This post advocates for clear, legible mathematical handwriting, emphasizing the importance of distinguishing similar symbols. It offers specific guidelines for writing letters (like lowercase 'x' and 'times,' 'u' and 'union,' and Greek letters), numerals (particularly distinguishing '1,' '7,' and 'I'), and other mathematical symbols (such as plus/minus, radicals, and various brackets). The author stresses vertical alignment within equations, proper spacing, and the use of serifs for improved clarity. Overall, the goal is to enhance readability and avoid ambiguity in handwritten mathematics, benefiting both the writer and anyone reading the work.
John Kerl's 2007 guide, "Orthography of Mathematics," provides a comprehensive and detailed exploration of best practices for writing mathematical notation by hand, aiming for clarity, precision, and aesthetic appeal. Kerl emphasizes that effective mathematical handwriting transcends mere legibility, serving as a crucial tool for clear communication of complex ideas and facilitating the very process of mathematical thought. He posits that a standardized approach to notation improves the transmission of mathematical concepts between individuals and reduces the likelihood of misinterpretations arising from ambiguous or poorly formed symbols.
The guide begins by establishing the importance of distinguishable characters, stressing the need to clearly differentiate between similar-looking symbols such as zeros and the letter 'o', ones and the letter 'l', and twos and the letter 'z'. Kerl provides specific recommendations for writing each of these characters, often suggesting slight modifications or exaggerations to enhance their distinctness. He advocates for the adoption of specific stylistic choices, like a slashed zero or a looped 'l', to avoid confusion.
Further extending the discussion of individual characters, Kerl delves into the nuances of writing Greek letters, both uppercase and lowercase. He acknowledges the potential for ambiguity between certain Greek and Latin characters and offers guidance on how to distinguish them effectively in handwritten form. This includes recommendations for the curvature and proportions of each letter.
Moving beyond individual symbols, the guide then addresses the correct formation of more complex mathematical constructs. Kerl elucidates the proper ways to write fractions, emphasizing the importance of clear horizontal fraction bars and appropriately sized numerators and denominators to avoid misinterpretation as mixed numbers or separate entities. He also meticulously details the correct presentation of radicals and roots, providing explicit instructions on the placement of the radical sign and the positioning of the radicand, particularly when dealing with more complicated expressions involving multiple terms or nested radicals.
The importance of spacing and alignment in mathematical expressions receives substantial attention. Kerl argues that proper spacing not only enhances readability but also contributes to the visual clarity and aesthetic balance of the overall expression. He provides detailed advice on how to space variables, operators, and functions appropriately, ensuring that the relationships between different parts of the equation are clearly conveyed. He specifically addresses the proper alignment of elements within multi-line equations and inequalities, highlighting the role of consistent spacing in maintaining clarity and visual organization.
Finally, the guide offers practical tips for improving handwriting in general, such as choosing appropriate writing instruments, maintaining a consistent writing angle, and practicing regularly to develop muscle memory and fluidity. Kerl underscores the connection between legible handwriting and effective mathematical communication, arguing that clear and well-formed notation is essential for both conveying and understanding complex mathematical ideas. He concludes by encouraging readers to adopt a conscious and deliberate approach to mathematical handwriting, treating it as a valuable skill that contributes significantly to mathematical proficiency.
Summary of Comments ( 129 )
https://news.ycombinator.com/item?id=42985427
Hacker News users discuss the linked guide on mathematical handwriting, largely praising its practical advice. Several commenters highlight the importance of clear communication in mathematics, emphasizing that legible handwriting benefits both the writer and the reader. Some share personal anecdotes about struggling with handwriting and the impact it has on mathematical work. The suggestion to practice writing Greek letters resonates with many, as does the advice on spacing and distinguishing similar-looking symbols. A few commenters offer additional tips, such as using lined paper turned sideways for better vertical alignment and practicing writing on a whiteboard to improve clarity and flow. Overall, the comments reflect an appreciation for the guide's focus on the often-overlooked skill of legible mathematical writing.
The Hacker News post linking to John Kerl's "Tips for Mathematical Handwriting" has generated a modest discussion with several interesting comments. Many users agree with Kerl's advice, sharing their own experiences and adding further suggestions.
Several commenters emphasize the importance of clear handwriting in mathematics, particularly in educational settings. One commenter recounts their experience as a grader, highlighting the difficulty of deciphering poorly written symbols and the impact it has on both the grading process and the student's ability to communicate their understanding. Another user mentions the frustration of having to interpret messy handwriting during exams, especially under time pressure. This reinforces Kerl's point about the importance of legibility for effective communication.
The distinction between similar-looking characters is a recurring theme. Commenters specifically mention the importance of differentiating between 'u' and 'v', '0' and 'O', '1', 'l', and 'I'. One commenter humorously recalls their professor's mnemonic device for distinguishing 'epsilon' and 'element of' symbols. The need for clearly defined operators, such as the implication symbol, is also highlighted.
Practical tips from commenters include practicing writing Greek letters and other mathematical symbols and consciously focusing on forming distinct characters. Using lined or grid paper is suggested to help maintain consistent size and spacing. One user suggests starting with printed worksheets with large symbols for tracing to develop muscle memory for proper formation.
Beyond specific characters, the overall neatness and organization of written work are also discussed. Commenters advocate for deliberate spacing and using different sizes for different elements (e.g., larger symbols for summations and integrals) to improve visual clarity. The use of different colored pens for different parts of an equation is also suggested as a helpful technique.
A couple of comments offer alternative perspectives. One commenter mentions the increasing use of LaTeX and other typesetting tools, which might make handwriting less critical for professional mathematicians. However, they acknowledge the value of clear handwriting for educational purposes and personal note-taking. Another user points out cultural differences in handwriting styles and the potential challenges this presents.
In summary, the comments generally endorse the value of legible mathematical handwriting, echoing and expanding upon the points made in Kerl's article. They offer practical advice and personal anecdotes that underscore the importance of clear communication in mathematics, especially within the context of learning and teaching.