Tag Archives: math English

exposition, language of math, math, proof, understanding math

Forms of proofs

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Abstractmath.org is a website I have been maintaining since 2005. It is intended for people beginning the study of abstract math, often a course that requires proofs and thinking about mathematical structures. The Introduction to the website and the article Attitude explain the website in more detail.

One of the chapters in abstractmath.org covers Proofs. As everywhere in abstractmath.org, there is no attempt at complete coverage: the emphasis is on aspects that cause difficulty for abstraction-newbies. In the case of proofs, this includes sections on how proofs are written (math language is a big emphasis all over abstractmath.org). One of those sections is Forms of Proof. This post is a fairly extensive revision of that section.

More than half of the section on Proofs has already been revised (the ones entitled “abstractmath.org 2.0)”, and my current task is to finish that revision.

Normally, I post the actual article here on Gyre&Gimble, but something has changed in the operation of WordPress which causes the html processor to obey linebreaks in the input, which would make the article look chaotic.

So this time, I have to ask you to click a button to read the revised section on Forms of Proof. I apologize for the excessive effort by your finger.
 

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abstractmath.org, exposition, language, language of math, math, understanding math

The two languages of math

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I am revising the (large) section of abstractmath.org that concerns the languages of math. Below is most of the the introduction to that section, which contains in particular detailed links to its contents. All of these are now available, but only a few of them have been revised. They are the ones that say “Abstractmath 2.0” in the header.

Introduction

Mathematics in the English-speaking world is communicated using two languages:

  • Mathematical English is a special form of English.
  • It uses ordinary words with special meanings.
  • Some of its structural words (“if”, “or”) have different meanings from those of ordinary English.
  • It is both written and spoken.
  • Other languages also have special mathematical forms.

  • The symbolic language of math is a distinct, special-purpose language.
  • It has its own symbols and rules that are rather unlike those that spoken languages have.
  • It is not a dialect of English.
  • It is largely a written language.
  • Simple expressions can be pronounced, but complicated expressions may only be pointed to or referred to.
  • It is used by all mathematicians, not just those who write math in English.

Math in writing and in lectures involve both mathematical English and the symbolic language. They are embedded in each other and refer back and forth to each other.

Contents

The languages of math are covered in three chapters, each with several parts. Some things are not covered; see Notes.

Links to other sites


Notes

Math communication also uses pictures, graphs and diagrams, which abstractmath.org doesn’t discuss. Also not covered is the history and etymology of mathematical notation. 

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