Where does mathematics come from?

Is mathematics invented or discovered? Do mathematical objects pre-exist in some transcendental plane, are they abstractions of our sensory experiences, or are they just fictional objects invented by our minds? Would an alien species specify mathematical abstractions in a different way? These are the questions which are explored under the “Philosophy of mathematics”. Several competing theories such as Logicism, Intuitionism, Formalism and Platonism have been proposed to explain the nature of mathematics.   Here, I shall present some insights by Sri Aurobindo and the Mother which are connected to this topic.

Mathematicians who get breakthroughs in flashes of intuition solemnly aver that mathematical objects must pre-exist in some transcendental plane. Srinivasa Ramanujan claimed that the Goddess Namagiri would visit him in dreams and give him those astounding equations that continue to boggle the minds of mathematicians.  Paul Dirac said that it was his keen sense of beauty that enabled him to divine the Dirac equation for the electron which others had searched in vain. The renowned Hungarian mathematician Paul Erdos used to say that there was a “Book” in which God kept the most elegant proofs of all theorems.  He wasn’t religious per se but this was his way of expressing the sheer delight that he and other mathematicians experience whenever they come across an ingenious mathematical solution.  Jacques Hadamard stated that the moment of breakthrough felt similar to the moment when we suddenly recognize someone’s face.   The French mathematician Andre Weil expressed it poetically when he wrote:

«Rien  n’est  plus  fécond,  tous  les  mathématiciens  le  savent,
que  ces obscures analogies,
ces troubles reflets d’une théorie à une autre,
ces furtives caresses,
ces brouilleries inexplicables:
rien aussi ne donne plus de plaisir au chercheur.
Un  jour  vient  où  l’illusion  se  dissipe;
le pressentiment se change en certitude

les théories jumelles révèlent leur source commune avant de disparaître Comme l’enseigne la Gita on atteint a la connaissance et a l’difference en meme temps

La metaphysique est devenue mathematique, prête à former la matière d’un traité dont la beauté froide ne saurait plus nous émouvoir »

English translation:

“Nothing is more fruitful—all mathematicians know it—
than those obscure analogies,
those disturbing reflections of one theory on another;
those furtive caresses,
those inexplicable discords;
nothing also gives more pleasure to the researcher.
The day comes when this illusion dissolves:
the presentiment turns into certainty;
the yoked theories reveal their common source
before disappearing.
As the
Gita teaches, one achieves
knowledge and indifference at the same time

Metaphysics has turned into mathematics, ready to form the contents of a treatise whose cold beauty could no longer move us.

Is it really possible to characterize and qualify the beauty that mathematicians feel when they come across an elegant solution ?

In a recently published paper, researchers at the University College, London found that the experience of mathematical beauty activates the same region of the emotional brain — namely the medial orbito-frontal cortex — as the experience of beauty derived from art or music.

Professor Semir Zeki, lead author of the paper from the Wellcome Laboratory of Neurobiology at UCL, said: “To many of us mathematical formulae appear dry and inaccessible but to a mathematician an equation can embody the quintescence of beauty. The beauty of a formula may result from simplicity, symmetry, elegance or the expression of an immutable truth. For Plato, the abstract quality of mathematics expressed the ultimate pinnacle of beauty.”

“This makes it interesting to learn whether the experience of beauty derived from such as highly intellectual and abstract source as mathematics correlates with activity in the same part of the emotional brain as that derived from more sensory, perceptually based, sources.”

…”We have found that activity in the brain is strongly related to how intense people declare their experience of beauty to — even in this example where the source of beauty is extremely abstract. This answers a critical question in the study of aesthetics, namely whether aesthetic experiences can be quantified.”

“We have found that, as with the experience of visual or musical beauty, the activity in the brain is strongly related to how intense people declare their experience of beauty to be — even in this example where the source of beauty is extremely abstract. This answers a critical question in the study of aesthetics, one which has been debated since classical times, namely whether aesthetic experiences can be quantified.”

