Big Ideas Simply Explained (BISE) Introduction to The Math Book

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Big ideas simply explain the math book big ideas simply explain the math book introduction you’re listening to world reading club presented by hakeem ali-bocas alexander

Here on callin social podcasting presented by hakeem ali-bocas alexander for world reading club in association with uniquilibrium this edition’s reading focus comes to us from big ideas simply explained the math book introduction

And we’ll get right into that hello curtis curtis j all right let’s take a look at this the history of mathematics reaches back to prehistory when early humans found ways to count and quantify things

In doing so they began to identify certain patterns and rules in the concepts of numbers sizes and shapes they discovered the basic principles of addition and subtraction

For example that two things whether pebbles berries or mammoths when added to another two invariably resulted in four things while such ideas may seem obvious to us today

They were profound insights for their time they also demonstrate that the history of mathematics is above all a story of discovery rather than invention

Although it was human curiosity and intuition that recognized the underlying principles of mathematics and human ingenuity that later provided various means of recording and notating them

Those principles themselves are not a human invention the fact that two plus two equals four is true independent of human existence the rules of mathematics

Like the laws of physics are universal eternal and unchanging when mathematicians first showed that the angles of any triangle in a flat plane when added together

Come to 180 degrees a straight line this was not their invention they had simply discovered a fact that had always been and will always be true early applications the process of mathematical discovery began in prehistoric times with the development of ways of counting things people needed to quantify

At its simplest this was done by cutting tally marks in bone or stick a rudimentary but reliable means of recording numbers of things in time words and symbols were assigned to the numbers

And the first systems of numerals began to evolve a means of expressing operations such as acquisition of additional items or depletion of a stock the basic operations of arithmetic as huntergatherers turned to trade and farming

And societies became more sophisticated arithmetical operations and a numeral system became essential tools in all kinds of transactions to enable trade

Stock taking and taxes in uncountable goods such as oil flour or plots of land systems of measurement were developed putting a numerical value on dimensions such as weight and length

Calculations also became more complex developing the concepts of multiplication and division from addition and subtraction allowing the area of land to be calculated

For example in the early civilizations these new discoveries in mathematics and specifically the measurement of objects in space became the foundation of the field of geometry knowledge that could be used in building and toolmaking

In using these measurements for practical purposes people found that certain patterns were emerging which could in turn prove useful a simple but accurate carpenter square can be made from a triangle with sides of three

Four and five units without that accurate tool and knowledge the roads canals ziggurates and pyramids of ancient mesopotamia and egypt could not have been built

As new applications for these mathematical discoveries were found in astronomy navigation engineering bookkeeping taxation and so on further patterns and ideas emerged

The ancient civilizations each established the foundations of mathematics through this interdependent process of application and discovery but also developed a fascination with mathematics for its own sake

So caller queue mathematics from the middle of the first millennium bce the first pure mathematicians began to appear in greece and slightly later in india and china

Building on the legacy of the practical pioneers of the subject the engineers astronomers and explorers of earlier civil although these early mathematicians were not so concerned with the practical applications of their discoveries

They did not restrict their studies to mathematics alone in their exploration of the properties of numbers shapes and processes they discovered universal rules and patterns that raised metaphysical questions about the nature of the cosmos and even suggested that these patterns had mystical properties

Often mathematics was therefore seen as a complementary discipline to philosophy many of the greatest mathematicians through the ages have also been philosophers and vice versa

And the links between the two subjects have persisted to the present day arithmetic and algebra so began the history of mathematics as we understand it today the discoveries

Conjectures and insights of mathematicians that form the bulk of this book as well as the individual thinkers and their ideas it is a story of societies and cultures

A continuously developing thread of thought from the ancient civilizations of mesopotamia and egypt through greece china india and the islamic empire to renaissance europe and into the modern world

As it evolved mathematics was also seen to comprise several distinct but interconnected fields of study the first field to emerge and in many ways the most fundamental

Is the study of numbers and quantities which we now call arithmetic from the greek word arithmes numbers at its most basic it is concerned with counting and assigning numerical values to things

But also the operations such as addition subtraction multiplication and division that can be applied to numbers from the simplest concept of a system of numbers comes the study of the properties of numbers and even the study of the very concept itself

Certain numbers such as the constants pi e or the prime and irrational numbers hold a special fascination and have become the subject of considerable study

I think e isn’t it euler’s number euler’s number I’m pretty sure that is euler’s number another major field in mathematics is algebra which is the study of structure

The way that mathematics is organized and therefore has some relevance in every other field what marks algebra from arithmetic is the use of symbols such as letters

To represent variables variables unknown numbers in its basic form algebra is the study of the underlying rules of how those symbols are used in mathematics in equations

