In2012, a Japanese mathematician, Shinichi Mochizuki, from KyotoUniversity solved one of the most complex mathematical theories. Thetheory is termed as the ‘abc conjecture’ took him over four yearsto calculate and the 500-paged document can be found on his website. His achievement is currently being verified by his peers but ifapproved, it would be one of the greatest achievements inmathematics’ this century. The concept simply states that
Forevery ε > 0, there exist only finitely many triples (a, b, c) ofcoprime positive integers, with a + b = c, such that:
Theseand others are among some of the world’s most complex concepts thathave proved challenging to prove or calculate.
Frompast knowledge and understanding of mathematics, I can’t agree withthis concept for now because mathematics is dynamically changing. Forinstance, the equation 0+100=0 may seem mathematically incorrect fornow but in a few years or decades, some mathematical genius would beable to prove it. For now, we just know that zero represents a nullor an empty set, any number added to zero is mathematically acceptedas that number itself. So for 0+100=0 is incorrect, the correctversion would be 0+100= 100. Working with the value zero is quiteinteresting for example addition and subtractions are interestinglysimple. Zero minus any number is negative of that number that is0-987= -987. It is like deducting something from nothing, trying toget something where nothing existed before. However, multiplicationis strictly zero. Any number multiplied by zero is a zero, no matterhow small or large the number is. Complexity starts when you startthe division process 100÷0 is completely different from 0÷100. Howso? If you divide a number by zero you get an infinite number but ifyou divide zero by any number, you get zero. For instance, 100÷0 isinfinite denoted by ∞ symbol but 0÷100= 100. We could go on and onabout this interesting bit of this puzzle but it’s just a tip ofthe big mathematics.
Mathematicshas been around for millions of years, in fact, it is nearly as oldas humanity itself from notched bones of ancient man to theHellenistic empires of Greece and the mathematical advances in Egyptand Mesopotamia. The name comes from the Greek word ‘mathema’which means –what one gets to know. Mathematics can be defined asthe study of relationships between magnitudes, quantities, and theirproperties. It also involves logical operations where there aredeductions of unknown parameters from known parameters. Historicallymathematics has always been regarded as the science of magnituderegarding geometry or in arithmetic numbers or mostly thegeneralization of the combination of both. Some sections ofmathematics are concerned with the study of patterns and shapes. Itwas not until the 19th century that mathematics suddenly startedgetting interests in drawing logical conclusions and involvesdifferent standard fields. Some of the fields involved in mathematicsinclude algebra, mathematical logic, number theory, calculus, andgeometry. Also, it involves more applied mathematics like statisticsand probability theory. The most important invention was the numberline, ranging from zero to nine all other numbers are pegged ontothese ten digits. The number line is a straight line that denotes theabstraction of real numbers or integers. The line is mostly appliedto use in the Cartesian planes. Right at the center of the numberline is the number zero.
TheHistory of Zero
Zerois both a numerical digit and a number used to represent a positionin the number system. It is the separator between the positive andnegative integers on the number line. However, as a digit, itspurpose is place-holding in the place value system. The nameoriginated from the Italian contraction of the word ‘zevero’which means empty. In English, it has several names like null, zero,naught, nil and naught. Other common informal or slang terms refer tozero as zilch or zip. According to Wallin (2002), zero is aphenomenal figure since it was born many centuries ago. He claimsthat from the stories made, something can be made from nothing. Itwas Brahmagupta who first brought the idea of the zero effect around650 AD. Early history differs from this statement by claiming thatzero was independently by the Mayans, Babylonians, and the Indianswhich could be true to an extent. Initially, he denoted a zero byplacing dots on numbers. He referred to these dots as ‘sunya’,meaning ‘empty place’ he was able to do operations like additionand subtraction, but the division of figures by zero only came lateron through G.W Leibniz and Isaac Newton. Another great mathematicianwho brought zero into great play was Rene Descartes. She found theCartesian coordinate system which greatly relies on the zero conceptsto date. If you have tried graphing a parabola or a triangle, thenyou must have come across Descartes origin which means the zeroorigins (0, 0). Today the use of zero is very common almost to thepoint of not being discussed, but it was the likes of Newton andLeibniz who finally made it easy to understand the concept of zero bydeveloping calculus.
