Talk:Abstraction (mathematics)

"Mathematics without formulas" section - reasons for removal

I have removed the following new section from the article:

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General real world comparisons

Abstract mathematics, also known as "mathematics without formulas" can be treated as a "geography without maps". As maps supply information about the places depicted in a very concentrated ways - they do not show the places. The same way the formulas give precise and capacitive descriptions, they do nt reveal pure facts. Formulas are treated as "the language of mathematics", but the soul of mathematics is a real world.

• Logically serial array of statements — is the most significant property of mathematics.

Arithmetics deals with numbers. IT also implies letters in algebraic formulas. It is hard to state that something mathematically significant is hidden in integers and figures. So what does mathematic means? If we imagine MATH as a single huge house, "we should imagine the scientists who built this house, naturally as brick layers. And this comparison is based on something. When a brick layer makes a wall, then every brick is firmly laid on the bricks which are laid before, and then are bound by a special cement. Mathematics reasons similarly every statement is supported by already proven statements. It is cemented by the laws of Logic.

• IN every building, getting lower and lower from the high floors to the foundation, finally we rich it. This fashion we can work with theorems. Earlier and later we get to the statements, truthfulness of which is accepted without any proofs. They are called AXIOMS and POSTULATES.

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My reasons for this removal are as follows:

• This section is not about the process of abstraction. It should be in a different article.
• It contains unencyclopaedic language e.g. "the soul of mathematics is a real world".
• It contains POV statements e.g. "Logically serial array of statements — is the most significant property of mathematics".
• It contains numerous grammatical errors e.g. "So what does mathematic means?", "finally we rich it", "This fashion we can work with theorems".
• It is unsourced.

If someone wants to tidy it up, add sources and put it in a different article, that's fine — but I don't think it belongs in this article. Gandalf61 10:42, 12 January 2007 (UTC)

12 years old 41.116.34.41 (talk) 17:36, 20 July 2023 (UTC)

Important abstraction

One could write something about Stefan Banach, who even said something about deep analogies. konradek (talk) 22:11, 4 October 2008 (UTC)

removing any dependence on real world objects

Is there a source for this interesting claim? Tkuvho (talk) 08:36, 22 May 2012 (UTC)

Removed reference material

Material removed, due presumably to a POV.

Books

General

• Mathematics. By Ernest William Hobson.
• The Foundations of Mathematics: A Contribution to the Philosophy of Geometry. By Paul Carus.

Other

• The Principles of Mathematics, Volume 1. By Bertrand Russell. Pg 219
• School Science and Mathematics, Volume 22. Pg 526
• The Logic and Utility of Mathematics. By Charles Davies. Pg 32.
• Mathematics simplified and made attractive: or, The laws of motion explained. By Thomas Fisher. Pg 15.
• The new encyclopædia; or, Universal dictionary ofarts and sciences. By Encyclopaedia Perthensi. Pg 49
• An easy introduction to the mathematics: Volume 2. By Charles Butler. pg 253
• The Mathematical Principles of Natural Philosophy, Volume 1. By Sir Isaac Newton, John Machin.
• Fundamental conceptions of modern mathematics.By Robert Porterfield Richardson, Edward Horace Landis. Pg 102
• The Teaching of Mathematics in the Elementary and the Secondary School. By Jacob William Albert Young.
• Mysticism in Modern Mathematics. By Hastings Berkeley. pg 160

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Also ... Applicable information removed. --J. D. Redding 04:08, 23 July 2013 (UTC)

I removed this material. As I explained in my edit comment, I removed them because they appear to be random snippets from Google Books - it looks as if they were created by just searching for the terms "abstraction" and "mathematics". For example, what, exactly, does Newton's Principia Mathematica have to say about abstraction in mathematics ? I am all in favour of giving the reader references to relevant books that discuss the topic of the article, but overloading the References section with these random lookups helps noone.

I also removed the paragraph:

"Abstract Mathematics is what treats of magnitude or quantity, absolutely and generally conferred, without regard to any species of particular magnitude, such as Arithmetic and Geometry, In this sense, abstract mathematics is opposed to mixed mathematics; wherein simple and abstract properties, and the relations of quantities primitively considered in mathematics, are applied to sensible objects, and by that means become intermixed with physical considerations; Such are Hydrostatics, Optics, Navigation, &c.".

This archaic definition, copied word for word from an 1807 encyclopedia, is completely out of date and bears no relation to the modern concept of abstraction in mathematics. This is an example of the dangers of quote-hunting without properly understanding the subject of the article.

The rest of my edit was removing or fixing ungrammatical and badly worded sentences. For example "Though, one can substituted mathematics for real world objects, and wander off through equation after equation, and can build a concept structure which has no relation to reality" (sic). Gandalf61 (talk) 08:14, 23 July 2013 (UTC)

They are references. Wikipedia:Citation needed requires it. Wikipedia content is verifiable. Source-based edits requires it. But, according to this comment, one is to rely on non-authoritative judgement (sic., "properly understanding").

As to Newton's work, it talks of how he "connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena". You left in that sentence in without understanding the full implication of it ... it seems.

The quote gives insight to the differences of 'abstract versus applied' (something highly relevant to pure mathematics) ... of abstract mathematics as opposed to mixed mathematics (applied mathematics). (And a link to the relevant article should be place in the article too.)

These references and content should be restored. Giving the reader references and a better understanding of the topic.

As to the "no relation modern concept of abstraction" in mathematics ... as a self-referenced mathematician, imagine that POV would be held.

Ungrammatical? Badly worded? Favour? ... Grammar arguments are the last resort of specious attacks. And Wikipedia is not British (nor American). Hardly even wanted to address this point, 'cause it asinine.

One last thing, for now. Never understood the objection to the use of public domain material. Wikipedia was founded on the principle.

Got to go, bbl. --J. D. Redding 12:21, 23 July 2013 (UTC)

1. I have no problem with references that are specific and relevant to the contents of the article. I agree that this article needs more references. But the links that you added under "General" and "Other" were not useful and relevant references - they were the result of random quote farming.
2. You quoted an 1807 definition of abstract mathematics, which is an old-fashioned synonym for what is today called pure mathematics (and, indeed, the term redirects to that article). This article is not about "abstract mathematics". It is about abstraction in mathematics, which is a different topic. But you don't have to take my word for this - we can raise this question at Wikipedia talk:WikiProject Mathematics to determine consensus.
3. I have no problem with American/British spelling variants. But bad grammar (such as "one can substituted mathematics") is usually a sign of vague and imprecise thinking. I know that some Wikipedia editors think it is acceptable to throw in poorly worded contributions and leave other editors to tidy up after them. I don't buy this. Failing to take the time to write clearly and proofread your contributions before you save them shows a lack of respect for readers. Gandalf61 (talk) 14:05, 23 July 2013 (UTC)

1. They are not "random quote farming". It is relevant material.
2. Not gonna buy into Wikiality; especially at the 'help desk' location you are a "reg" at.
3. What the phrase, "Improve it" ... and this would not have be a "one time edit", as is characterized above ... would have had more. People wonder why the participation in Wikipedia fell over the years.

Regardless, articles are made of many edits ... cooperate and improve it [but maybe that is dead in Wikipedia]; or just hinder the information and do block reverts ...

And the conception of "don't buy this" of contributions is a clearly non-cooperative ... and is a distortion of the history of Wikipedia. --J. D. Redding 04:44, 24 July 2013 (UTC)

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