book of Calculation). The book showed the practical use and value of the new Arabic numeral system by applying the numerals to commercial bookkeeping, converting weights and measures, calculation of interest, money-changing, and other applications. Liber Abaci was well received throughout educated Europe and had a profound impact on European thought.

Leonardo Fibonacci, the 

In late medieval Europe the symbols (P (with line p̄) was used for plus, and M (with line m̄) for  minus.)  The "+" & "-" wase first used in Johannes Widmann's 1489 German treatise Behende und hüpsche Rechenung auff allen Kauffmanschafft  (Nimble and neat calculation in all trades) when he referred to the symbols − and + as minus and mer.

The equal sign ("=") was invented in 1557 by Welsh mathematician Robert Recorde, who was fed up with writing "is equal to" in his equations. He chose the two lines because "no two things can be more equal."

Recorde first used the equal sign in his 1557 book The Whetstone of Witte. The work is also notable for being the first book in English to use the plus and minus signs

The passage in The Whetstone of Witte introducing the equals sign

The invention of logarithms as an aid to calculation is attributed to a Scottish nobleman named John Napier (1550- April 4, 1617) .

Though Napier is also credited with creating one of the earliest calculating machines, known as 'Napier's Bones', and with popularizing the use of the decimal point, he only considered his mathematical studies to be a mere hobby. A fervent Protestant, he regarded his book The Plaine Discovery of the Whole Revelation of St. John (1593), an explanatory work on the Book of Revelation, to be his most important contribution to society.

John Napier

Fermat’s Last Theorem is a mind-blowing mathematical conundrum dreamed up by Pierre de Fermat in 1637. The French mathematician wrote in the margin of his work he’d proved it himself — but didn’t bother to note how.

One of the most important mathematical books ever written, Isaac Newton's Principia Mathematica, needed 360 pages to prove that 1 + 1 = 2. The book itself, first published on July 5, 1687, is considered so advanced and hard to understand that it's rarely used in academia at all.

Principia Mathematica contained a simple calculation error that went unnoticed for 300 years. A college student found it.

The Greek letter pi was introduced in 1706 for the ratio of a circle's perimeter to its diameter by the Welsh mathematician William Jones (1675-1749). He chose the Greek for p as it was the first letter of "periphery" or "perimeter" which were the words then used for circumference.

Goldbach's conjecture is one of the most famous unsolved problems in mathematics. It was first proposed by the mathematician Christian Goldbach in a letter to Leonhard Euler in 1742.

The conjecture states that every even natural number greater than 2 can be expressed as the sum of two prime numbers. For example, 4 = 2 + 2, 6 = 3 + 3, 8 = 3 + 5, and so on. While the conjecture has been extensively tested and found to be true for all even numbers up to at least 4 × 10^18, no one has been able to prove it for all even numbers.

Many mathematicians have worked on Goldbach's conjecture over the years, and there have been numerous partial results and related conjectures proposed. However, despite considerable effort, the conjecture remains unproven.

The inaugural International Mathematical Olympiad (IMO) began on July 21, 1959 in Romania. This event marked the beginning of what would become one of the most prestigious and well-known competitions for pre-university students worldwide, focusing on mathematics.

In an episode of Star Trek The New Generation aired in 1989 Picard states that Fermat's last theorem would still be unsolved 700 years in the future. Picard was wrong. In 1994 British mathematician Andrews Wiles solved the conundrum.

Futurama writer Ken Keeler (who holds a PhD in applied mathematics), created a mathematical theorem just for the purpose of using it in a Futurama episode to expose young people to higher level math.

Americans call mathematics 'math', saying that the function of the same is a singular noun and with that logic, they prefer saying 'math', which is singular too. On the other hand, speakers of British English would always say the plural 'maths'.

“Math anxiety" is a condition that causes people to perform poorly in mathematics. Scans have revealed that the area of the brain that is triggered when someone has math anxiety overlaps the same area of the brain where bodily harm is registered.

Fibonacci

Fibonacci was the name given to medieval Italian mathematician Leonardo Bonacci also known as Leonardo of Pisa, who was born in 1175 and died around 1250.

The name came from a misreading of "filius Bonacci" (son of Bonaccio) on a manuscript.

19th century statue of Fibonacci in Camposanto, Pisa. By Hans-Peter Postel 

The Fibonacci sequence, begins 1,1,2,3,5,8 with each number equal to the sum of the previous two.