(Read the full report over at sciencedaily)

The general question of “Where does mathematics comes from?” is studied under the field  called “Philosophy of Mathematics”.   Philosophers have proposed many theories such as Platonism, Constructivism, Intuitionism, Logicism to explain the origin of mathematics.  Platonists believe that mathematical objects reside in some transcendental plane and mathematicians are really just discovering them.  Formalism, proposed by David Hilbert, claims that mathematical equations are just consequences of certain string manipulation rules.  Logicism developed by Frege seeks to reduce all mathematics to pure logical rules.  There are others who believe that mathematics is just an outcome of the cognitive activity of the human brain. (Aristotle was the first who proposed the germ of this theory).

An analogy might help us understand the differences between these theories. Consider an exotic object such as a Swiss Army knife. If you felt that the knife was so incredibly perfect that its design must pre-exist in some mythical world, then you are a Platonist. If you thought the knife was constructed using step-by-step rules, you are a formalist. If you felt that the knife evolved from the repeated trial-and-error experiments of many scientists, you are an empiricist.

We won’t enter deeply in this philosophical  debate for now but we will present a few remarks by the Mother which are connected to this topic.  Her views can be said to be aligned with Platonism and with the recent finding that mathematical beauty and artistic beauty awaken the same region of the brain.

Scientific and artistic imagination are complimentary

Question: How is it that in people occupied with scientific studies artistic imagination is lacking? Are these two things opposed to each other?

Mother: They do not belong to the same domain. It is exactly as though you had what is called “a torchlight”, a small beacon-light in your head at the place of observation. Scientists who want to do a certain work turn the beacon in a particular way, they always put it there and the beacon remains thus: they turn it towards matter, towards the details of matter. But people with imagination turn it upward, because up above there is everything, you know, all inspirations of artistic and literary things: this comes from another domain. It comes from a much more subtle domain, much less material. So these turn upward and want to receive the light from above. But it is the same instrument. The others turn it downwards, and it is just a lack of gymnastic skill. It is the same instrument. It is the same power of a luminous ray upon something. But as one has made it a habit of concentrating it in a certain direction, one is no longer supple, one loses the habit of doing things otherwise.

But you can at any time do both the things. When you are doing science, you turn it in one direction and when you do literature and art, you turn it in the other direction; but it is the same instrument: all depends on the orientation. If you have concentration, you can move this power of concentration from one place to another and in every way it will be effective. If you are occupied with science, you use it in a scientific way, and if you want to do art, you use it in an artistic way. But it is the same instrument and it is the same power of concentration. It is simply because people do not know this that they limit themselves. So the hinges get rusty, they do not turn any more. Otherwise, if one keeps the habit of turning them, they continue to turn. Moreover, even from the ordinary point of view, it is not rare to find a scientist having as his hobby some artistic occupation – and the reverse also. It is because they have found that the one was not harmful to the other and that it was the same faculty which could be utilised in both.

Essentially, from the general point of view, particularly from the intellectual viewpoint, the most important thing is the capacity of attention and concentration, it is that which one must work at and develop. From the point of view of action (physical action), it is the will: you must work and build up an unshakable will. From the intellectual point of view, you must work and build up a power of concentration which nothing can shake. And if you have both, concentration and will, you will be a genius and nothing will resist you.

(Collected Works of the Mother, vol 5, p 128-129)

Ideas comes from the Universal Mind

Mother: Ideas have a higher origin than the mind. There is a region of the mind, higher than the ordinary mind, in which there are ideas, typal ideas, really prototypes; and these ideas descend and are clothed in mental substance. So, in accordance withhow to put it?the quality of the receiver, they either keep all their own qualities and original nature or become distorted, coloured, transformed in the individual consciousness. But the idea goes far beyond the mind; the idea has an origin much higher than the mind. So, the functioning is the same from both the universal and the individual point of view; the individual movement is only representative of the universal one. The scale is different, but the phenomenon is the same. Of course, these are no longer “thoughts” as we conceive thoughts; they are universal principles— but it’s the same thing—universal principles on which the universes are built.

In another conversation, she expounded on the different transcendental planes which are the source of creativity:

The first zone you encounter is the zone of painting, sculpture, architecture: everything that has a material form…They are not forms as we know them, but rather typal forms; you can see garden types, for instance, wonderfully colored and beautiful, or construction types.

Then comes the musical zone, and there you find the origin of the sounds that have inspired the various composers. Great waves of music, without sound. It seems a bit strange, but that’s how it is.

