Sanskrit is not only the language of Vedas, Itihāsas and Purānas, but also the language of learning Sciences. It was customary in India among the authors and mathematicians to commence their work with a maṅgalācarana, invocation or prayer, so that they can complete the work without any difficulty. Along with praying to the Lord, the mathematicians bring out also the importance of mathematics. Here we shall see some important works in mathematics and the invocatory verses given in them.
Āryabhaṭīya
The Āryabhaṭīya (499 CE) was written by Āryabhaṭa I (476-550 CE). This earliest available printed text in mathematics and astronomy, containing 121 stanzas in all, is marked for its brevity and conciseness. It is divided into four pādas namely Gītikāpāda, Gaṇitapāda, Kālakriyāpāda and Golapāda. The second pāda is on mathematics and others are on astronomy. While beginning the work, Āryabhaṭa writes the invocatory verse in which he praises Brahma.
प्रणिपत्यैकमनेकं कं सत्याम् देवताम् परं ब्रह्म ।
आर्यभटस्त्रीणि गदति गणितं कालक्रियां गोलम् ॥
“Having paid obeisance to Lord Brahma- who is one and many, the real God, the Supreme Brahman- Āryabhaṭa sets forth the three, viz., mathematics (gaṇita), reckoning of time (kālakriyā) and celestial sphere (gola).”
Then he pays obeisance to the planets and indicates his place of learning as Kusumapura, in the beginning of Gaṇitapāda, the second chapter .
ब्रह्म-कु- शशि- बुध-भृगु-रवि- कुज- गुरु- कोण- भगणान् नमस्कृत्य ।
आर्यभटस्त्विह निगदति कुसुमपुरे अभ्यर्चितं ज्ञानम्॥
‘Having bowed with reverence to Brahmā, Earth , Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn and asterisms, Āryabhaṭa sets forth here the knowledge honoured at Kusumapura.”
Brāhmasphuṭasiddhānta
The Brāhmasphuṭasiddhānta (BSS) is an astronomical treatise written by Brahmagupta at the age of 30, in 628 CE. There are twenty-four chapters and about thousand verses in the BSS. In this work, chapters twelve, eighteen and nineteen deal with mathematics. Other chapters are on astronomy. Brahmagupta has also written Khaṇḍakhādyaka.
In the invocatory verse in Brāmhasphuṭasiddhānta Brahmagupta, being a devotee of Śiva, praises Mahādeva.
जयति प्रणतसुरासुरकिरीटरत्नप्रभाछुरितपादः ।
कर्ता जगदुत्पत्तिस्थितिविलयानां महादेवः ॥
Mahādeva triumphs, who is the source of creation, existence and destruction of the world and whose feet are illuminated by the lustre of the crowns of the devas and demons, who bow before Him.
In the beginning of the Khaṇḍakhādyaka also, Brahmagupta salutes Mahādeva:
प्रणिपत्य महादेवं जगदुत्पत्तिस्थितिप्रलयहेतुम् ।
वक्ष्यामि खण्डखाद्यकमाचार्यार्यभाटतुल्यफलम् ॥
“I bow to Mahādeva, the cause of creation, existence and destruction of the Universe. I now write the Khaṇḍakhādyaka, which gives more practicable results than those obtained from Āryabhaṭa’s formulae.”
Āryabhaṭīya–bhāṣya
Bhāskara 1 was a Hindu and a worshipper of Lord Śiva. Just like the mathematicians, the commentators also begin their work with verse of prayer. In Āryabhaṭīya–bhāṣya, a commentary on Āryabhaṭīya, Bhāskara 1 gives the maṅgalācaraṇam verse for the Gītikāpāda. In the beginning of his commentary, Bhāskara 1 paid obeisance to Lord Brahma following Āryabhaṭa, who had paid obeisance to Lord Brahma as the founder of the school. Later in the beginning of the second and third chapters Bhāskara 1 offer prayers to Lord Śiva.
यस्मावशेषजगतां प्रभवं स्थितिञ्च
संहारमप्युपदिशन्ति समग्रधोकाः।
भृग्वङ्गिर्ः प्रभृतयो विदितान्तरायाः
तस्मै नमः कमलजाय चतुर्मुखाय ।।
Salutation to that four faced God, born of the lotus, by whom the whole world is created, protected and destroyed, as realised by Bhrugu, Āṅgiras and others.