Fibonacci introduced the Fibonacci sequence in a discussion of a problem about breeding rabbits.

Fibonacci numbers play a part in describing many natural processes, particularly in the field of botany.

November 23 marks the celebration of Fibonacci Day. It is observed every year on November 23 – really 11/23, since formatting makes a difference here. 

The number of petals on a daisy is always a Fibonacci number, with 21, 34 or 55 most common.

If you trace back the family tree of a drone bee, the number of parents in each generation follows the Fibonacci sequence.

A game for two called Fibonacci, played on a hexagonal board, was invented by Thomas Naylor in 1990.

The last year that was a Fibonacci number was 1597. The next one will be 2584.

Now best known for his sequence, Fibonacci's real claim to fame is the major part he played in introducing the numbers we now use to replace Roman numerals. He did so in his Liber Abaci (Book Of Calculation) in 1202. He also wrote the Practica Geometriae, which includes eight chapters of theorems based on Euclid’s Elements and Divisions.

A page of Fibonacci's Liber Abaci from the Biblioteca Nazionale di Firenze

Source Daily Express

Calculus

Calculus as the math of motion and change; while basic math deals with static objects, calculus uses derivatives to measure how fast something is changing at a specific moment and integrals to add up those tiny changes to find a total result, like distance or area.

The word "calculus" comes from the Latin for "small stone", referring to the pebbles used on an abacus. 

Mathematics involving infinitesimals dates back to ancient Greece, where Archimedes developed early methods for computing areas and volumes. 

The Babylonians were using a rudimentary form of calculus to calculate Jupiter's displacement each day along the ecliptic, the path that the sun appears to trace through the stars. Historians had thought such techniques did not emerge until more than 1,400 years later, in 14th-century Europe. 

On November 11, 1675, Gottfried Leibniz demonstrated integral calculus for the first time, finding the area under the graph of y = ƒ(x). Isaac Newton independently developed his own form of calculus around the same time, and the two men became embroiled in a bitter priority dispute. Leibniz is credited with introducing much of the notation still used in calculus today. 

Leibniz at his candlelit desk writing the integral calculus notation on parchment.

Nikola Tesla was able to do integral calculus in his head, leading his teachers to believe he was cheating. 

Calculus as a formal discipline underpins much of modern science and engineering, from calculating planetary orbits to modelling the spread of disease.

Calculator

In 1642 Blaise Pascal designed and built a mechanical adding machine. It was the first mechanical calculator in history.

On June 14, 1822 English mathematician, Charles Babbage, proposed a difference engine, an automatic, mechanical calculator designed to tabulate polynomial functions. The proposal was made in a paper presented to the Royal Astronomical Society, titled "Note on the application of machinery to the computation of astronomical and mathematical tables". His proposed machine used the decimal number system and was powered by cranking a handle.

The first difference engine built from Babbage's design. Wikipedia

The American Arithmometer Company was established in St. Louis, Missouri in 1886 to produce and sell an adding machine that William Seward Burroughs was developing. The inventor received a patent for the first successful adding machine in the US on August 21, 1888. American Arithmometer Company, became Burroughs Corporation and evolved to produce electronic billing machines and mainframes, and eventually merged with Sperry to form Unisys.

An early Burroughs adding machine

Beat author William S. Burroughs was a grandson of William Seward Burroughs. He wrote  a collection of essays called The Adding Machine.

American inventor Herman Hollerith invented the first device that recorded data on a medium, which could then be read by a machine in the late 1880s. He was inspired by conductors using holes punched in different positions on a railway ticket to record traveler details such as gender and approximate age.

Hollerith developed his electromechanical punched card tabulator to assist in summarizing information and, later, accounting. He was issued US patent #395,791 for the 'Art of Applying Statistics' on January 8, 1889. His invention of the punched card tabulating machine marks the beginning of the era of semiautomatic data processing systems.

Hollerith built machines under contract for the Census Office, which used them for the 1890 census. Clerks used keypunches to punch holes in the cards entering age, state of residence, gender, and other information from the returns.

Replica of an early Hollerith punched card tabulator and sorting box Photo by Adam Schuster Flickr:

In 1896 Hollerith started his own business when he founded The Tabulating Machine Company. Many major census bureaus around the world leased his equipment and purchased his cards, as did major insurance companies.

Hollerith built machines under contract for the Census Office, which used them for the 1890 census.

In 1948 the Curta calculator, a hand-cranked, barrel-shaped calculator small enough to fit in the pocket and capable of basic calculations was introduced.