Beyond the musical zone lies thought: thoughts, organized thoughts for plays and books, abstractions for philosophies. That is the third zone. What you find there are thought formations that are expressed in each person’s brain in his own language. There are thought combinations for novels, plays, even philosophical systems. They are combinations of pure thought, not formulated in any language, but they are automatically expressed in each one’s brain according to his particular language. It is the domain of pure thought….

Higher up, there is a fourth zone, a zone of colored lights, plays of colored lights;… it is a zone of forces, a zone which appears as colored lights. No forms – colored lights representing forces. And one can combine these forces so that they work in the terrestrial atmosphere and bring about certain events. It’s a zone of action, independent of form, sound and thought; it is above all that. (Mother’s Agenda, 27 Oct 1962)

In other words, mathematical objects per se do not exist in some transcendental world but the generic patterns of thinking which influence our ideas do exist.  These ideas descend into our mind through the four levels of Vedic Vak covered in an earlier article.  Also check the articles on Roger Penrose versus Sri Aurobindo which explores this topic further.

Related Articles

  1. Roger Penrose and Sri Aurobindo on the Mind
  2. How to develop intuition
  3. Four Powers of Intuition
  4. Study of science as an aid in Yoga
  5. The role of intellectual development in the spiritual path
  6. How does the mind change with Yoga?
  7. All thoughts come from outside
  8. Distinguishing between stilling the mind and dynamizing meditation
  9. Syncretism in Sri Aurobindo’s thought – part 1
  10. Syncretism in Sri Aurobindo’s thought – part 2
  11. How does the brain absorb new ideas?
  12. Vedic Vak: illustration of Para Vak
  13. Brain imaging can reveal the movies in our mind
  14. The brain is not the mind as per Yoga psychology
  15. Perception of Time changes with the concentration of consciousness
  16. Difference between genius and mysticism
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31 thoughts on “Where does mathematics come from?

  1. Stephen Britton

    Dear Sandeepji,

    Thanks for this timely article; it appeared at the same time in which I’ve been more closely musing on the intersection of mathematics and spirituality. Ancient history, up to modern times, continually affirms a connection between the experience of intense contemplation on pure mathematical ideas and spirituality. In addition to Srinivasan Ramanujan’s attribution of his discoveries to the Goddess Namagiri, other instances of mathematicians recounting visitations from mathematical Muses include Georg Cantor’s (discoverer of modern Transfinite Set Theory) visions of heavenly messengers affirming his theory of the Infinite as a Divine revelation of the Absolute Infinite and Alexander Grothendieck’s encounter with a supraphysical female being, known as Flora or Lucifera, according to temperament. Mother’s explanation of Ideas having an origin higher than the ordinary mind is a reaffirmation of my own natural Platonistic perspective on the nature of math.

    Sandeep, do you think perhaps some mathematicians had access to the Supramental Truth-Consciousness by virtue of their years of disciplined mathematical contemplation and discriminative intuition? Or, to put it another way, can pure mathematics be used effectively as a form of Yoga-Sadhana? Franklin Merrell Wolff thought so. He even said,

    “[Mathematics] is that portion of ultimate truth that descended from the upper hemisphere, to use the terminology of Aurobindo, into the Adhar with minimum distortion, and thus becomes the Ariadne thread by which we may ascend again, most directly, most freely. (Merrell-Wolff, 1995a, p. 27)” (http://www.cejournal.org/GRD/Wolff.htm)

    Happy Darshan Day and may all fellow Sadhaks and Devotees in the Purna Yoga continue to progress from Light to Greater Light, on this 136th Birthday Anniversary of the Mother.

    Reply
    1. Sandeep Post author

      Stephen

      What a pleasant surprise. I didn’t think the article would get a sympathetic nod from anyone knowledgeable in mathematics, given that I don’t even mention Zermelo-Frankel axioms, etc and offer no proof for my contentions. On top of it, here is a commenter who respectfully calls me “Sandeep-ji” 🙂

      The number of professional mathematicians and scientists who are sympathetic to Sri Aurobindo and the Mother’s insights remains small.

      Stephen: Or, to put it another way, can pure mathematics be used effectively as a form of Yoga-Sadhana?

      I dont believe mathematicians had access to the highest plane of Supramental consciousness but they might have access to the Overmind and the Intuitive Planes that Sri Aurobindo outlined.

