We get pleasure and satisfaction by doing Mathematics. Thinking over math problems and solving them does give us some pleasure. According to Buddhism, what is this pleasure categorized as? A sensual pleasure ? Or is it like pleasure we get from Jhana?
I think it would be classed as household joy;
"And what are the six kinds of household joy? The joy that arises when one regards as an acquisition the acquisition of forms cognizable by the eye — agreeable, pleasing, charming, endearing, connected with worldly baits — or when one recalls the previous acquisition of such forms after they have passed, ceased, & changed: That is called household joy. (Similarly with sounds, smells, tastes, tactile sensations, & ideas.)
The other types of joy are tied up with renunciation;
"And what are the six kinds of renunciation joy? The joy that arises when — experiencing the inconstancy of those very forms, their change, fading, & cessation — one sees with right discernment as it actually is that all forms, past or present, are inconstant, stressful, subject to change: That is called renunciation joy. (Similarly with sounds, smells, tastes, tactile sensations, & ideas.) MN137
One like this thinks; i am good because of this [solving], delights in thinking, dwells in solving, neglects seclusion and does not attend to the teacher's message.
I think it's like entertainment, a hobby or a sport.
There are three feelings, pleasant, painful and neutral. The first two feelings are familiar in terms of sensual desire (e.g., coveting another's body). However, the third feeling, the neutral feeling, may be unfamiliar. In mathematics, we often encounter the neutral feeling.
When given a math problem we initially have a neutral feeling. It is neutral because we do not know if the problem can be solved or not. If we engage and solve the problem, we feel pleasure in knowledge gained. If we engage and struggle with the problem without progress, we feel pain at our continued ignorance.
MN44:24.4: Neutral feeling is pleasant when there is knowledge, and painful when there is ignorance.”
Because neutral feelings can lead to pleasure, we may get caught up in chasing knowledge for that very pleasure. Mathematics is in the field of thought. In Buddhism, the mind is the sixth sense, so yes, craving the joy of mathematics would be a "sensual pleasure".
SN35.247:2.8: When they know a thought with their mind, if it’s pleasant they hold on to it, but if it’s unpleasant they dislike it. They live with mindfulness of the body unestablished and a limited heart. And they don’t truly understand the freedom of heart and freedom by wisdom where those arisen bad, unskillful qualities cease without anything left over.
Mathematics itself isn't at issue here. Solving a mathematical problem while building a house is perfectly fine. But if we daydream about mathematics while being paid as a carpenter, that would lead to smashed thumbs and other suffering.
Solving mathematical problems can be pleasant work. In that sense it is like jhana. However, mathematics is limited (see Goedels Incompleteness Theorem) and has nothing to do with the end of suffering. Practice jhana for the end of suffering relying on wisdom, truth, generosity and peace.
We are think of everything as illusion, idea, so we should analysis first...
Thinking over math problems and solving them does give us some pleasure
"Thinking over" can be assembled by 3 elements--wholesome factors, unwholesome factors, or neither wholesome nor unwholesome factors.
"math problems" is neither wholesome nor unwholesome factors.
"solving" can be assembled by 3 elements--wholesome factors, unwholesome factors, or neither wholesome nor unwholesome factors.
"some pleasure" can be assembled by 3 elements--wholesome factors, unwholesome factors, or neither wholesome nor unwholesome factors.
Wholesome karma is assembled by at least 31 wholesome mind and mind factors. Wholesome karma causes at least 2 benefits of 3 benefits (this life, next life, Nibbāna) with 2 benefits of of 3 benefits (own, surrounded people, universe society)[Less benefit, less wisdom]. So...
- Thinking over math problems and solving them to help drowning people, giving us some wholesome pleasure.
- (Buddhist insider) Thinking over math problems and solving them to help drowning people and to practice own mind for higher meditation to enlightenment, giving us some higher and higher wholesome practice to get Nibbāna.
