4 ms·

In western mathematics? Maybe. In India analytic geometry was the norm and Indians used infinity and negative numbers for over a millennia before Europeans.

ncmncm 5y ago
Yes. The West saw extremely limited contact with ancient Indian mathematics until quite recently. I think India itself largely forgot about its own mathematical tradition well before it was occupied by European powers.
- jimsimmons 5y ago
  Agreed
  - ncmncm 5y ago
    The Wikipedia page on Analytic Geometry utterly fails to so much as mention classical Indian work on the topic. I presume some officious editor is keeping it well-scrubbed of any non-Western credits.
    - jimsimmons 5y ago
      That’s pretty common. The issue is it’s hard to have well referenced scholarly sources for these things. Indians have a tendency to mystify their past. Such shame really. One of my long term goals in life is to create a authoritative, non religious, simple source for Indian Classics.
alentist 5y ago
> In India analytic geometry was the norm Source?
- jimsimmons 5y ago
  Hard to give a concrete source because it’s simply not there. See my comment in the sibling thread. I can make a case and you can judge for yourselves. The key insight in analytic geometry is that geometric shapes and algebra are facets of the same underlying concept. This allowed Descartes to develop coordinate system. This in turn allowed development of calculus and everything else. This was a striking discovery in the western world. The practice of using equations for geometry however was very common in India. Brahmagupta was the first to have a formula for area of cyclic quadrilateral in 6th century [2]. Notably the proof used trigonometry. Earlier similar result in West is Heron’s formula for the area of triangle. However the proof doesn’t use any algebra. Bhaskara had devised ideas of differential calculus by 11th century [2]. A concrete example of this is the use of sine and cosine series in Kerala School of Mathematics [3]. This is really just the tip of the iceberg because majority of Indian mathematics is simply lost. What remains is poorly understood. But when reliable translations are available you can see that idea of using geometry and algebra interchangeably was common. Maybe I’m biased. Curious to know what others make of this [1] https://en.wikipedia.org/wiki/Brahmagupta%27s_formula https://en.wikipedia.org/wiki/Brahmagupta%27s_formula [2] https://en.wikipedia.org/wiki/Bh%C4%81skara_II https://en.wikipedia.org/wiki/Bh%C4%81skara_II [3] https://en.wikipedia.org/wiki/Kerala_school_of_astronomy_and_mathematics https://en.wikipedia.org/wiki/Kerala_school_of_astronomy_and...
  - alentist 5y ago
    > Brahmagupta was the first to have a formula for area of cyclic quadrilateral in 6th century That's not analytic geometry. > Bhaskara had devised ideas of differential calculus by 11th century [2]. A concrete example of this is the use of sine and cosine series in Kerala School of Mathematics [3]. I don't think these count as analytic geometry. Analytic geometry has a specific meaning: https://en.wikipedia.org/wiki/Analytic_geometry https://en.wikipedia.org/wiki/Analytic_geometry
    - jimsimmons 5y ago
      Yeah read the distance and angle section. Describing geometric objects with equations in coordinate system is analytic geometry. Anyway I’m not going to seriously discuss with you because it’s clear from your post history that your replies are avalanches of pedantry. If you think it has a specific meaning, elaborate it and identify the point of divergence or express what your view is. I don’t have an obligation to convince you.

ncmncm 5y ago

Yes. The West saw extremely limited contact with ancient Indian mathematics until quite recently. I think India itself largely forgot about its own mathematical tradition well before it was occupied by European powers.

jimsimmons 5y ago
Agreed
- ncmncm 5y ago
  The Wikipedia page on Analytic Geometry utterly fails to so much as mention classical Indian work on the topic. I presume some officious editor is keeping it well-scrubbed of any non-Western credits.
  - jimsimmons 5y ago
    That’s pretty common. The issue is it’s hard to have well referenced scholarly sources for these things. Indians have a tendency to mystify their past. Such shame really. One of my long term goals in life is to create a authoritative, non religious, simple source for Indian Classics.

alentist 5y ago

> In India analytic geometry was the norm Source?

jimsimmons 5y ago
Hard to give a concrete source because it’s simply not there. See my comment in the sibling thread. I can make a case and you can judge for yourselves. The key insight in analytic geometry is that geometric shapes and algebra are facets of the same underlying concept. This allowed Descartes to develop coordinate system. This in turn allowed development of calculus and everything else. This was a striking discovery in the western world. The practice of using equations for geometry however was very common in India. Brahmagupta was the first to have a formula for area of cyclic quadrilateral in 6th century [2]. Notably the proof used trigonometry. Earlier similar result in West is Heron’s formula for the area of triangle. However the proof doesn’t use any algebra. Bhaskara had devised ideas of differential calculus by 11th century [2]. A concrete example of this is the use of sine and cosine series in Kerala School of Mathematics [3]. This is really just the tip of the iceberg because majority of Indian mathematics is simply lost. What remains is poorly understood. But when reliable translations are available you can see that idea of using geometry and algebra interchangeably was common. Maybe I’m biased. Curious to know what others make of this [1] https://en.wikipedia.org/wiki/Brahmagupta%27s_formula https://en.wikipedia.org/wiki/Brahmagupta%27s_formula [2] https://en.wikipedia.org/wiki/Bh%C4%81skara_II https://en.wikipedia.org/wiki/Bh%C4%81skara_II [3] https://en.wikipedia.org/wiki/Kerala_school_of_astronomy_and_mathematics https://en.wikipedia.org/wiki/Kerala_school_of_astronomy_and...
- alentist 5y ago
  > Brahmagupta was the first to have a formula for area of cyclic quadrilateral in 6th century That's not analytic geometry. > Bhaskara had devised ideas of differential calculus by 11th century [2]. A concrete example of this is the use of sine and cosine series in Kerala School of Mathematics [3]. I don't think these count as analytic geometry. Analytic geometry has a specific meaning: https://en.wikipedia.org/wiki/Analytic_geometry https://en.wikipedia.org/wiki/Analytic_geometry
  - jimsimmons 5y ago
    Yeah read the distance and angle section. Describing geometric objects with equations in coordinate system is analytic geometry. Anyway I’m not going to seriously discuss with you because it’s clear from your post history that your replies are avalanches of pedantry. If you think it has a specific meaning, elaborate it and identify the point of divergence or express what your view is. I don’t have an obligation to convince you.