Understanding WTS in Mathematical Proofs: Origins, Usage, and Alternatives

Mathematical proofs are structured arguments that establish the truth of a mathematical proposition. Within these proofs, certain abbreviations and acronyms help mathematicians communicate their thoughts more efficiently. One such abbreviation is WTS, which stands for “want to show”. In this article, we will delve into the meaning, historical context, and alternatives to WTS in mathematical proofs.

What Does WTS Mean?

WTS is an acronym used in mathematical proofs to indicate the goal or the conclusion that the author aims to demonstrate. It serves as a shorthand for the phrase “want to show”.

For example, in a proof, one might write:

We need to show that (some statement) is true.

This can be abbreviated as:

WTS (some statement) is true.

Alternatives to WTS

While WTS is a useful acronym, it is not widely used in professional mathematical literature. Common alternatives include:

These alternatives are generally more verbose but may be easier for readers to understand, especially those who are new to mathematical proofs.

Origins and Usage

The origin of WTS is not well-documented, and its use appears to have been short-lived in professional mathematical literature. Some have suggested that it may be more commonly found in schoolwork or informal settings rather than in formal academic papers.

One mathematician expressed confusion about its prevalence, stating:

“WTS? I’ve never seen that one either. It seems to be a relic from a time when proofs were written informally or for educational purposes.”

However, the acronym has a similar function to QED (quod erat demonstrandum), which is a Latin phrase used to denote the end of a proof.

Historical Context

QED, meaning “which was to be demonstrated” in Latin, is often placed at the end of a proof to signify that the proposition has been fully established. In this sense, WTS can be seen as a precursor to QED, indicating what needs to be demonstrated next.

Acronyms such as “iff” (if and only if) and “wlog” (without loss of generality) are more commonly used in mathematical texts. These acronyms have become standard due to their widespread use and ease of comprehension within the mathematical community.

Evolution of Mathematical Verbiage

The evolution of mathematical language, including acronyms and notations, reflects the changing norms and standards within the field. The use of WTS is an example of how certain terms and abbreviations can gain or lose popularity over time based on their effectiveness and association with the prevailing mathematical paradigms.

The study of how mathematical notations and acronyms evolve can provide insights into the broader patterns of scientific communication and the way mathematicians think and work.

Conclusion

In conclusion, WTS stands for “want to show”, a useful but less common abbreviation in mathematical proofs. While its use is not widespread, it serves as a reminder of the language and tools mathematicians use to structure and communicate their arguments. As with other mathematical acronyms, understanding the context and evolution of WTS can deepen our appreciation for the nuances of mathematical communication.