https://mklab.gr/ Sat, 12 Sep 2026 06:10:44 +0000 MyBB https://mklab.gr/showthread.php?tid=1477 Fri, 31 Jul 2026 01:43:45 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1477 Summary: Terry Tao’s “Advice on Writing Papers” Terry Tao explains that good mathematical writing does not follow a fixed formula; instead, authors should develop a style that matches their strengths, the subject, and the intended audience. A successful paper should begin by clearly presenting and motivating its main ideas, using the introduction to highlight the importance of the results while remaining accurate and honest. 

The organization of the paper is essential: authors should choose good notation, divide complex arguments into manageable sections or lemmas, and provide enough detail so readers can understand the key ideas without being overwhelmed by routine calculations. Tao recommends creating a quick prototype draft before polishing the final version, writing in a professional but personal voice, and using natural language rather than relying only on mathematical symbols. 

Authors should focus their effort on the most important and innovative parts of the work, while avoiding unnecessary optimization that may make the paper longer or less clear. Before submission, a paper should be carefully proofread and sent to an appropriate journal. Ultimately, Tao emphasizes that mathematical writing is about communication: the goal is not only to present correct results but also to help readers understand why those results matter and how the ideas fit together. 

Key takeaways:

• A paper should communicate ideas, not just contain proofs.
  
• The introduction should explain the significance of the results.
  
• Good structure and notation greatly improve readability.
  
• Give more space to important ideas and less to routine details.
  
• Write a draft quickly, then refine it.
  
• Avoid perfectionism that harms clarity or efficiency.
  
• Submit only a polished, carefully checked final version.
  

ARTICLE]]> Summary: Terry Tao’s “Advice on Writing Papers” Terry Tao explains that good mathematical writing does not follow a fixed formula; instead, authors should develop a style that matches their strengths, the subject, and the intended audience. A successful paper should begin by clearly presenting and motivating its main ideas, using the introduction to highlight the importance of the results while remaining accurate and honest. 

The organization of the paper is essential: authors should choose good notation, divide complex arguments into manageable sections or lemmas, and provide enough detail so readers can understand the key ideas without being overwhelmed by routine calculations. Tao recommends creating a quick prototype draft before polishing the final version, writing in a professional but personal voice, and using natural language rather than relying only on mathematical symbols. 

Authors should focus their effort on the most important and innovative parts of the work, while avoiding unnecessary optimization that may make the paper longer or less clear. Before submission, a paper should be carefully proofread and sent to an appropriate journal. Ultimately, Tao emphasizes that mathematical writing is about communication: the goal is not only to present correct results but also to help readers understand why those results matter and how the ideas fit together. 

Key takeaways:

• A paper should communicate ideas, not just contain proofs.
  
• The introduction should explain the significance of the results.
  
• Good structure and notation greatly improve readability.
  
• Give more space to important ideas and less to routine details.
  
• Write a draft quickly, then refine it.
  
• Avoid perfectionism that harms clarity or efficiency.
  
• Submit only a polished, carefully checked final version.
  

ARTICLE]]> https://mklab.gr/showthread.php?tid=1160 Thu, 16 Jul 2026 19:21:02 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1160 How to Write a 21st Century Proof 
BY Leslie Lamport

Summary

In "How to Write a Proof," Leslie Lamport argues that the traditional way mathematicians write proofs in long paragraphs often makes them difficult to follow and increases the risk of overlooking errors. Instead, he proposes a hierarchically structured approach, where a proof is organized into clear, numbered steps that begin with the main idea and gradually reveal more detailed arguments only when needed. This style allows readers to first understand the overall strategy before diving into technical details, much like navigating an outline or a well-designed computer program. 

Lamport explains that this method improves readability, makes complex proofs easier to verify, and helps authors avoid logical mistakes by forcing each claim to be explicitly justified. Although structured proofs may initially seem longer than conventional ones, he argues that they are ultimately more practical, easier to maintain, and far more reliable. His central message is that mathematicians can greatly improve the clarity and correctness of their work by adopting proof-writing techniques inspired by the hierarchical organization long used in software engineering. 

ARTICLE [PDF]]]> How to Write a 21st Century Proof 
BY Leslie Lamport

Summary

In "How to Write a Proof," Leslie Lamport argues that the traditional way mathematicians write proofs in long paragraphs often makes them difficult to follow and increases the risk of overlooking errors. Instead, he proposes a hierarchically structured approach, where a proof is organized into clear, numbered steps that begin with the main idea and gradually reveal more detailed arguments only when needed. This style allows readers to first understand the overall strategy before diving into technical details, much like navigating an outline or a well-designed computer program. 

