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Have there been any Buddhist texts addressing geometry, calculation or abstract algebra?

I recently read a composite biography of several mathematicians through history. While some had schizophrenia, few had serious mood disorders. Cardano was mentioned as a possibility. Proofs require a mindfulness of thought. There is also the stereotype of ivory tower nerds being emotionless or stoic. There seem to be therapeutic effects of learning mathematics or minds resistant to emotional pains are better at math than average.

Buddhism has a lot to do with handling emotional pain. Has me wondering if mathematics might have been a point of interest. Numbers seem to be. Four Noble Truths, Eightfold Path, Three Marks if Existence.

On the other hand, a straight forward, linear, literal approach to understanding doesn't quite feel like Buddhism .

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Have there been any Buddhist texts addressing geometry, calculation or abstract algebra?

I don't know much about the History of Mathematics.

This History of 0 (zero) mentions Pingala -- that's "Maurya or post-Maurya" era, perhaps they were mostly-all kind of Buddhists then.

I read elsewhere that, later (e.g. at the time of the Islamic invasion), it was the educated/urban/merchant class who were mostly-Buddhist -- whereas it was the rural/peasant class who were 'Hindu'. That (being merchants, trading, travelling) might imply they (i.e. the lay people/society who supported the Buddhist monastics) had uses for mathematics.

While some had schizophrenia, few had serious mood disorders.

I don't know if you might have read it, Zen and the Art of motorcycle Maintenance mentions, some instructions for assembling a bicycle,

"... I’ve a set of instructions at home which open up great realms for the improvement of technical writing. They begin, ‘Assembly of Japanese bicycle require great peace of mind.’"

Buddhism has a lot to do with handling emotional pain. Has me wondering if mathematics might have been a point of interest. Numbers seem to be. Four Noble Truths, Eightfold Path, Three Marks if Existence.

I think the numbers there are to do with "list-making" -- a numbered list.

Also "analysis" -- i.e. dividing and categorising.

So instead of "there's a big problem" Buddhism gives "there are three poisons, ten fetters -- twelve nidanas -- etc."

That's not classical "mathematics" like greek geometry. It may be related to or contain (use or presume) logic -- see Catuṣkoṭi for example.

And deconstruction seems like it ought to be useful if you want to make something stop -- like taking apart a wrist-watch (which will stop it), and understanding the causes of things (like the French proverb that "to understand all is to forgive all").

I think that list-making is principally an "Abhidhamma" kind of thing -- just one example among many might be the Paṭṭhāna.

Apparently the (several) abhidhammas (of the several schools) are summaries of doctrine. One of the ways to summarise elements of doctrine is to list or index them.

Here's a collection of some of the most famous lists -- Dhamma Lists

On the other hand, a straight forward, linear, literal approach to understanding doesn't quite feel like Buddhism.

There are many forms of maths, aren't there. I don't know them all of course, it seemed to me that maths was good at taking things apart (analysis), abstraction (maybe number theory), putting things together (maybe induction) -- and inventing systems, based on sets of axioms.

And when you choose useful axioms (which e.g. match observations) then it's science.

It seems to me, I guess, that Buddhism is more like a science than mathematics -- doctrines like the four noble truths being axiomatic.

Also Buddhism kinds of warns against constructing things (like sankharas).

And maybe warns against too much deconstruction too, like if the west tradition has a subjective/objective dichotomy (these being two extremes) then buddhism teaches "the middle way" meaning "neither extreme".

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Have there been any Buddhist texts addressing geometry, calculation or abstract algebra?

