Mathematics: A Universal Language or a Foreign One?

Does math serve as a universal language, or is it something more akin to a foreign language that we must actively learn? To understand the nature of mathematics as a form of communication, we must explore the differences between natural and formal languages, and the unique role that mathematical notation plays in a globalized world.

Mathematics - Not Quite a Natural Language

Mathematics might be compared to a language, but it is not a natural language like English, Spanish, or Mandarin. Unlike natural languages, where one acquires fluency through immersion or socialization within a community, mathematical proficiency requires structured learning and practice. Just as one learns a foreign language in a classroom setting, mathematical concepts are often introduced and mastered in educational institutions.

The Essence of Mathematical Notation

Mathematics, at its core, is a formal and specialized language. Its notation is based on a limited set of abstract symbols and concepts. This rigour and precision allows mathematicians to communicate and collaborate across borders and cultures with relative ease. However, this formal nature also limits its applicability in the realm of everyday communication.

Mathematical Notation: A Transliteration of Ideas

Mathematical notation is a powerful tool for expressing abstract ideas. It serves as a universal script, much like ideograms or pictographs, which represent concepts rather than concrete words. This characteristic allows mathematicians from diverse linguistic backgrounds to understand and communicate complex ideas without the need for verbal language.

The Limitations of Mathematical Notation

Despite its power, mathematical notation has its limitations. It is rooted in a finite set of abstract symbols, making it unsuitable for conveying an unlimited range of qualitative concepts. Mathematical notation excels at expressing concepts at various levels of abstraction, from the most concrete to the most general. However, it fails to capture the full spectrum of human experience and emotion that natural languages can.

Attempts to create truly ideographic scripts that represent qualitative concepts rather than linguistic words have met with limited success. Books such as "In the Land of Invented Languages" by Arika Okrent and "The Search for the Perfect Language" by Umberto Eco delve into these challenges and the historical efforts to bridge the gap between ideographic and phonographic scripts.

Conclusion

Mathematics, while it may appear universal and abstract, is indeed a form of formal language that requires structured learning to master. Despite its limitations in everyday communication, mathematical notation remains a critical tool for expressing complex, abstract ideas with precision and clarity. However, natural languages continue to play an essential role in expressing the nuances and emotions of human experience.

Our journey through the nature of mathematical language invites us to appreciate the unique contributions of both formal and natural languages in shaping our understanding and communication of the world around us.