Unwholesome karma is assembled by not over more than 23 unwholesome mind and mind factors. Unwholesome karma causes only 1 benefits of 3 benefits (this life, next life, Nibbāna) with only 1 benefits of of 3 benefits (own, surrounded people, universe society). So...
- Thinking over math problems and solving them to get only pride and only wholesome pleasure.
- (Going to hell) Thinking over math problems and solving them to do Akusalakammapatha 10 (Tenfold unwholesome course of action).
neither wholesome nore unwholesome factors
Neither wholesome nore unwholesome factors are unmeditatable such as resultants, or perfectly meditated wholesome of Arahanta's mind.
So, in Abhidhamma Vibhaṅga...
the book of analysis
- Analysis Of The Heart Of The Teaching
Therein what is “wisdom by means of thinking”? Because of work invented by ingenuity or because of craft invented by ingenuity or because of the branches of science invented by ingenuity, so these wisdom are acquired by one without hearing from others--"Karma is one’s own possession" wisdom or "form is impermanent; feeling; Is impermanent. perception; Is impermanent. volitional activities; Is impermanent. or consciousness is impermanent;" conformity with truth wisdom like that which is conformity with truth, ability (to comprehend) with truth, view of truth, choice of truth, opinion with truth, seeing the truth, ability to apprehend (these) dhammas. This is called wisdom by means of thinking.
Therein what is “wisdom by means of hearing”? Because of work invented by ingenuity or because of craft invented by ingenuity or because of the branches of science invented by ingenuity, so these wisdom are acquired by one by hearing from others--"Karma is one’s own possession" wisdom or "form is impermanent; feeling; Is impermanent. perception; Is impermanent. volitional activities; Is impermanent. or consciousness is impermanent;" conformity with truth wisdom like that which is conformity with truth, ability (to comprehend) with truth, view of truth, choice of truth, opinion with truth, seeing the truth, ability to apprehend (these) dhammas. This is called wisdom by means of hearing.
All the wisdom of one who has attained, is, wisdom by means of development.
There are three types of cravings in Iti 58:
This was said by the Blessed One, said by the Arahant, so I have heard: "There are these three cravings. Which three? Craving for sensuality, craving for becoming, craving for non-becoming. These are the three cravings."
And there are six senses from MN 148:
"'The six internal media should be known.' Thus was it said. In reference to what was it said? The eye-medium, the ear-medium, the nose-medium, the tongue-medium, the body-medium, the intellect-medium. 'The six internal media should be known.' Thus was it said. And in reference to this was it said. This is the first sextet.
"'The six external media should be known.' Thus was it said. In reference to what was it said? The form-medium, the sound-medium, the aroma-medium, the flavor-medium, the tactile sensation-medium, the idea-medium. 'The six external media should be known.' Thus was it said. And in reference to this was it said. This is the second sextet.
The desire to solve mathematical problems comes from the craving of sensual pleasures, specifically of intellect and ideas.
From dependent origination, we know that craving leads to clinging. There are four types of clinging in MN 11:
"Bhikkhus, there are these four kinds of clinging. What four? Clinging to sensual pleasures, clinging to views, clinging to rules and observances, and clinging to a doctrine of self.
Obviously, clinging to the pleasure of solving mathematical problems is a clinging to sensual pleasures. But how does this happen? This is answered in SN 35.63:
"There are sounds cognizable via the ear... aromas cognizable via the nose... flavors cognizable via the tongue... tactile sensations cognizable via the body... ideas cognizable via the intellect — agreeable, pleasing, charming, endearing, fostering desire, enticing — and a monk relishes them, welcomes them, & remains fastened to them. As he relishes them, welcomes them, & remains fastened to them, delight arises. There being delight, he is impassioned. Being impassioned, he is fettered. A monk joined with the fetter of delight is said to be a person living with a companion.
But the story doesn't end there.