Lamport explains that this method improves readability, makes complex proofs easier to verify, and helps authors avoid logical mistakes by forcing each claim to be explicitly justified. Although structured proofs may initially seem longer than conventional ones, he argues that they are ultimately more practical, easier to maintain, and far more reliable. His central message is that mathematicians can greatly improve the clarity and correctness of their work by adopting proof-writing techniques inspired by the hierarchical organization long used in software engineering. 

ARTICLE [PDF]]]> https://mklab.gr/showthread.php?tid=896 Sun, 05 Jul 2026 19:04:42 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=896 MathSphere Mathematical Dictionary

Summary

This book is essentially a maths vocabulary dictionary for school use, designed to help students quickly understand key mathematical terms.
It explains maths language in simple, clear definitions, covering topics like numbers, arithmetic, algebra, geometry, measurements, shapes, and basic statistics. Each entry is meant to be short and easy to understand, often giving just the core meaning of a term so learners can recognize and use it correctly in class.
In short: it works as a quick-reference glossary that builds maths literacy, helping students move from “not knowing the word” to confidently understanding and using mathematical language in everyday learning.

BOOK (PDF)]]> MathSphere Mathematical Dictionary

Summary

This book is essentially a maths vocabulary dictionary for school use, designed to help students quickly understand key mathematical terms.
It explains maths language in simple, clear definitions, covering topics like numbers, arithmetic, algebra, geometry, measurements, shapes, and basic statistics. Each entry is meant to be short and easy to understand, often giving just the core meaning of a term so learners can recognize and use it correctly in class.
In short: it works as a quick-reference glossary that builds maths literacy, helping students move from “not knowing the word” to confidently understanding and using mathematical language in everyday learning.

BOOK (PDF)]]> https://mklab.gr/showthread.php?tid=646 Tue, 23 Jun 2026 11:30:31 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=646 The nuts and bolts of writing mathematics
by Dave Richeson

Summary

The article “The Nuts and Bolts of Writing Mathematics” explains that writing mathematics is not just about finding the right answer, but about communicating ideas clearly and logically. It compares mathematical writing to any other form of writing: you need planning, a first draft, revision, and careful editing. A good proof should be concise, precise, and written for the reader, avoiding unnecessary words, vague explanations, or too many symbols.
The author emphasizes that mathematicians should guide the reader through their reasoning using clear language, proper structure, and a natural flow. Writing mathematics well is a skill that improves with practice, and a beautiful proof is not only correct—it is also easy for others to understand. 

ARTICLE]]> The nuts and bolts of writing mathematics
by Dave Richeson

Summary

The article “The Nuts and Bolts of Writing Mathematics” explains that writing mathematics is not just about finding the right answer, but about communicating ideas clearly and logically. It compares mathematical writing to any other form of writing: you need planning, a first draft, revision, and careful editing. A good proof should be concise, precise, and written for the reader, avoiding unnecessary words, vague explanations, or too many symbols.
The author emphasizes that mathematicians should guide the reader through their reasoning using clear language, proper structure, and a natural flow. Writing mathematics well is a skill that improves with practice, and a beautiful proof is not only correct—it is also easy for others to understand. 

ARTICLE]]> https://mklab.gr/showthread.php?tid=618 Mon, 22 Jun 2026 15:26:34 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=618 Glossary of mathematical jargon 
BY wikiepdia

Summary

The Wikipedia article “Glossary of Mathematical Jargon” presents a collection of informal expressions, specialized phrases, and cultural shorthand commonly used by mathematicians that often carry meanings quite different from their everyday English usage. It explains terms such as canonical, deep, nice, regular, almost all, and abstract nonsense, along with common proof-related language like iff (“if and only if”), by contradiction, and angle chasing. The glossary highlights how mathematicians frequently use concise, informal terminology to communicate complex ideas efficiently while still maintaining rigorous underlying meanings, providing insight into the language and culture of mathematical practice beyond formal definitions and symbols. 

