I Finally Found You
( What is mathematics ,really? by Reuben Hersh)
When you ask the internet about mathematics there will be hundreds of definitions about it. I will mention some of them, according to
www.freedictionary.com
1. (Mathematics) (functioning as singular)
a group of related sciences, including algebra, geometry, and calculus,
concerned with the study of number, quantity, shape, and space and
their interrelationships by using a specialized notation
2. (Mathematics) (functioning as singular or plural) mathematical operations and processes involved in the solution of a problem or study of some scientific field www.Merriam-webster.com
Mathematics is the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations.
www.cut-the-knot.org/math_intro.shtml
math-e-mat-ics n. (used with a sing. verb). The study of the measurement, properties, and relationships of quantities, using numbers and symbols. [From Middle English mathematik, from Old French mathematique, from Latin mathematica, from Greek mathematike (tekhne)]
math-e-mat-ics n. ... the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations.
Webster's New Collegiate Dictionary
Relevant quotations
Mathematics is a language.Relevant quotations
To those who do not know Mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty of nature. ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.
Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
Bertrand Russell. 1872-1970
British philosopher, mathematician.
Mysticism and Logic
Relevant quotations
All science requires Mathematics.
The knowledge of mathematical things is almost innate in us... This is
the easiest of sciences, a fact which is obvious in that no one's brain
rejects it; for laymen and people who are utterly illiterate know how to
count and reckon.British philosopher, mathematician.
Mysticism and Logic
Relevant quotations
Roger Bacon. 1214-1294
English philosopher, scientist.
Opus Maius
We do not teach arithmetic in Kindergarten. A knowledge of mathematics is not necessary to a four year old. Any premature instruction arrests development.
English philosopher, scientist.
Opus Maius
Philosophy of Froebel Kindergarten.
Pictured Knowledge, p899, several editions 1916-1927
Marshall Hughes Co.
Pictured Knowledge, p899, several editions 1916-1927
Marshall Hughes Co.
These definitions are all abstract and shallow to especially to a person who's in the process of developing his/her mathematical abilities or to a very curious person who have no idea why he have to study math when math is different from his/her field of interest or field of study.
I guess the book "What is mathematics, Really?" written by Reuben Hersh will be the perfect book to answer few of your questions. He wrote this after reading the book of Richard Courant and Herbert Robbins. Not contented by with what he read, after reading it with delight and curiosity he was still left asking, " What is mathematics, Really?"
Hershe's book debunks the idea of Platonism, formalism and Noe-Fregeanism in the philosophy of mathematics. Mathematics is part of a human life, he calls is humanism because he believe that mathematics must be understood as a part of human culture, historically involved and developed and as part of human activity not as an alien language or inhuman. What is formalism? Most of the formalist in the philosophy of mathematics states that "mathematics is a meaningless game" it is a rule without following a rule a simple logic but Hersh said that mathematics is not part of a rule-governed game and it is not a game for heaven's sake! It is a concept and ideas developed by the working society through interacting with each other not making it but discovering and philosophizing it. Mathematics follows a pattern and concepts for it to be correct. How did they know that it is correct? Through understanding and interacting with each other and criticizing.
One of the many arguments about mathematics is that, is mathematics created or discovered. Well according to Hersh mathematics are both created and discovered, why? When a group of mathematician or even group of people solve a well stated math problem they will get the same answer so they discover the correct way to answer it but when they try to make theories for their math solution they will create different theories, this time they created math.
Reuben Hersh’s What is Mathematics, Really? is, for me, the best introduction to mathematical for all of us considering those who says mathematics is not their forte. As I noted earlier, it serves as a very useful mind enriching tool mentioning other mathematical issues - principally methodological - from a mathematical perspective, and in doing so it showed why mathematics always has this overwhelming wonders.
More importantly the book demonstrate a very good argument for seeing mathematics as a fundamentally human activity. It made me realize that mathematics is like a boy in the process of growing up. The people around him will contribute a lot to his future same as mathematics the people who studies and love mathematics will be the developers and the contributors to the fate of mathematics. If you want to be one of them then start reading "What is mathematics, Really?", a life changing creation of Reuben Hersh that is destined change our fate.
Work Cited
marian <3
wow. hands down with the research on the definitions of math. however, too much of it is distracting. i think its better to cut it short. nice analogy though :)
ReplyDeleteI like how you used the various definitions of math on the internet for comparison but it is too much that it overpowers what you really want to say. Kudos on the great analogy on the last part though, it makes the thought of the author clearer in a way :)
ReplyDeleteThe different definitions of mathematics from different sources is a good idea. It persuades me to read more. :) But I have to agree with the first comment, three definitions will do. But over all, good job!
ReplyDelete