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Based on extensive research in Sanskrit sources, Mathematics in India chronicles the development of mathematical techniques and texts in South Asia from antiquity to the early modern period. Kim Plofker reexamines the few facts about Indian mathematics that have become common knowledge--such as the Indian origin of Arabic numerals--and she sets them in a larger textual and cultural framework. The book details aspects of the subject that have been largely passed over in the past, including the relationships between Indian mathematics and astronomy, and their cross-fertilizations with Islamic scientific traditions. Plofker shows that Indian mathematics appears not as a disconnected set of discoveries, but as a lively, diverse, yet strongly unified discipline, intimately linked to other Indian forms of learning.

This paper aims to examine the enunciation ( ) time intervals for , a fifteen seed-syllable ( ) related to the homonymous school or . Following the indications provided in the , with commentary by Amṛtānanda, and the by Bhāskararāya with auto-commentary, the research finds that these durations are not arbitrary at all but rather the result of a rigorous assessment. Moreover, the duration values suggest a specific conceptual goal that the mathematical rigor manifested by the authors seeks to fulfil: the progressive diminution of time intervals in order to achieve an atemporal dimension. The choice of the units of measurement itself is designed to meet this metaphysical and ritual need. By counting the intervals (both relative and overall) of recitation, it is also possible to confirm the resonance nature of the sounds following nasalisations, sounds conceived by the authors as entirely independent of the reciter’s phonatory activity.

Piṅgaḷa in his book on Chandaśśāstra , a text related to the description and analysis of meters in poetic work, describes algorithms that deal with Combinatorial Mathematics and are tail-recursive in nature. Later after almost a millennium in around 800 CE, Kedāra Bhaṭṭa provides iterative algorithms for the same operations. Another major difference between the two works is stylistic. Piṅgaḷa uses a cryptic style of sūtras while Kedāra Bhaṭṭa uses a verse style. The purpose of this paper is to highlight the methodological differences between Piṅgaḷa’s algorithms and the corresponding algorithms of Kedāra Bhaṭṭa. We look at the algorithms described by both scholars, and express them in modern mathematical notation or in algorithmic style in order to understand the differences. Recursive algorithms are easy to conceptualise. However, the iterative algorithms are easy from the learner’s point of view. The transition from sūtras to verses and from recursion to iteration in the later period might be due to pedagogy.

The conceptualisation of negative numbers represents a fascinating aspect of mathematical development, characterised by its evolution over time and its multifaceted applications across various disciplines. This paper embarks on a scholarly exploration of this intriguing subject, focusing on a salient segment from Kṛṣṇa Daivajña’s Bījapallava , a detailed commentary of Bhāskarācārya’s Bījagaṇita . It situates the discussion within its historical and scholarly context by examining the complexities inherent in understanding ‘negative’ quantities. While briefly referencing the evolution of negative numbers by notable mathematicians such as Brahmagupta and Bhāskara, the primary focus remains on dissecting a section of the “ dhanarṇaṣaḍvidha ” excerpt from Bījapallava , thereby shedding light on significant aspects of the discussion on negative numbers.

Since the Vedas are religious texts produced by poets, we cannot expect in them enough information for systematically describing the mathematical knowledge of those times. We can only gather scattered terms for whole numbers, for basic fractions, and for simple geometric figures. The Rgveda contains a number of numerical expressions. Before the introduction and spread of horoscopic astrology and mathematical astronomy to the Indian subcontinent, the occupation that, in Indian society, required calculations most seems to have been that of the accountant, since he was called either ganaka or samkhyayaka, both meaning “a calculator.” The seventh century saw a restructuring of Indian mathematics.

This paper examines the cited and citing pattern of Indian Journal of Pure and Applied Mathematics (IJPAM) in terms of source, authorship, subject diversity, accessibility, citation-age, quantity & citing-life. This study is based on the data collected from 5 Volumes, consisting of 30 issues, carrying 171 articles, citing 2754 references from 575 citing sources of IJPAM published from 2009 to 2013. Whereas for collecting cited references, every published article from the official website of the journal namely Indian National Science Academy (INSA) was downloaded, for citing references, Google Scholar and Scopus both were explored to recognize the maximum number of citing sources during October 2017.The study revealed that journal articles are the most cited references, whereas citing references are mostly from the journals of foreign origin. Majority of cited articles are available in non-open access form, though the citations came from both, open and non-open journals. Joint authorship was found to be predominant, in both cited-citing references.

Yupana Inca Tawa Pukllay (YITP) is a ludic didactic resource based on semiotic alternation that, using the reading of numbers in the Inca numeral system, improves its equivalent Indo-Arabic reading. Twelve children from first to fourth grade of a bilingual (Spanish-Quechua), multi-grade elementary school in a small rural Peruvian community were assigned an electronic tablet with YITP and learned autonomously, without teachers during the COVID-19 pandemic. The results obtained show that: (a) they learned in a very short period of time (14 min-05h 41 min) (b) they improved digit reading accuracy on the first attempt (c) they improved digit reading speed d) they achieved a high percentage of correct reading of numbers containing at least one zero digit. The results suggest the potential of YITP as an educational tool in the teaching-learning process of arithmetic.

Numbers and languages are present around the world. While mathematics is deemed as universal, communities around the world have developed mathematical practices that align with their specific context and needs. Rooted in an Indigenous epistemological framework, this manuscript presents a dialogue among four co-researchers and teachers retelling their experiences teaching and learning Mesoamerican numbers in both monolingual (Spanish) and bilingual (Ixil and Spanish) contexts. With a strong desire to learn about and reconnect with the forces of Indigenous mathematical thought and language that move within the teaching and learning of these numbers, the authors collectively reflected on their “tellings” of prior work. It is worthy of note that these reflections on teaching and learning processes of naming Mesoamerican numbers, their symbols, and numerical values help realize that these concepts are more fully animated when presented in contexts that are onto-epistemologically relevant.

The Peruvian basic education and its curriculum have been impacted by the COVID-19 pandemic. As a result, certain trends and phenomena have emerged, which shape the new normality in society and have generated many effects on the mathematics curriculum. For this reason, it is necessary to pose the problem of sketching the orientations of mathematics curriculum for the new situation. In this position paper, I developed an outline based on a description of the problem situation, the demands that the world of work had already been making on the curriculum at the international level, and the research carried out by mathematics education. From these factors, I assert the significant role of critical mathematics education, particularly the motto of reading and writing the world with mathematics. I propose that orientations for the mathematics curriculum in basic education in the new normality should include ethical and political issues, statistical and financial literacy, digital skills as a part of a STEM approach, ethnomathematics from native people, and, finally, a problem-posing and problem-solving approach. In this list, ethical and political issues have primacy.

This article describes the initial work and next steps for the development of a mathematics curriculum in Ichishkiin, an Indigenous Yakama language. Framed by the Ichishkíin concept of pinak'inut'áwaas (mirror/window), our work seeks to answer the following questions: How are mathematical concepts represented in Yakama culture, and how is Yakama culture reflected in mathematical concepts? How can we respectfully and reflectively craft new Ichishkíin words to express mathematical concepts not reflected in Yakama culture? This is decolonizing work, and joins a growing body of Culturally Sustaining and Culturally Reviving Pedagogies, which center teaching and learning on the lived experiences of students while critiquing culture for the ways it both sustains and diminishes. Given the dominant nature of mathematical culture, a key tenet of our project is privileging Yakama culture and the development of Ichishkíin language. We discuss the values and respect that are foundational to our ongoing collaboration to craft curriculum.