      From my personal experience ( I am not a mathematician by training), I think the study of an abstract topic like mathematics can help in developing and enhancing mental silence. The mind cannot grasp difficult abstractions unless it remains in a state of heightened silence for long periods of time. I used to get a headache initially while reading math books but now I can grasp these abstractions (langlands correspondence!) comfortably.

      As Sri Aurobindo had written in the Synthesis of Yoga(Chapter XX, Intuitive mind)

      “A fourth method (of developing intuition) is one which suggests itself naturally to the developed intelligence and suits the thinking man. This is to develop our intellect instead of eliminating it, but with the will not to cherish its limitations, but to heighten its capacity, light, intensity, degree and force of activity until it borders on the thing that transcends it and can easily be taken up and transformed into that higher conscious action…”

      Happy (belated) Darshan day to you as well

      Reply
      1. Stephen Britton

        Sandeep: I dont believe mathematicians had access to the highest plane of Supramental consciousness but they might have access to the Overmind and the Intuitive Planes that Sri Aurobindo outlined.

        Right. Currently I’m reading Sri Aurobindo’s The Secret of the Veda, and the Master’s writings on the four faculties of the Ritam (Truth-consciousness), revelation, inspiration, intuition, intuitional discrimination, combined with the historical accounts given by mathematicians of their mathematical experience and spiritual experience, in particular, visitations from supraphysical Muses, likely prompted my association of the Truth-consciousness and the discipline of mathematics as a yogic discipline.


        I shall suggest that Dakshina
        like the more famous Ila, Saraswati and Sarama, is one of four
        goddesses representing the four faculties of the Ritam or Truth-consciousness,—
        Ila representing truth-vision or revelation,
        Saraswati truth-audition, inspiration, the divine word, Sarama
        intuition, Dakshina the separative intuitional discrimination.
        Daksha then will mean this discrimination whether as mental
        judgment on the mind-plane or as intuitional discernment on
        the plane of the Ritam.”

        (The Secret of the Veda, Chapter VII, Varuna-Mitra and the Truth, p. 73)


        Letters (and the testimony of colleagues who knew him) reveal that Cantor believed he
        was chosen by God to bring the truths of set theory to a wider audience. He also regarded
        the successive waves of manic-depression that began to plague him in the 1880’s — peaks
        of intense activity followed by increasingly prolonged intervals of introspection — as
        divinely inspired. Long periods of isolation in hospital provided opportunities for
        uninterrupted reflection during which Cantor envisioned visits from a muse whose voice
        reassured him of the absolute truth of set theory, whatever others might say about it.”

        (Georg Cantor and the Battle for Transfinite Set Theory, p.11, Joseph W. Dauben)

        Of course, Sri Aurobindo’s subtle typology of the various grades of consciousness, including subgrades within those grades, must be remembered in any attempt to assign inner experiences to planes of consciousness. Aurobindo wrote about the classification of mentalities into sense-mind, vital-mind, and mental-mind, or pure reflective mentality.




        and
        as there are, according to the Veda, three planes of mentality
        in us, so there are three portions of the ghrta dependent on the three gods Surya, Indra and Soma, and the Soma also is offered in three parts, on the three levels of the hill, trisu sanusu. We may hazard the conjecture, having regard to the nature of the
        three gods, that Soma releases the divine light from the sense
        mentality, Indra from the dynamic mentality, Surya from the
        pure reflective mentality.

        (The Secret of the Veda, Chapter XVIII, The Human Fathers, pp. 193-194)

        To my understanding and from my little experience, the pure reflective mentality, pure thought on abstract concepts, leads at least to the the lower range of the spiritual mind with its subgrades of Higher mind, Illumined mind, Intuitive mind, and Overmind. So, when you say


        From my personal experience ( I am not a mathematician by training), I think the study of an abstract topic like mathematics can help in developing and enhancing mental silence.

        I have to agree; your experience accords well with my own experience. Thinking about the Absolute Infinite as reflected in the lower infinities (reflection principle), through properties such as inaccessibility, the great Vastness of proper classes, seemed to inevitably lead my mind to periods of silence. I just wonder how far intellectual development, with an emphasis on the development of mathematical faculties, could lead in spiritual experience and realisation.