GLOSSARY]]> Glossary of mathematical jargon 
BY wikiepdia

Summary

The Wikipedia article “Glossary of Mathematical Jargon” presents a collection of informal expressions, specialized phrases, and cultural shorthand commonly used by mathematicians that often carry meanings quite different from their everyday English usage. It explains terms such as canonical, deep, nice, regular, almost all, and abstract nonsense, along with common proof-related language like iff (“if and only if”), by contradiction, and angle chasing. The glossary highlights how mathematicians frequently use concise, informal terminology to communicate complex ideas efficiently while still maintaining rigorous underlying meanings, providing insight into the language and culture of mathematical practice beyond formal definitions and symbols. 

GLOSSARY]]> https://mklab.gr/showthread.php?tid=478 Thu, 18 Jun 2026 09:37:28 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=478 The Definitive Glossary of Higher Mathematical Jargon

Summary

The Math Vault Mathematical Glossary is a comprehensive reference guide to the language of higher mathematics, explaining more than 100 important mathematical terms and concepts that appear across many fields. It focuses on the specialized vocabulary mathematicians use to describe ideas such as abstraction, algorithms, axioms, proofs, structures, infinity, equivalence, uniqueness, rigor, and transformations, providing definitions, examples, and context for each term.

The glossary aims to help students and enthusiasts better understand how mathematicians communicate abstract ideas, showing how precise language and concepts form the foundation of advanced mathematical thinking.

GLOSSARY

]]> The Definitive Glossary of Higher Mathematical Jargon

Summary

The Math Vault Mathematical Glossary is a comprehensive reference guide to the language of higher mathematics, explaining more than 100 important mathematical terms and concepts that appear across many fields. It focuses on the specialized vocabulary mathematicians use to describe ideas such as abstraction, algorithms, axioms, proofs, structures, infinity, equivalence, uniqueness, rigor, and transformations, providing definitions, examples, and context for each term.

The glossary aims to help students and enthusiasts better understand how mathematicians communicate abstract ideas, showing how precise language and concepts form the foundation of advanced mathematical thinking.

GLOSSARY

]]> https://mklab.gr/showthread.php?tid=361 Sun, 14 Jun 2026 18:40:42 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=361
The article argues that mathematical notation is not just a neutral way of recording ideas, but a “technology” that actively shapes how people think and what kinds of mathematics become possible. It explains how different writing systems—such as Roman versus Hindu-Arabic numerals or Newton’s geometric calculus versus Leibniz’s symbolic notation—don’t just represent math differently, but actually influence ease of computation, collaboration, and the development of entire fields.
 The piece also shows that competing notations can coexist and even drive major breakthroughs in logic and computation, since studying different formal systems helped lead to results by Gödel, Turing, and Church. Overall, it emphasizes that changes in how mathematics is written have repeatedly changed the direction and power of mathematical thought itself.

ARTICLE]]>
The article argues that mathematical notation is not just a neutral way of recording ideas, but a “technology” that actively shapes how people think and what kinds of mathematics become possible. It explains how different writing systems—such as Roman versus Hindu-Arabic numerals or Newton’s geometric calculus versus Leibniz’s symbolic notation—don’t just represent math differently, but actually influence ease of computation, collaboration, and the development of entire fields.
 The piece also shows that competing notations can coexist and even drive major breakthroughs in logic and computation, since studying different formal systems helped lead to results by Gödel, Turing, and Church. Overall, it emphasizes that changes in how mathematics is written have repeatedly changed the direction and power of mathematical thought itself.

ARTICLE]]> https://mklab.gr/showthread.php?tid=294 Thu, 11 Jun 2026 20:37:55 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=294 A Few Tips On Writing Papers With Mathematical Content
John N. Tsitsiklis

Summary  The document offers practical advice on drafting scientific and engineering papers that feature heavy mathematical content (such as optimization, systems control, and applied probability). Its primary objective is to make information transfer as effortless as possible for the reader, which simultaneously increases a solid paper's chances of publication.

ARTICLE PAGE]]> A Few Tips On Writing Papers With Mathematical Content
John N. Tsitsiklis

Summary  The document offers practical advice on drafting scientific and engineering papers that feature heavy mathematical content (such as optimization, systems control, and applied probability). Its primary objective is to make information transfer as effortless as possible for the reader, which simultaneously increases a solid paper's chances of publication.

ARTICLE PAGE]]> https://mklab.gr/showthread.php?tid=39 Tue, 25 Mar 2025 21:26:01 +0200 mklabgr]]> https://mklab.gr/showthread.php?tid=39
https://www.maths.ox.ac.uk/outreach/oxfo...s-alphabet]]>
https://www.maths.ox.ac.uk/outreach/oxfo...s-alphabet]]>