In the beginning of Gaṇitapāda of Āryabhaṭīya–bhāṣya, the prayer-verse goes as follows, saluting Śiva:
यन्नामसंस्मरणमात्रभवाभवानि
श्रेयोऽशुभानि विबुधासुरमानवानाम् ।
तस्मै सकृष्णकमलोद्भवमौलिधृष्ट-
पादारविन्दयुगलाय नमः शिवाय ॥
“I bow to Lord Śiva, whose lotus-like feet are rubbed by the foreheads of the lotus-born Brahma and Kṛṣṇa, to Him, a mere recollection of whose name is a source of fortune and end of misfortune for gods, demons and men.”
In the beginning of Kālakriyāpāda of Āryabhaṭīya–bhāṣya, the invocation verse, praising Lord ŚIva, given by Bhāskara I:
सूर्येन्दुखाग्निमरुदप्क्षितिदीक्षिताख्यम्
मूर्त्यष्टकं सकललोकहितार्थभावम् ।
योऽभूत् स्वयं हि करुणातनुरप्रमेयः।
तस्मै नमस्त्रिभुवनस्थितये शिवाय ॥
“I bow to God Śiva, the support of the three worlds, Who, though inconceivable by nature, being mercy incarnate, assumed the eight forms viz. the Sun, the Moon, the Ether, Fire, Air, Water, Earth and Sacrificer, for the benefit of the entire world.”
Bhāskara 1 has written the astronomical works namely the Laghubhāskarīya and Mahābhāskarīya. This work deals with the results regarding celestial objects and suitably Bhāskara 1 salutes the Sun, in the invocation in Laghubhāskarīya :
भास्कराय नमस्तस्मै स्फुटेयं ज्योतिषां गतिः।
प्रक्रियान्तरभेदेऽपि यस्य गत्याऽनुमीयते॥
“I bow to the Sun- to Him with the help of whose motion, this true motion of the heavenly bodies is inferred even though the methods (adopted for the purpose by different writers) be different.”
Pāṭīgaṇitam of Śrīdhara: The general accepted date of his work is 750 CE. His rules are quoted by the later authors. The invocation verse in this work :
सृष्टिस्थितिलयहेतुम् जगतामजमीश्वरं प्रणमाम्यहम् ।
लोकव्यवहारार्थं गणितं संक्षेपतो वक्ष्ये ॥
“Having paid obeisance to the Unborn God, the cause of creation, preservation and destruction of the worlds, I shall briefly state the( pāṭī) gaṇita , for the use of the people.”
Gaṇitasārasaṅgraha
Mahāvrācārya (9th cent. CE), a Digambara Jain of Karnataka, has written Gaṇita-Sāra-Saìgraha (GSS), a complete treatise on mathematics. It is devoted to topics in arithmetic, algebra, geometry etc. It is written in the style of a text book with rules followed by several examples and it was used for many centuries in South India. Being a Jain, Mahāvīra offers his obeisance to Jinendra.
अलङ्घ्यं त्रिजगत्सारं यस्यानन्तचतुष्टयम् ।
नमस्तस्मै जिनेन्द्राय महावीराय तायिने ॥
“Salutations to Mahāvīra, the Lord of the Jinas, the protector of the faithful, whose four infinite attributes (faith, understanding, blissfulness and power), worthy to be esteemed in all the three worlds, are unsurpassable in excellence.”
सङ्ख्याज्ञानप्रदीपेन जैनेन्द्रेण महात्विषा ।
प्रकाशितं जगत्सर्वं येन तं प्रणमाम्यहम् ॥
“ I bow to the highly glorious Lord of the Jinas, by whom, as forming the shining lamp of the knowledge of numbers, the whole of the universe is made to shine.”
Along with this Mahāvra gives a number of verses praising mathematics and the various fields where mathematics has been used. He says that in all the three worlds, there is nothing that exists without mathematics.