After clinging to the sensual pleasure of solving mathematical problems, you may want to become a professional mathematician or maybe you want to start a YouTube channel showing your mathematical skills, passion and joy. That's the craving of becoming - you want to become somebody. That leads to clinging to views and clinging to the doctrine of the self too, that "I am a famous mathematician" or "I am a famous math enthusiast".
And then looking at Dependent Origination again, craving leads to clinging, which leads to becoming, which leads to the birth of personhood, which then leads to all suffering.
In my experience there are several components to the pleasure.
One is social. As students we are told -- for example by teachers, parents, maybe peers -- that mathematical activity is praiseworthy (that it's ethical, harmless, maybe useful, and so on) -- and obviously some students like to know what society wants and to do what society tells them.
Another is to do with peace of mind. Mathematical activity i.e. solving a maths problem requires you to stop thinking about things other than the problem in question. In modern terms I expect the brain is less active than when you're distracted by other thoughts (e.g. by thoughts about the past or the future) -- it's a specialised form of thinking which requires some activity from some parts of the mind, and the ability to switch off or let go of all distractions and purposeless worry.
Following from 2., f I recall correctly, a component of that peace (or absence of mental activity) is some amount and some type of egolessness. You're solving a problem set (discovered) by someone else, you're learning someone else's (mathematicians') way of thinking, and you're necessarily (at least temporarily) forgetting about any and all "personal" and other "social" and "physical" problems.
Following from 3., instead of having a mental state of "worry and restlessness", "or "sloth", or "pursuit of sensuality", what you need as a mental state might be (or at least might resemble) the factors of awakening -- or the strengths (faculties), the bases of power, and even the exertions.
Perhaps the fact that mathematics involves/requires this kind of activity, training, discipline, is one of the reasons why the subject is considered worthwhile to be taught in schools -- i.e. not only for its own sake as a useful subject (which it isn't very useful necessarily, it's very rare that I ever use any "maths" more complicated than arithmetic, since leaving school), but also as a form of mental training -- perhaps like sports are also considered worthwhile, not necessarily as a subject in themselves but as a form of (healthy) physical training and development.
At least at the student level of mathematics, the "problems" which you're working on are finite and have a solution. The solution is simpler than the problem, when you're looking for a solution you're looking to reduce the problem to a simple solution ("Q.E.D."). The act of (successfully) simplifying is (mentally) rewarding for the various reasons given above. It's also a taste of peace or freedom -- i.e. solving the problem means that the problem is experienced as finished and completed (ceased).
I'm not sure if -- but I hope that -- this answer counts as "Buddhist enough" for this site. It's based on my personal experience of "doing" mathematics (and other similar work) at school and afterwards. I suppose (though I don't know) that the other answers are true -- e.g. that it can be categorised as "sensual", if the mind's consciousness of and pursuit of mental objects is categorised as the sixth "sense". Instead of answering the question in general (i.e. "how does Buddhism categorise...?"), I was hoping to analyse in detail (i.e. "what is this pleasure?").
So far as I can tell, it shares some of the same mental "reward mechanisms" as a training in Buddhism might. I assume you already know enough Buddhist doctrine to recognise parallels between the components I listed and the suttas.
It might also share some of the disadvantages of other pleasures, for example:
- Wanting to experience it again after it has ceased
- Wanting to do that instead of other, better activity
- Identification -- e.g. "I am a mathematician", "I am better at this than other people are", "This skill at (training in) mathematics is me/mine/myself", and so on.
- Reification -- e.g. mistaking maths for something "real", and thinking "only this is true", etc.
I don't know what any Buddhists say about mathematics (I studied maths before Buddhism and not with Buddhists). I presume it's classified as a householder activity/chore, and maybe good if it's done ethically. Possibly something like sweeping the floor, or even cooking, would be a more worthwhile activity. It's presumably subject to the three characteristics, like almost everything else -- and its not being or its not becoming a cause of suffering depends on stopping and letting go.