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Introduction to Vedic Maths
“Vedic Maths is not merely a collection of tricks—it is a unified system, an art, and a science.” – Jagadguru Śrī Bhāratī Kṛṣṇa Tīrthaji Maharaj
What is Vedic Maths?
Vedic Maths is an ancient system of Indian maths that offers an incredibly fast, simple, and mental approach to solving mathematical problems.
Unlike conventional methods, Vedic Maths emphasizes intuitive techniques and mental shortcuts. This helps us to solve complex problems in just a few steps. Often, we find that there is no need for pen and paper at all, as a solution can be found through simple mental calculations.
Vedic Maths is not just about speed, but it is a way of thinking that promotes logical clarity, creativity, and holistic intelligence.
Who discovered Vedic maths?
Vedic Maths was rediscovered in the early 20th century by Jagadguru Śrī Bhāratī Kṛṣṇa Tīrthaji Maharaj (1884–1960), the Shankaracharya of Govardhana Matha in Puri.
He is said to have reconstructed this system from ancient Indian scriptures, particularly the Atharva Veda, through deep meditation and intuitive insights. He compiled his discoveries in the book “Vedic Maths”, first published in 1965 after his death.
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How many sutras are there in Vedic Maths?
The Vedic system is based on 16 main sutras (mathematical formulas in Sanskrit) and 13 sub-sutras (corollaries).
Each sutra encapsulates a specific pattern or principle that can be applied to various areas of maths, such as:
- Arithmetic (addition, subtraction, multiplication, division)
- Algebra (factorization, equations)
- Geometry and Trigonometry
- Calculus (to some extent)
The 16 Main Sutras (Slokas)
| Sanskrit Sutra | English Meaning |
| 1. एकाधिकेन पूर्वेण (Ekādhikena Pūrveṇa) | By one more than the previous one |
| 2. निखिलम् नवतश्चरमं दशतः (Nikhilam Navataścaramam Daśataḥ) | All from 9 and the last from 10 |
| 3. ūrdhva-tiryagbhyām (ऊर्ध्वतिर्यग्भ्याम्) | Vertically and crosswise |
| 4. परावर्त्य योजयेत् (Parāvartya Yojayet) | Transpose and adjust |
| 5. शून्यं साम्यसमुच्चये (Śūnyam Sāmyamuccaye) | When the sum is the same that sum is zero |
| 6. ānurūpyena (आनुरूप्येण) | Proportionately |
| 7. संकलन व्यवकलनाभ्यां (Saṅkalana-vyavakalanābhyām) | By addition and subtraction |
| 8. पूर्वापरसमुच्चयः (Pūrvāparasamucchayaḥ) | The sum of the first and the last |
| 9. चलनकलनाभ्यां (Calanakalanaābhyām) | By differentiation |
| 10. यावदूनम् (Yāvadūnam) | Whatever the extent of its deficiency |
| 11. व्यस्तिसंस्थापनम् (Vyastisamsthāpanam) | By alternative elimination and retention |
| 12. शेषाण्यङ्के गच्छः (Śeṣāṇyaṅke Gacchaḥ) | The remainders by the last digit |
| 13. सोपान्त्यद्वयमन्त्यम् (Sopāntyadvayamantyam) | The ultimate and twice the penultimate |
| 14. एकन्यूनेन पूर्वेण (Ekanūnena Pūrveṇa) | By one less than the previous one |
| 15. गुणितसंघ्यायाः समान्यः गुणः (Guṇitasamghyāyāḥ Sāmānyaḥ Guṇaḥ) | The common factor in the group of quantities |
| 16. गुणकैः पूर्ववत् (Guṇakaiḥ Pūrvavat) | Like the previous one with the multipliers |
The 13 Sub-Sutras
| Sanskrit Sub-Sutra | English Meaning |
| 1. Anurūpyeṇa | Proportionally |
| 2. Śiṣyate Śeṣa Sañjñāḥ | The remainder remains constant |
| 3. Ādyaṁ Ādyena Antyaṁ Antyena | The first by the first and the last by the last |
| 4. Kevalaih Saptakam Ghaṭikā Samyam | For 7, the multiplicand is nearly equal |
| 5. Yāvadūnam Tāvadūnam | Whatever the deficiency, subtract that much |
| 6. Yāvadūnam Tāvadūnīkritya Vargañca Yojayet | Whatever the deficiency, square it and add |
| 7. Antyayordasake’pi | Last digits together give 10 |
| 8. Antyayoreva | Only the last terms |
| 9. Samuccayagunitah | The sum of the coefficients in the product |
| 10. Lopanasthāpanabhyām | By alternate elimination and retention |
| 11. Vilokanam | Observation |
| 12. Gunitasamuccayah Samuccayagunitaḥ | The product of the sum is the sum of the products |
| 13. The last digits together give 10 | Flag digit (or Digit under the flag) |
Benefits
| Benefit | Description |
| Speed | Perform calculations 10–15x faster than traditional methods |
| Simplicity | No need to memorize long formulas — just understand patterns |
| Mental Math | Improves concentration, memory, and calculation without writing |
| Accuracy | Reduces careless mistakes in exams |
| Confidence | Builds mathematical intuition and reduces fear of numbers |
Conclusion
Vedic Maths is a gift from India to the world. It connects learners to India’s rich mathematical heritage and empowers them to see numbers as not painful, but playful.
The sutras can be put into use by all aspirants preparing for tough competitive exams like
- UPSC CSAT, SSC, Bank PO, CAT, Railways, NDA, etc.
- Aptitude tests and campus placements
- Olympiads and entrance exams like JEE or NEET (for mental boost)
The Vedic Maths sutras will help the students in finding answers to mathematical questions quickly, thus saving precious time.
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References