Līlāvatī
Līlāvatī is written by Bhāskarācārya II in 1150CE, at the age of 36 years. Līlāvatī is the first out of four parts of Siddānta Śiromaṇi. Līlāvatī is written in the form of 272 verses. It contains rules and methods for mathematical operations followed by interesting examples where the rules are applied to solve them. It starts with an invocatory verse praying Lord Gaṇeśa.
प्रीतिं भक्तजनस्य यो जनयते विघ्नं विनिघ्नन्स्मृत –
स्तं वृन्दारकवृन्द वन्दितपदं नत्वा मतङ्गाननम् ।
पाटीं सद्गणितस्य वच्मि चतुरप्रीतिप्रदां प्रस्फुटां
संक्षिप्ताक्षरकोमलामलपदैर्लालित्यलीलावतीम् ॥
‘After saluting elephant headed Lord Gaṇeśa, whose feet are adored by devas, who, after removing the obstacles, generates happiness to the devotees who worship him, I propound this work of mathematical calculation, which is pleasing to the learned, clear, concise, soft, pure and delightful by its elegance.’
Bhāskara II is a great mathematician as well as an excellent poet. It is seen in his invocatory verse itself. Here we see Bhāskara is devoted to Lord Gaṇeśa and has the belief that He would remove any obstacle on his way. The word līlā (play) is generally used to refer to the great deeds of God such as the action of creation etc. is a ”play” for Him. Having this in mind, we find a dhvani here that the text Līlāvatī is “playful”, i.e. making mathematics easy like a play. It implies that the verses and examples are sweet, flawless and with precision and purity. Before commencing the operations on numerals again he writes a verse of invocation on Lord Gaṇeśa.
The following is an invocatory verse (L.9) before starting the parikarmāṣṭaka :
लीलागललुलल्लोलकालव्यालविलासिने ।
गणेशज्ञाय नमो नीलकमलामलकांतये॥
‘Salutations to Gaṇeśa, who is resplendent like the blemishless blue lotus and who is playing with the dark serpent which is gracefully swaying, coiling and uncoiling around the neck.’
Here we find the letter ‘ल’ is repeated and so the śabdālaṅkāra vṛtti-anuprāsa is present. नीलकमलामलकांतये, (is resplendent like the blemishless blue lotus) is an example for upamā-alaṅkāra. Gaṇeśa is usually described as śaśivarṇa (white like moon). But here he is described as blue-hued. Gaṇeśa is the son of Lord Śiva, who is adorned with a snake around his neck. It may be interpreted that the black colour of the snake around Śiva’s neck is reflecting on the fair skin of Gaṇeśa, while he is playing with the snake around his father’s neck, and making him resplendent like the blue lotus. This is an example of Kāvyaliṅga-alaṅkāra. Gaṇeśa acquires the blue shine of the snake shedding his own white splendour. Hence this is also an example of Tadguṇa– alaṅkāra.
Buddhivilāsinī
Gaṇeśa Daivajña, in his commentary Buddhivilāsinī on Līlāvatī , in the beginning of every unit, writes a verse of prayer. Gaṇeśa has composed several verses with poetic beauty embellished with alaṅkāras and citrabandhas ( see Dilip vol.Jul-Sept.2025, pp.23-25); also the name of the chapter in hand is woven into the verse. Like Bhāskara II, Gaṇeśa was also a poet. Gaṇeśa is fond of Śleṣa, Upama and Anuprāsa. His father’s name being Keśava, that facilitated him to write verses with Śleṣa. For constructing bandhas repetition of letters is necessary and so Anuprāsa is employed by him. Here we shall see one verse which brings out his poetic talent. One can perceive Gaṇeśa’s poetic genius in the first invocatory verse of BV (p.1) adorned with both bhaṅgaśleṣa and khaṇḍaśleṣa :
श्रीविद्याधरसेवितो द्विजपतिश्रीवर्धनो यस्त्रयी-
मूर्ति: स्वोद्गमनात्सदा सुमनसामानन्दपूरप्रद:।
कव्याचार्यविदोऽपि यत्पदमिता: स्यु: स्वप्रकाशा अपि
द्युत्यूना जयति क्षितौ खगपति: श्रीकेशव: सद्गुरु:॥
In this verse Gaṇeśa praises simultaneously his father Keśava who was also his Guru, Lord Viṣṇu and Sun God stating ‘jayati kṣitau Śrī Keśava’ (Śrī Keśava triumphs in this world). The adjective-phrases in this verse give three meanings.