The mathematics master of Harrow Schhol predicted to the Mathematical Association in a speech on April 9, 1953 that by 2003, schoolchildren would be working out sums on calculating machines and there would be no multiplication tables. He said: "Each maths room will have its calculating machine, and the child on duty for the day will do any calculating needed."

The ANITA Mark VII and ANITA Mark VIII calculators were launched simultaneously in late 1961 as the world's first all-electronic desktop calculators.

Photo of Anita Mk VIII calculator by MaltaGC at English Wikipedia

The first handheld calculator was a 1967 prototype called "Cal Tech", whose development was led by Jack Kilby at Texas Instruments in a research project to produce a portable calculator.

The first portable calculator, The Canon Pocketronic, was placed on sale in Japan in 1970, and were soon marketed around the world. A development from the "Cal-Tech" project, it was designed around three MOS circuits it could add, subtract, multiply, and divide and sold for less than $400. The Pocketronic had no traditional display; numerical output was on thermal paper tape.

Texas Instruments introduced its first calculator, the Datamath (or TI-2500), in 1972. The device carried out basic arithmetic and sold for $149.95.

The first slimline digital pocket calculator was the Sinclair Executive, which was launched in 1972. It cost about three times the average weekly wage but set the standard. The Sinclair calculators were successful because they were far cheaper than the competition.

The HP-35, the world's first handheld scientific calculator, was introduced by Hewlett-Packard on February 1, 1972. This small, yet powerful calculator, named for its 35 keys, could perform functions like trigonometry, logarithms, and exponentials, which were previously only available on large desktop calculators or done manually using slide rules. Its compact size and innovative features quickly made it a hit, even exceeding sales expectations, and ultimately led to the decline of the slide rule.

An HP-35 pocket calculator. By Seth Morabito 

Source The Independent 3/11/07

Arithmetic

Arithmetic is literally, the art of counting. The word, in its oldest Greek form, comes from the word 'arithmetike,' which combines the ideas of two words in Greek, arithmos, meaning "number," and techne, referring to an art or skill.

In ancient China, Egypt, Babylon, and early civilizations generally, arithmetic was used for commercial purposes, records of taxation, and astronomy.

The Ancient Egyptians used sums of unit fractions (1/n), supplemented by the fraction 2/3, to express all other fractions. For example, the fraction 2/7 was the sum of the fractions 1/4 and 1/28. Using this system, the Egyptians were able to solve all problems of arithmetic that involved fractions.

The big contribution to the development of arithmetic was made by the ancient Greek mathematicians, in particular Pythagoreans, who tried to define all regularities of the world in terms of numbers.

Legend has it that when listening to the sounds made by a blacksmith striking his anvil, Pythagoras was led to a perception of the relationship between arithmetic ratios and harmonic intervals in music.

Diophantus was an third century Alexandrian Hellenistic mathematician, who was the author of a series of books called Arithmetica, many of which are now lost. He used a special sign for minus, and adopted the letter s for the unknown quantity.

Title page of the original 1621 edition of the Latin translation

It wasn't until about 500AD that some Indian mathematicians suggested the use of the symbol “0” meaning zero or nothing.

During the Dark Ages in Europe, knowledge of arithmetic was preserved in India and later among the Arabs.

With the development of trade and overseas exploration in Europe. Hindu-Arabic numerals replaced Roman numerals, allowing calculations to be made on paper, instead of by the abacus.

The invention of logarithms by Scottish mathematician John Napier in 1614 and of the slide rule ten years later helped make the manipulation of the arithmetic processes easier.

The step reckoner was a digital mechanical calculator invented by the German mathematician Gottfried Wilhelm Leibniz around 1672 and completed in 1694. It was the first calculator that could perform all four arithmetic operations - addition, subtraction, multiplication and division.

Replica of Leibniz's stepped reckoner in the Deutsches Museum . By User:Kolossos

Although an excellent mathematician, Sir Isaac Newton was incapable of performing simple mental arithmetic.

A number is divisible by 3 if the sum of the digits is divisible by 3. We know the number 627, for instance, is divisible by 3 because 6+2+7=15, which is divisible by 3.

Algebra

Algebra is a method of solving mathematical problems by the use if symbols (letters and signs) when figures are inadequate. More advanced algebra is used to work out general problems such as the equations derived by Albert Einstein.

Early forms of algebra were developed by the Babylonians.

