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I've had a similar thought as the author, and often wondered - could we develop alternative systems for intermediate-to-advanced mathematical concepts that woul

I've had a similar thought as the author, and often wondered - could we develop alternative systems for intermediate-to-advanced mathematical concepts that would make it easier to parse?

adam930 11y ago
Yes, in fact there already is such a formalism: http://faculty.luther.edu/~macdonal/ http://faculty.luther.edu/~macdonal/ From the first page: "Geometric algebra and its extension to geometric calculus unify, simplify, and generalize vast areas of mathematics that involve geometric ideas, including linear algebra, multivariable calculus, real analysis, complex analysis, and euclidean, noneuclidean, and projective geometry. They provide a unified mathematical language for physics (classical and quantum mechanics, electrodynamics, relativity), the geometrical aspects of computer science (e.g., graphics, robotics, computer vision), and engineering."
Yomammas_Lemma 11y ago
Category theory?
- charlieflowers 11y ago
  It has been called many things ("general abstract nonsense", etc.), but I don't know if it has ever been called "an easier way to explain things to non-mathematicians." :)
  - eli_gottlieb 11y ago
    Nobody thinks category theory is easy for nonmathematicians, but the point of it is that it provides a common language for talking about common behaviors across many different, seemingly disparate, fields of mathematics, for mathematicians.
    - charlieflowers 11y ago
      Fair enough.
- johncolanduoni 11y ago
  Very much so. This has in recent times become something of a lingua franca for mathematicians in recent times. The most useful (and astounding) property is that it gives formal definitions that apply across disciplines, which often perfectly coincide with informal usages of the same names for similar constructs in different fields. For example, in mathematics we often have the notion of a product of two structures. The simplest is the product of two sets A and B, which in computer programming terms would just be a structure containing a field of type A and a field of type B. There are more subtle and sophisticated examples in other fields like topology, but it turns out that the categorical definition[1] matches the definition of product mathematicians were already using in each of these fields, even though it came about much later! [1]: https://en.wikipedia.org/wiki/Product_(category_theory) https://en.wikipedia.org/wiki/Product_(category_theory)

I've had a similar thought as the author, and often wondered - could we develop alternative systems for intermediate-to-advanced mathematical concepts that would make it easier to parse?

adam930 11y ago

Yes, in fact there already is such a formalism: http://faculty.luther.edu/~macdonal/ http://faculty.luther.edu/~macdonal/ From the first page: "Geometric algebra and its extension to geometric calculus unify, simplify, and generalize vast areas of mathematics that involve geometric ideas, including linear algebra, multivariable calculus, real analysis, complex analysis, and euclidean, noneuclidean, and projective geometry. They provide a unified mathematical language for physics (classical and quantum mechanics, electrodynamics, relativity), the geometrical aspects of computer science (e.g., graphics, robotics, computer vision), and engineering."

Yomammas_Lemma 11y ago

Category theory?

charlieflowers 11y ago
It has been called many things ("general abstract nonsense", etc.), but I don't know if it has ever been called "an easier way to explain things to non-mathematicians." :)
- eli_gottlieb 11y ago
  Nobody thinks category theory is easy for nonmathematicians, but the point of it is that it provides a common language for talking about common behaviors across many different, seemingly disparate, fields of mathematics, for mathematicians.
  - charlieflowers 11y ago
    Fair enough.
johncolanduoni 11y ago
Very much so. This has in recent times become something of a lingua franca for mathematicians in recent times. The most useful (and astounding) property is that it gives formal definitions that apply across disciplines, which often perfectly coincide with informal usages of the same names for similar constructs in different fields. For example, in mathematics we often have the notion of a product of two structures. The simplest is the product of two sets A and B, which in computer programming terms would just be a structure containing a field of type A and a field of type B. There are more subtle and sophisticated examples in other fields like topology, but it turns out that the categorical definition[1] matches the definition of product mathematicians were already using in each of these fields, even though it came about much later! [1]: https://en.wikipedia.org/wiki/Product_(category_theory) https://en.wikipedia.org/wiki/Product_(category_theory)