The description in the verse can be presented in a table form as follows:
| ADJECTIVES | ŚRIKEŚAVA | VIṢṆU | SUN |
| श्रीकेशव: | name of author’s father and guru | epithet of Viṣṇu | who has beautiful rays |
| सद्गुरु: | master of learned men, good teacher and a mahāguru | guru who imparted knowledge to Uddhava, Arjuna | guru who taught the astrology to Romaka, Mayāsura and others. |
| श्रीविद्याधरसेवित: | worshipped by the scholars learned in the fourteen vidyās. | worshipped by Lakṣmi and Vidyādharas. | worshipped by the Vidyādharas |
| द्विजपतिश्रीवर्धन | increases the wealth of knowledge of the worthy and best of the dvijas. | increases the power and strength of Garuòa, the best of the birds | makes the moon shine |
| त्रयीमूर्ति: | the form of Brahmā, Viṣṇu and Śiva, and exponent of the three Vedas with their angas. | the embodiment of the three Vedas, three agni and three bhuvana | has the form of three Vedas, three vyāhåtis |
| स्वोद्गमनात्सदा सुमनसामानन्दपूरप्रद: | gives pleasure to the good-minded people by his presence | gives pleasure to those with pure mind, by showing his own form | while rising creates happiness among the good minded people and deities |
| कव्याचार्यविदोऽपि यत्पदमिता: स्यु: स्वप्रकाशा अपि
द्युत्यूना |
the scholarship of even the great teachers, scholars and poets pale into insignificance and resorting to whom they become scholastic | by reaching his feet ordinary people become great poets like Vālméki, ācāryas like Båhaspati and self-effulgent | in whose presence Śukra, Båhaspati and Budha cannot display their lustre; by resorting to him they reflect his glory |
| खगपति: | has Sun as his God for worship. | the Lord of Garuòa | Lord of the planets. |
Bījagaṇitam : Bhāskara in his Algebraic work gives the following invocatory verse:
उत्पादकं यत् प्रवदन्ति बुद्धेः अधिष्ठितं सत्पुरुषेण सांख्याः ।
व्यक्तस्य कृत्स्नस्य तदेकं बीजम् अव्यक्तमीशं गणितं च वन्दे॥
“That, which wise men call as generator of intelligence, and as the basis of arithmetic of numbers, but remains unmanifested, to that, Mathematics and the God Almighty, I offer my praṇāms.”
This verse indicates that in Bhāskara’s view, the vyakta (the manifest) is developed as the product of the avyakta (the unmanifest). This means, on the one hand, that all the phenomena of the material world have developed from the unmanifest Supreme Being. On the other hand, Bījagaṇita (Algebra) is the source of Paṭīgaṇita (Arithmetic). The verse refers to three (i) Gaṇeśa, the Lord of intellect and remover of obstacles, with his father Śiva, the source of all;(ii) Maheśvara (also the name of Śiva), Bhāskara’s father and (iii) algebra.
Bījagaṇitāvatamsa of Nārayaṇa paṇḍita (1356 CE)
The verse of invocation given in this work:
यस्मादेतत्सकलं विश्वमनन्तं प्रजायते व्यक्तम् ।
अव्यक्तादपि बीजाच्छिवं च गणितं च तं नौमि ॥
Nārayaṇa is saying that as from the unmanifest, the entire manifest and the entire world is produced, so from the unmanifest bīja (algebra) the entire arithmetic with its various rules in arithmetic is produced.
Gaṇitakaumudī of Nārayaṇa paṇḍita (1356 CE)
The verse offering prayer is as follows:
नत्त्वेशं गणितार्णव वर्धनहेतुं तमोनुदं विमलाम् ।
बहुजनचकोरजीवनसंपत्तिं गणितकौमुदीं वक्ष्ये ॥
“Having bowed to the Almighty, describe this Gaṇitakaumudī, for removing the darkness (of ignorance) and increasing the knowledge of spotless mathematics (which is like) a sea and (which is the life of many people (just as chakava is the life of) cakora.”
There are a lot more works in mathematics which give varieties of verses of prayers on different deities. Here a selected few are presented.