The tradition of Babylonian algebra was revived by the Greeks in Alexandria, where Diophantus wrote a treatise called Arithmetica in about AD 200. He used a special sign for minus, and adopted the letter s for the unknown quantity.

Greek algebra in its turn spread to India, China and Japan. But it achieved its widest influence through the Arabic transmission of Greek culture.

Algebra comes from the Arabic word al-jabr, an ancient medical term meaning "the reunion of broken parts."

‘Algebra’ was originally the name given to the study of equations. In the 9th century, the Arab mathematician Muhammad ibn-Musa al-Khwarizmi used the term al-jabr for the process of adding equal quantities to both sides of an equation. When his treatise was later translated into Latin, al-jabr became ‘algebra’ and the word was adopted as the name for the whole subject. 

Al-Khwarizmi’s name was Latinized as Algorithmi (the word algorithm is his name).

Summa de arithmetica, thought to be the first printed work on algebra, was written by Luca Pacioli and first published in 1494. It contains a comprehensive summary of Renaissance mathematics, including practical arithmetic, basic algebra, basic geometry and accounting, written for use as a textbook and reference work.

1994 Italian stamp commemorating the 500th anniversary of Summa

Welsh mathematician Robert Recorde invented the equal sign in 1557 as he was fed up with writing “is equal to” in his equations. He chose the two lines (“=”) because “no two things can be more equal”. 

Recorde' introduced the equal sign in his book The Whetstone of Witte, whiche is the seconde parte of Arithmeteke: containing the extraction of rootes; the cossike practise, with the rule of equation; and the workes of Surde Nombers .With the publication of this book Recorde is credited with introducing algebra into England. 

In the 16th century, prestigious mathematics professorships could be "won" by defeating the current professor in a public algebra competition.

Rene Descartes's system of mathematical co-ordinates (using numbers to locate a point on a surface) meant that geometrical problems could be solved by using algebra. He was also the first to use the last letters of the alphabet to designate unknown quantities and first letters to designate known ones. (As in a(b+c) ).

Queen Victoria was so charmed with Alice in Wonderland that she requested something else by the same author be brought for her perusal. She was not amused when she received a copy of Lewis Carroll's Syllabus of Plane Algebraical Geometry.

As a child Albert Einstein spent his evenings with his Uncle Jakob working through algebraic problems. Uncle Jakob compared algebra to hunting a little animal. You didn't know the name of the animal, so you called it "x". When you finally caught the animal you gave it the correct name.

When he published his equations of general relativity Einstein failed to notice that his theory predicted an expanding universe. Alexander Friedmann, a Russian mathematician, found to his amazement Einstein had made an elementary algebraic error that caused him to overlook a solution to his own equations. Einstein had divided by zero at one point in his calculations, a mathematical impossibility. 

People in Madagascar perform algebra on tree seeds in order to tell the future. The centuries-old practice, called Sikidy, derives from Islamic influence brought to the island by medieval Arab traders.

Abacus

An abacus is a tool that has been used since ancient times for performing arithmetic calculations. It consists essentially of a tablet or frame bearing parallel wires or grooves on which counters or beads are moved.

Use of the abacus, with its beads in a rack, was first documented in Han Dynasty China in about AD 190.

According to legend, the abacus was invented by a man named Li Sou working for the Yellow Emperor. Li used a big mud plate and white pearls, which were divided into 10 strings of 10 beads.

"Abacus" derives from the Hebrew ibeq, meaning to " wipe the dust" or from the Greek abax, meaning "board covered with dust", which describes the earlier calculating devices used by the Babylonians.

Photo Abacus 1680-1117 by Paul Schadler

The Chinese version was the speediest way to do sums for centuries and, in the right hands, can still outpace electronic calculators.

The abacus is still in regular use in eastern countries, and in China it is called a suanpan (computer tray).

The soroban is an abacus developed in Japan. It is derived from the ancient Chinese suanpan, imported to Japan in the 14th century.

In Japan, the latest versions of the abacus include a dual bead and digital calculator.

The standard size of a modern Japanese abacus is smaller than the Chinese one. The Japanese abacus has 1+4 beads per row, rather than 2+5 for the Chinese.

A suanpan (top) and a soroban (bottom). 

There are classes in Japan that teach kids how to use the Soroban abacus to develop faster skills in arithmetic. After a few years they no longer even need to use a real abacus to perform fast mental calculations since they can already visualize an image of it.

Source The Independent November 3, 2007