Imaginehaving one less zero on your paycheck! It is only then that oneunderstands the importance of a zero. Take for instance the digit onehundred with an extra zero added it ceases to be just a hundred butone thousand, a tremendous change by adding a single placeholder.Zero is very transformative and is the basis of the coordinatesystem, the calculus and finally paved the way for more developmentin the engineering, financial economy, and the computer system. Ithas paved a way for more complex branches of mathematics in a waythat is too deep for basic understanding. Interestingly, zero hasunique characteristics for instance, it is an even number andbecause of its divisibility by two. It is neutral that means it isneither positive nor negative and is, therefore, the smallestnon-integer.
Thereare simple rules that determine the usage of the integers and areincorporated in the BODMAS system- Bracket Order DivisionMultiplication Addition and Subtraction. It is very easy tomanipulate simple operations that contain only two numbers, but whenthere are several numbers, it is easy to get it all mixed up.Luckily, mathematics is an organized discipline that determines rulesfor assistance in solving the problems. In this case BODMAS is anacronym that will guide you in the order in which to solve amathematical problem. If you don’t follow the BODMAS rule, then theanswer will be wrong. The rule is simple, to work out thecalculation, you have to work out what lies inside the bracketsfirst. You are then required to work out anything that involvespowers or a square root and all this time you have an obligation towork from left to right. Thirdly, calculate the divisions andmultiplication and finally complete with the additions andsubtractions. (About BODMAS)
BODMASis just the fundamentals of mathematics which has a broad spectrum.It is the basis of all calculations which eventually build up to formthe three most important fields of mathematics. (University ofColumbia, 2016) These are-
Thefoundation of mathematics involves the study of the set theories andmathematical logic. Whereas natural sciences investigate entitiesbased on time and space, mathematics applies different techniques inits investigation. According to Leon Horsten (2007) Natural sciencesuse Inductive methods of research whereas mathematical sciences useanalytical techniques from existing principles.
Thiscategory of mathematics is further broken down into quantity wherereal numbers, integers, and natural numbers are used in arithmeticoperations. It further explains the number system with complexnumbers that run to infinity. Other areas are structures and spacebased on the Cartesian planes. A very influential section of puremathematics is the concept of change and calculus was speciallyinvented to investigate the change.
Finally,this is the branch which concerns itself with specialized knowledgeused in engineering, business, science, and industry. All theseloosely fall into two categories, computational mathematics, andstatistics and other decision-making sciences.
Arguably,mathematics is by far one of the most prestigious and importantsubjects in the entire world. It makes the world go around leadingscientists have said that mathematics is life because all othersubjects are dependent on its principles and philosophies. Other thanits advantages to the daily lives of all individuals, it has one ofthe most prestigious awards similar to the Nobel Prize called FieldsMedal. It is awarded every four years to four people who have madesignificant achievements and accomplished in the mathematics world.Other recognizable prizes are the Wolf Prize in Mathematicsestablished in 1978, the Abel Prize, an international awardintroduced in 2003 and the Hilbert’s Problems which lists 23 openproblems that are very tough to solve and each problem solvedguarantees the winner a large sum of money. Despite its importance inthe application of various arrays of subjects like physics,chemistry, and the business world, studying mathematics developscritical and analytical skills in an individual. It also makes themhave clear, logical and imaginative brains that create developmentsand advances in the mathematical field. Who knows, maybe soon we willbe able to figure out that 0+100=0. For now, it remains to bemathematically wrong by all standards and rules. A number plus a zerois that number.
"Mathematics:Branches Of Mathematics". Infoplease.com.N.p., 2016. Web. 24 Mar. 2016.
"TheStory Of Mathematics – A History Of Mathematical Thought From AncientTimes To The Modern Day". Storyofmathematics.com.N.p., 2016. Web. 24 Mar. 2016.
Horsten,Leon. "Philosophy Of Mathematics". Plato.stanford.edu.N.p., 2007. Web. 24 Mar. 2016.
Weisstein,Eric W. "abcConjecture." From MathWorld–AWolfram Web Resource. http://mathworld.wolfram.com/abcConjecture.html