For example methods of solving equations even quite complex quadratic equations had been discovered as early as the ancient babylonians but it was medieval mathematicians of the islamic golden age who pioneered the use of symbols to simplify the process

Giving us the word algebra which is derived from the arabic algebra more recent developments in algebra have extended the idea of abstraction into the study of algebraic structure known as abstract algebra

Geometry and calculates a third major field of mathematics geometry is concerned with the concept of space and the relationships of objects in space the study of the shape

Size and position of figures it evolved from the very practical business of describing the physical dimensions of things in engineering and construction projects

Measuring and apportioning plots of land and astronomical observations for navigation and compiling calendars in mathematics the art of asking questions is more valuable than solving problems

George canter german mathematician repeating quote in mathematics the art of asking questions is more valuable than solving problems george canter german mathematician a particular branch of geometry trigonometry the study of the properties of triangles proved to be especially useful in these pursuits

Perhaps because of its very concrete nature for many ancient civilizations geometry was the cornerstone of mathematics and provided a means of problem solving and proof in other fields

This was particularly true of ancient greece where geometry and mathematics were virtually synonymous the legacy of great mathematical philosophers such as pythagoras

Plato and aristotle was consolidated by euclid whose principles of mathematics based on a combination of geometry and logic were accepted as the subject’s foundation for some 2000 years

In the 18 hundreds however alternatives to classic euclidean geometry were proposed opening up new areas of study including topology which examines the nature and properties not only of objects in space

But of space itself since the classical period mathematics had been concerned with static situations or how things are at any given moment it failed to offer a means of measuring or calculating continuous change

Calculus developed independently by gottfried leibniz and isaac newton in the 16 hundreds provided an answer to this problem the two branches of calculus

Integral and differential offered a method of analyzing such things as the slope of curves on a graph and the area beneath them as a way of describing and calculating change

The discovery of calculus opened up a field of analysis that later became particularly relevant to for example the theories of quantum mechanics and chaos theory

In the 1900 revisiting logic the late 19th and early 20th centuries saw the emergence of another field of mathematics the foundations of mathematics this revived the link between philosophy and mathematics

Just as euclid had done in the third century bce scholars including gottlieb frieg and bertrand russell sought to discover the logical foundations on which mathematical principles are based

Their work inspired a reexamination of the nature of mathematics itself how it works and what its limits are this study of basic mathematical concepts is perhaps the most abstract field

A sort of metamathematics yet an essential adjunct to every other field of modern mathematics new technology new ideas the various fields of mathematics arithmetic

Algebra geometry calculus and foundations are worthy of study for their own sake and the popular image of academic mathematics is that of an almost incomprehensible abstraction

But applications for mathematical discoveries have usually been found and advances in science and technology have driven innovations in mathematical thinking

A prime example is the symbiotic relationship between mathematics and computers originally developed as a mechanical means of doing the donkey work of calculation to provide tables for mathematicians

Astronomers and so on the actual construction of computers required new mathematical thinking it was mathematics as much as engineers who provided the means of building mechanical and then electronic computing devices which

In turn could be used as tools in the discovery of new mathematical ideas no doubt new applications for mathematical theorems will be found in the future

Too and with numerous problems still unsolved it seems that there is no end to the mathematical discoveries to be made the story of mathematics is one of exploration of these different fields and the discovery of new ones

But it is also the story of explorers the mathematicians who set out with a definite aim in mind to find answers to unsolve problems or to travel into unknown territory in search of new ideas

And those who simply stumbled upon an idea in the course of their mathematical journey and were inspired to see where it would lead all right and inspired to see where it would lead

The various fields of mathematics new technology new ideas the various fields of mathematics arithmetic algebra geometry calculus and foundations good

All right continuing sometimes the discovery would come as a game changing revelation providing a way into unexplored fields at other times it was a cause of standing on the shoulders of giants

Developing the ideas of previous thinkers or finding practical applications for them this book presents many of the big ideas in mathematics from the earliest discoveries to the present day

Explaining them in layperson’s language where they came from who discovered them and what makes them significant some may be familiar others less so

With an understanding of these ideas and an insight into the people and societies in which they were discovered we can gain an appreciation of not only the ubiquity and usefulness of mathematics

But also the elegance and beauty that mathematicians find in the subject quote mathematics rightly viewed possesses not only truth but supreme beauty

Bertrand russell british philosopher and mathematician repeating mathematics rightly viewed possesses not only truth but supreme beauty bertrand russell

British philosopher and mathematician you’ve been listening to world reading club presented by hakita alibocus alexander here on colin social podcasting presented for world reading club in association with uniquilium

This edition’s reading focus has come to us from big ideas simply explained the math book and was the introduction introduction coming up next in the math book is going to be ancient and classical periods from 3500 bce to 500 ce

Which is also part of the introduction but will come in a separate part

Till then stay well