3.  Logic (from the Greek λογική, logikē has two senses; it is the study of modes of reasoning (those which are valid, and those which are fallacious) as well as the use of valid reasoning. In the latter sense, logic is used in most intellectual activities, including philosophy and science, but in the first sense, it is primarily studied in the disciplines of philosophy, mathematics, semantics, and computer science. It examines general forms that arguments may take. In mathematics, it is the study of valid inferences within some formal language. Logic is also studied in argumentation theory.  Logic was studied in several ancient civilizations, including India, China,, Persia and Greece. In the West, logic was established as a formal discipline by Aristotle, who gave it a fundamental place in philosophy. The study of logic was part of the classical trivium, which also included grammar and rhetoric. In the East, logic was developed by Buddhists and Jainists.

4.  I am interested about the logic math it is because I like answering logical question and it is one of the easiest topic I have learned in math and I can easily understand it, unlike the other topic is very complicated and there is too much process of calculation. Logic is about reasoning and I rather like reasoning than calculating.

5.  Math is important because it helps us to calculate and solved problem. Everyday we always use are math skills when we buy something we use math to calculate, when we look at the date of the calendar we see numbers which is part of math, we also use math to know how old we are right now.  What if there's no math? I think the world would become horrible because if there is no math, no measurements, no calculations, you don’t even know what is your exact age.

6.  The history of logic is the study of the development of the science of valid inference (logic). Formal logic was developed in ancient times in China, India, and Greece. Greek logic, particularly Aristotelian logic, found wide application and acceptance in science and mathematics.  Aristotle's logic was further developed by Islamic and Christian philosophers in the Middle Ages, reaching a high point in the mid- fourteenth century. The period between the fourteenth century and the beginning of the nineteenth century was largely one of decline and neglect, and is regarded as barren by at least one historian of logic.  Logic was revived in the mid-nineteenth century, at the beginning of a revolutionary period when the subject developed into a rigorous and formalistic discipline whose exemplar was the exact method of proof used in mathematics. The development of the modern so-called "symbolic" or "mathematical" logic during this period is the most significant in the two-thousand-year history of logic, and is arguably one of the most important and remarkable events in human intellectual history.

7.  The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.  Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. The most ancient mathematical texts available are Plimpton 322 (Babylonian mathematics c. 1900 BC),the Rhine Mathematical Papyrus (Egyptian mathematics c. 2000-1800 BC) and the Moscow Mathematical Papyrus (Egyptian mathematics c. 1890 BC). All of these texts concern the so-called Pythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.  Mathematical logic emerged in the mid-19th century as a subfield of mathematics independent of the traditional study of logic (Ferrero's 2001, p. 443). Before this emergence, logic was studied with rhetoric, through the syllogism, and with philosophy. The first half of the 20th century saw an explosion of fundamental results, accompanied by vigorous debate over the foundations of mathematics.

8.  The evolution of mathematics might be seen as an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction, which is shared by many animals, was probably that of numbers: the realization that a collection of two apples and a collection of two oranges (for example) have something in common, namely quantity of their members.  Mayan numerals  Evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have also recognized how to count abstract quantities, like time – days, seasons, years.  More complex mathematics did not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic, algebra and geometry for taxation and other financial calculations, for building and construction, and for astronomy. The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns and the recording of time.  In Babylonian mathematics elementary arithmetic (addition, subtraction, multiplication and division) first appears in the archaeological record. Numeracy pre-dated writing and numeral systems have been many and diverse, with the first known written numerals created by Egyptians in Middle Kingdom texts such as the Rhind Mathematical Papyrus.  Between 600 and 300 BC the Ancient Greeks began a systematic study of mathematics in its own right with Greek mathematics.  Mathematics has since been greatly extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today. According to Mikhail B. Sevryuk, in the January 2006 issue of the Bulletin of the American Mathematical Society, "The number of papers and books included in the Mathematical Reviews database since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The overwhelming majority of works in this ocean contain new mathematical theorems and their proofs." ]