      2. Sandeep Post author

        I wonder how much of Cantor’s claims regarding some Godly connection is related to the fact that he lived in a time when mathematicians had to take courses in theology during their university training. Newton was also a Bible enthusiast if I recall. In that era, these scientists saw mathematics as an attempt to uncover the “divine symmetry” which had been created by some transcendental being. It is only in the late 19th century that mathematics became disconnected from physical world concepts.

        I recall reading about this in Morris Kline’s book “Mathematical thought from ancient to modern times

        I just wonder how far intellectual development, with an emphasis on the development of mathematical faculties, could lead in spiritual experience and realisation.

        Intellectual activity helps awaken the Sahasrara Chakra at the top of the head, but not the heart Chakra which also needs to be awakened in the spiritual path. See https://auromere.wordpress.com/2009/12/20/how-to-rawaken-the-soul-psychic-being/

  2. Darius

    Sandeep, Perelman definitely would disagree with you. He claims he can rule Universe since he solved Poincare’s conjecture. I doubt he could do so if he had no access to Suprmental consciousness 🙂

    On more serious note I can’t recall any famous scientist who rather advanced on spiritual path. Do you know anyone?

    I wonder is a mathematical language less distorted truth than human language? IMO there are figures and formulas on one side and letters words and sentences on another side. I see no differnce it’s just different codification.

    Reply
    1. Sandeep Post author

      Perelman definitely would disagree with you. He claims he can rule Universe since he solved Poincare’s conjecture.

      Has he spoke in public ? He is a reclusive and eccentric genius (in that respect, these scientists are like yogis!) who has hardly spoken in public.

      On more serious note I can’t recall any famous scientist who rather advanced on spiritual path. Do you know anyone?

      No, thats because they have developed themselves in a different direction – higher mind well-developed but not much in terms of the psychic being. Human beings are not malleable enough to develop radically different abilities in a single lifetime. See the Mother’s comments “Difference between genius and mysticism

      I wonder is a mathematical language less distorted truth than human language?

      Mathematical language address a narrower field of abstractions than human language. There is a whole field called philosophy of language/linguistics which will need to be studied to answer your question.

      Language apart, the central question is where mathematical objects emerge from, and whether that question is pertinent to addressing where sound and general human concepts emerges from.

      Reply
  3. Kris

    Hello guys;
    from the viewpoint of a mathematician i can narrate my story on the subject “is mathematics leading towards spirituality”:
    I studied mathematics like a lunatic, that is, being full in love with the letters, the formulas, the contents these formulas embody and that day and night alternatively sober or fully drunk kind of every third day; once i complained to my fellows at university “oh i dont have a girl friend like you, what shall i do ? ”
    They laughed and replied:
    “What ??? You have even to gals, her names are Lina and Ana ! ” To explain that, Lina is shortcut for linear algebra and Ana stands for Analysis. So, this really consoled me as i felt they are right – I love maths and feel her touch, even if not a physical touch;
    But now lets look little closer at the objects a mathematican is handling;

    a.) the first thing that goes towards spirituality even if mathematicians must not admit it that way, is the concept of infinity; you always have to do with incredible infinite sets, you can take out of them even an infinity yet infinity remains; does that not remind you on some upanishads ? This is Fulness, Fullness taken out of Fullness, Fullness remains; something like that.

    b.) The next thing, math is teeming with, are dimensions; you operate often in spaces, that have even an uncountable infinite number of dimensions and you must develop a relationship with them, you can not just say, “Oh, after all there are only these 3 dimensions i can see, all these math fancies are only a cloud with no reality” – with that atitude you can not study for long, no it wil be rather the other way round, a space that has only a finite number of dimensions is so boring to you, that you have the feeling you can not breathe there; Does that remind you on something in spirituality ? The Mother said your soul is in a kind of forth dimension; that could be another dimension in quality: the 3 dimensions you know already are matter, life and mind – here in this context , you soul is something different from them you must find a completely new quality, vibration in you. Or that could be a new spacial dimension: Then the 3 known dimensions are lenght, width, hight and your soul needs to be contacted via contact with another spacial dimension; Or it coul mean another new dimension not here covered, try to think yourself what it actually means, what The Mother said here. Anyway, in order to find a new dimension you first must believe that there are other dimensions; and this part is for a math easy, he had to believe and work with other dimensions all the time;