Not as far as I know. It is in the foundations of mathematics that Buddhism becomes fascinating since it overcomes Russell's paradox.for a fundamental theory, but at a higher level I'm not aware of any maths texts or much interest in the topic

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    I'm curious about how you see Buddhist thought overcoming Russell's paradox. Can you explain? – Ted Wrigley Dec 28 '19 at 15:21
  • @TedWrigley - Aha. Well spotted. One explanation is given by George Spencer Brown in his book 'Laws of Form'. He describes the logic of ontology, if I may put it like this, and the emergence of form from formlessness, and to do so must overcome R's paradox. Russell agreed it solved his problem but missed its metaphysical message and the clear connection with Buddhism and Taoism. Brown's description itakes the form of a simple calculus and it models Nagarjuna's metaphysics. A fundamental theory must overcome R's paradox and the Middle Way view does exactly this. . . . , . – PeterJ Dec 29 '19 at 13:15
  • @TedWrigley - In short, the Middle Way view does not reify sets but the origin of sets, so reducing them for a fundamental theory is not a problem. – PeterJ Dec 29 '19 at 13:17
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Yes, Buddhism is "deceptively" related to mathematics, but only those who are lucky enough to be able to appreciate the Mahayana (Chinese lineage) teachings, they can fathom it.

Example A, 108 is an "infinite" number, it gets applied to the number of Arhats, fetters, features/beauties (minor) of the Buddha... 108 = 9x12 = 3x3x3x4 > 3+3+3+4=13 (our world is on the 13th petal of the Avatamsaka Universe) ; 108 > 1+0+8=9 > 3x3 or 3+6 (3,6,9 are magic numbers that can divide any number if its digits added reduced to 3,6,9).

Example B, the Eight-Consciousness and number 3, 3 is a "fundamental" number, as the Dao De Jing said 3 gives birth to all things. To stabilize any object it needs 3 points, say, a tripod. Meanwhile 8=23 or 2x2x2. Why 2? Because our world is in dual, I/you, subject/object, consciousness/cognize, smell/scent, vision/form...

Example C, numbers are related to sound, i. e., Dharani, which the raw element is the letters, or vowels and consonants... OK, let me find reference to continue

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    The special status attributed to the number 108 is actually derived from Hinduism, the predominant religion in the Buddha's time. Hindu and Buddhist Jamala for example both have 108 beads. As for the Taoist example, the Chinese text doesn't refer to the math number 1 in this verse, but about the undifferentiated oneness of all things , that we render into dualistic language. In Literary Chinese , 一生二 "one gives birth to two", the first two characters (一生) also mean "from beginning to end; all-encompassing". This is lost in translation. – Codosaur Dec 28 '19 at 21:51
  • @Codosaur I hope your mentioning of 108 & Hinduism not an indication you the fetish of knowledge like a Buddhist sect who declared anything written in Sanskrit is Brahmin, not Buddhist, impure. Btw, that is Brahmin-ism, Hinduism was later than Buddhism. Also, inherited knowledge doesn't mean it not Buddhist knowledge, like Karma; but Buddha perfected the knowledge. Einstein also shared knowledge with Newton... Copernius, say, the earth circling the sun - impure, not physics? Mathematically, 3 incl. 1+2, and I've never heard 1 meant beginning, for next said, 二生三, here 生 is 生ing, a verb. Thks :D – Mishu 米殊 Dec 29 '19 at 1:45
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    @Codosaur - Excellent point. translations of that verse of the Tao Te Ching often bother me. – PeterJ Dec 29 '19 at 13:09
  • No no no, @Codosaur missed the point, PeterJ. Before 一生二 is 道生一 (The Dao gives birth to One), Dao is the "origin/undifferentiated", not One. Remember the verses? 道可道,非常道。名可名,非常名。无名,天地之始;有名,万物之母 (The Dao has... name that can be named is not The Name... Nameless, is the beginning of heaven and earth...) Therefore, if you can say "one", it is named, it is not the beginning. Ok? Why don't you two consult someone who is fluent and an adept in Chinese, but listening to the foreigners ¯_(ツ)_/¯? ... peculiar men... – Mishu 米殊 Dec 30 '19 at 11:25
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    @Mishu米殊 - Agree about 1.2.3 and the other numbers. Also agree that a fundamental theory must go deeper than the numbers. . – PeterJ Dec 30 '19 at 21:03

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