9.  Some people have supposed that mathematics is a creation of human beings, like the printing press or the internal combustion engine. But are numbers and laws of mathematics really inventions of man? Things that are designed and created by people could have been designed and created differently. When two people independently invent the same type of thing, there are differences in the design and construction since each person has taken a different creative approach to solving an engineering problem. Moreover, the designs of various manmade contraptions are often improved down the line as innovative new solutions are proposed and new technologies are developed.  If mathematics were manmade, then we would expect it to exhibit these characteristics as well. We would expect different mathematical laws for different mathematicians, and improvements to such laws as time progresses. As society changed, so would laws of mathematics. Is this what we find?  Undoubtedly, the written expression of mathematical laws is manmade. There are several different notations used in various fields of mathematics, and various mathematicians in the past have used different notations to express mathematical truths. Some notations are more useful than others, while less useful notations often fall into disuse. However, these different symbols are merely different ways of expressing the same mathematical reality. For example, Roman numerals express the same numbers as the more familiar Arabic system. All mathematicians have the same laws of mathematics, although they may use different systems and different notations to express those laws.  Laws of mathematics are discovered by people and written down by people. But they were not created by people. As discussed above, laws of mathematics do not change with time. Therefore, they existed before people existed. So they obviously cannot be a creation of man. The equation 2+3=5 was true long before any human being thought about it, realized it, or wrote it.

10.  Mathematics is important to us because we use it everyday. I was wondering what will happen to the world if there is no mathematics?  How can we calculate are money when we buy in store if there's no math?  How can we measure things if there is no math?  How can we know the date today if there no math? How can we know are exact age or birthday if there is no math?  I think without math the world will become undeveloped because without knowledge about math we cannot invent new things.

11.  We did not math we discover math. Math is used to calculate and to study and enhance our brain. Studying math is very interesting this is were you will challenge your knowledge an how you solved complicated problems.  1. In 2010 on World Maths Day, 1.13 million students from more than 235 countries set a record correctly answering 479,732,613 questions. 2. Americans called mathematics ‘math’, arguing that ‘mathematics’ functions as a singular noun so ‘math’ should be singular too. 3. They have been calling maths ‘math’ for much longer than we have called it ‘maths’. 4. ‘Mathematics’ is an anagram of ‘me asthmatic’. 5. The only number in English that is spelled with its letters in alphabetical order is ‘forty’. 6. The only Shakespeare play to include the word ‘mathematics’ is The Taming Of The Shrew. 7. Notches on animal bones show that people have been doing mathematics, or at least making computations, since around 30,000BC. 8. The word ‘hundrath’ in Old Norse, from which our ‘hundred’ derives, meant not 100 but 120. 9. “Pure mathematics is, in its way, the poetry of logical ideas.” (Albert Einstein). 10. “Mathematics [is] the subject in which we never know what we are talking about nor whether what we are saying is true.” (Bertrand Russell).

12.  As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. – Albert Einstein  Since the mathematicians have invaded the theory of relativity, I do not understand it myself any more. – Albert Einstein  The formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill. – Albert Einstein  All human actions have one or more of these seven causes: chance, nature, compulsions, habit, reason, passion and desire. – Aristotle  He who cannot describe the problem will never find the solution to that problem. - Confucius

13.  At one extreme, logic is a branch of mathematics. This kind of logic is closely related to the study of logic as a branch of philosophy. It can often differ quite dramatically from some of the reasoning that people will sometimes call "logic".  Mathematical logic makes use of operations that use "true" and "false" instead of numbers. There are two common types of mathematical logic: propositional calculus and first order predicate calculus. 

14.  Mathematical Logic and Reasoning. canada: 2013..  "history of logic." mathematics logic. canada: 2013..

15.  brown, andrew. "what is logic reasoning?." Mathematical Logic and Reasoning. UK: 2013..  "history and evolution of logic." Mathematical Logic and Reasoning. 2013..