    c.) At some advanced level in maths, you visit very special lectures, i once signed up for a lecture on rings and moduls in homology theory; some student dared to ask the professor (the one who gives the lecture) ” What is the suibject here, for what will the knowledge we gain here, be useful ?” The professor looked somewhat with pity and replied: ” You would not understand my answer; maths is like a widening of consciousness; you are now in this small circle and you want to undertand what is outside the circle and what is it good for to leave the circle; you have to agree to leave the circle and rely on me that i will teach you something that will bring you forward, later than you will understand. Or you decline and go ”
    After that, some left and some attained this series of lectures. Again, does that remind you on spirituality ?
    Sure, not only that we are also supposed to leave our small circle, the method is also the same, you have to rely on some guide either in form of a book or in form of a person but you dont expect already in the preface everything answered or understandable.

    So, after all that, what happend with me and math ? Soon after i finished my study at univerisity i did not know were to go, what to do next, i did not feel suddenly any longer satisfied just by more and more complex math formulas. Then the word yoga rose up from within, as indication where the purpose of my life is and 3 month later i found a small booklet on the Yoga of Sri Aurobindo and The Mother and now i have to find other dimensions outside math in the normal life. So, i can confirm, math can be a help towards spirituality but it must not be, it depends on the persons goal of life that remains for a very long time unknown.

    Reply
  4. mike

    l’m sure there are Yogi-scientists out there. One example comes to mind in the Japanese yogi Hiroshi Motoyama, who had realisation through Kundalini awakening which he described in detail in his book ‘Theories of the Chakras’. He is also involved in scientific projects. Here is a biographical description:

    “Hiroshi Motoyama (born December 15, 1925) is a Japanese parapsychologist, scientist, spiritual instructor and author whose primary topic is spiritual self-cultivation and the relationship between the mind and body therein. In doing so, he emphasizes the meditative practices of Samkhya/Yoga, karma, reincarnation and Hindu theories of the chakras. Dr. Motoyama is also the founder of the California Institute for Human Science. He holds Ph.D. degrees in Philosophy and Physiological psychology from the Tokyo University of Literature and Science.”

    Also, there were famous scientists who were friends of Swami Vivekananda, such as Nikola Tesla [l’m not sure if Tesla actually used Spiritual practice but he apparently had a great interest in Vedanta:
    “In 1893 Swami Vivekananda began a tour of the west by attending the Parliament of Religions held in Chicago. During the three years that he toured the United States and Europe, Vivekananda met with many of the well known scientists of the time including Lord Kelvin and Nikola Tesla. [7] According to Swami Nikhilananda:

    Nikola Tesla, the great scientist who specialized in the field of electricity, was much impressed to hear from the Swami his explanation of the Samkhya cosmogony and the theory of cycles given by the Hindus. He was particularly struck by the resemblance between the Samkhya theory of matter and energy and that of modern physics. The Swami also met in New York Sir William Thompson, afterwards Lord Kelvin, and Professor Helmholtz, two leading representatives of western science”

    Tesla also knew a scientist called walter russell who had Spiritual insights l believe:
    “Tesla and Russell

    Walter Russell was one of the most accomplished artists, sculptors, writers and scientists of this century. His periodic chart of the elements accurately predicted the location and characteristics of four elements years before they were discovered in laboratories. These are now known as Deuterium, Tritium, Neptunium, and Plutonium. Russell apparently entered into a heightened state of awareness after being struck by lightning. He began several weeks of drawing and writing about the basic nature and make up of the physical universe. Russells’ family finally called the family doctor to determine if Russell should be committed to an mental institution. The doctor, upon seeing the results of Russells weeks of work, said that he did not know what Russell was doing, but that he definitely was not mad.

    Although the exact time and occasion of their meeting has not yet been determined, Nikola Tesla and Walter Russell did meet and discuss their respective cosmologies. Tesla recognized the wisdom and power of Russells’ teaching and urged Russell to lock up his knowledge in a safe for 1,000 years until man was ready for it”.

    Reply
  5. Darius

    “Has he spoke in public ? He is a reclusive and eccentric genius (in that respect, these scientists are like yogis!) who has hardly spoken in public.

    http://english.pravda.ru/science/tech/28-04-2011/117727-Grigori_Perelman-0/ Some people think it’s fake interview. Any way my point was that math or matematicians have limited power to make
    Indeed he is very reclusive. He looks like a like yogi practising ascesis. He never cuts hair and nails eat poor food he has limited social interactions to the absolute minimum. A famous journalist Maria Gessen wrote book about him. However this fact did not help to arrange meeting with him despite her multiple attempts.
    Even if he didn’t say that he can control universe my thought was that math has limited influence on our lives and morevore on the universe.

    ” On more serious note I can’t recall any famous scientist who rather advanced on spiritual path. Do you know anyone?

    No, thats because they have developed themselves in a different direction – higher mind well-developed but not much in terms of the psychic being. Human beings are not malleable enough to develop radically different abilities in a single lifetime. See the Mother’s comments “Difference between genius and mysticism”

    My bad! I’ve entirely forgot Pavitra! Satprem wrote that he invented unique way how to free nuclear energy from many of common metal e.g copper aluminium etc. Bear in mind he was less than 30 years old then. Wasn’t he pure genius? However it was not an obstacle for him to advance on spiritual path.

    Sandeep, how to you manage to insert italicized text here? I tried to copy/paste from Word with no success. Is it only your privilege?

    Kris, great post!

    I just would like to add that if we looked closer we would find that almost any human activity can lead one to spirituality.

    Reply
  6. gopal.M

    maths and music have things in common. one can learn from the other and serve the truth. These are times for inter-disciplinary approaches to everything. Some where in the integral websites i found the word “transdisciplinarity” . Found it an apt way to describe the need of the current times, not just in material pursuits, but also in those of us in pursuit of integral spirituality.

    Reply
  7. Marco Masi

    Dear Sandeep, this is an interesting post which title recalls to my mind the famous article of Eugene Wigner “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”. Wigner, expressed the big question of why the universe seems to be so well described by math. Isn’t after all math just a creation of human mind, and mind an epiphenomenon of the brain? How is it then that nature adapts itself to a human faculty? But the mystery appears only if we start a priori with this assumption. As Sri Aurobindo put it nicely in the Life Divine: “the brain is not the creator of thought, but itself the creation, the instrument and here a necessary convenience of the cosmic Mind”. It might be worthwhile to read the last pages of the chapter entitled “Matter” where he describes the relation of mind to the cosmic Mind. There he describes how mind “by its very nature tends to know and sense substance of conscious-being, not in its unity or totality but by the principle of division. It sees it, as it were, in infinitesimal points which it associates together in order to arrive at a totality, and into these view-points and associations cosmic Mind throws itself and dwells in them.” – “… the nature of the action of cosmic Mind is the cause of atomic existence. Matter is a creation, and for its creation the infinitesimal, an extreme fragmentation of the Infinite, was needed as the starting-point or basis.” – “Therefore we arrive at this truth of Matter that there is a conceptive self-extension of being which works itself out in the universe as substance or object of consciousness and which cosmic Mind and Life in their creative action represent through atomic division and aggregation as the thing we call Matter.” – “Matter is Sachchidananda represented to His own mental experience as a formal basis of objective knowledge, action and delight of existence.”

    So, if our mind is a creation, instrument and necessary convenience of the cosmic Mind, which has thrown itself and dwells in the material universe causing atomic existence operating by division and fragmentation of the totality, it should be no surprise that math, which is a human mental cognitive reflex of it in form of a science of quantity, which works indeed by division, fragmentation and atomization of the totality, works so well and has become so successful in describing the natural material world. If we take this standpoint, the circle is closed and the mystery finds a self evident solution.

    Reply
    1. Sandeep Post author

      The mystery does resolve itself if we work from the fact that the mind is a creation of the Cosmic Mind, but how does one convince the mathematicians and scientists of that? One approach would be to elucidate where “intuitive flashes” come from. That is what I was attempting here.

      As a physicist, you might be more conversant with other approaches to proving the source of mathematics.

      Reply
      1. Marco Masi

        Yes, I think it is a good approach. I know all too well the closemindedness of several scientists, and have given it up to try to convince those who refuse to go beyond a strictly materialist standpoint. Nevertheless, there are also many who are open to new understandings, and those would already today accept to consider different approaches and conceptions of reality. Practices like meditation, mindfullness, silencing the mind, (I would add a ‘Goethian approach’), etc., in order to attain intuitions and access to new forms of knowledge, would certainly be welcomed. Unfortunately in universities the still strong present educational paradigm does not allow for that, we are still not there. But I’m sure these new approaches and paradigms are on its way into modern academia.

  8. anmol1

    I heard in a talk by one of the speakers on Sri Aurobindo that Mathematics was one of Mother’s favourite subjects. It is also a fact that as a young girl of about 9 or 10, when on one occasion, her brother’s maths tutor had given him a problem which he could not solve Mother solved it and the tutor told Mother’s mother that it is rather your daughter who should take up mathematics! Also I happened to peek into the article on “Vak” and from some of the Mother’s comments there I again realised how she is probably underthought of as an intellectual. That probably comes from a tendency to think of Sri Aurobindo as the intellectual side of the Two-in-One and herself as the lovey-dovey Mother but the fact is that she had read a whole library at the age of 13 and in her own words “There were periods in my life when I read ever so much – I am quite a library! (Page 76, Vol.3, Agenda”). I feel very strongly that if someone focuses just on his intellectual development through even just Mother’s writings (Sri Aurobindo is the greatest intellectual ever born on Earth) he can become a genius.

    Reply
  9. mike

    l don’t think Sri Aurobindo was actually using the intellect – at least not as most people see it. He said He could never have written the things He did, and certainly not in the space of time He did. lt all came from above through the Silent mind and not intellect or the ordinary mind, as far as l know.

    Reply
  10. mike

    Of course He was a great intellectual before taking up Yoga, but most of His writings were after the Change in Consciousness, l think.

    Reply
  11. mike

    Anmol l think Two-ln-One is was probably right [although, they might be interchangeable]. G V Wrekham describes SA and Mother in this way [Twinsoul Avatars], so l think you were right in the first place:

    “In 1995, Georges began writing his own books. Voorbij de Mens, Leven en Werk van Sri Aurobindo en De Moeder was published in 1995; he then transliterated it into English as Beyond Man, the Life and Work of Sri Aurobindo and The Mother. Itwas published in India in 1997 and became a highly acclaimed seminal book. Amal Kiran (K.D. Sethna) judged it “among the best that have been written on Sri Aurobindo and The Mother.” In this book Georges, for the first time, spoke about Sri Aurobindo and The Mother as the Two-in-One, the double-poled Avatar of the Supermind.”

    Also, SA describes in Savitra:

    “There he beheld in their mighty union’s poise
    The figure of the deathless Two-in-One,
    A single being in two bodies clasped,
    A diarchy of two united souls,
    Seated absorbed in deep creative joy;
    Their trance of bliss sustained the mobile world.”

    Reply
  12. Hari

    Dear Sandeep,

    Curious statement: Human beings are not malleable enough to develop radically different abilities in a single lifetime.

    There was a statement similarly by Sri Aurobindo in which as a reply to a sadhak he said that one can very well be good in one field alone and need not know other things, and can still make the same progress; something to the effect. Do you know from where this statement is? Have been trying to find this for quite sometime (nearly two years) and haven’t found yet.

    Thanks and Regards,
    Hari

    Reply
    1. Sandeep Post author

      It would be hard for me to find that remark by Sri Aurobindo without any specific phrase.

      My remark which you have quoted may apply to a large proportion of human beings but there can be exceptions.

      Reply
    2. Mark

      Hari: this may not be specifically what you are looking for:

      “Disciple: Is it not dangerous for small adhars to try to concentrate on these powers, because they may be swallowed by them?

      Sri Aurobindo: It may be. I can never understand that stupid fear of acquiring Siddhis — occult powers — which our people are having. Why should every one be spiritual? Those who want to attain power must do that. I mean if that is the only thing they can do in this life let them do it. He was telling me the same thing this morning. For instance, if a man is capable of writing good poetry why should he be expected to do all things in life? Let one thing be well done. That way the soul develops.” A.B. Purani Evening Talks, pg.75 [http://www.aurobindo.ru/workings/purani/00/evening_talks.htm]

      Reply
      1. Mark

        Hari, here too:

        “The curse of modern civilisation is specialisation. There has to be a total development. This craze for specialisation tends to narrow our interests, and one of the things which will be swept away as this old civilisation goes is this narrowing of the range of the soul.” M.P. Pandit, The Yoga of Self-Perfection, pg.177

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