Rushed 'Indianisation' could weaken both math teaching and the discipline itself
As reported in this newspaper on September 20, in an unprecedented move, mathematicians across the country came together to sign a petition against the draft of UGC's learning outcome-based curriculum framework (LOCF) for mathematics. Unprecedented, because the usually inert community of mathematicians thought it necessary to raise its voice against what it sees as an ill-conceived proposal to "reform" mathematics teaching and pedagogy.
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The draft curriculum has been put under the critical scanner by mathematicians such as Amber Habib and R Ramanujam, among others. Not only have they highlighted its antiquarian approach and disconnect from contemporary methods of teaching by including archaic textbooks and half-baked courses, but they have also underlined the potential repercussions of forcibly embedding contemporary mathematics within Indian Knowledge Systems (IKS). They rightly note that this results in a disservice to both mathematics and "Indian" traditions of knowledge by making the former a site for ideological trial and error and making the latter sound self-evident, in the sense of it being "Vedic" or "Sanskritik", without a sense of the multiple histories that lie beneath terms like "Indian", "tradition" and "knowledge".
As an anthropologist studying mathematical practice for the past several years, these developments have served to affirm a few principles of my research and sharing them here might help sustain the conversation around this important matter.
As a humanities scholar, one is expected to examine the underlying determinants behind any practice, and mathematical practice is no exception. Thus, important work has been produced on the humanly mediated nature of mathematical and scientific knowledge. While this is important, my work with mathematicians and mathematical texts has also taught me that methodologically and philosophically it is important to make the distinction between the "human" and the "mathematical". The implied autonomy of the latter from the former should not be taken to mean that it can't be critically interrogated, but that any such project must also pay heed to the grammar of mathematical work and hence attempt to recover the criticality of praxis itself.
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Insofar as UGC's draft curriculum aims to inflect mathematics with a representation of the "human" as "civilisational", it avoids the genuinely demanding work of making the raw material of mathematical work an object of democratic deliberation, and reworking the curriculum accordingly. Instead, it takes the easy way out by inserting "Indian" sounding topics into a self-reflexive and integrated formalisation which characterises mathematical knowledge. In so far, as it is implied that Indian Knowledge(s) constitutes a system, then at least it should be understood that mathematics too is a system and systems are distinguished by the complexity they embody, such that parachuting extra-systemic elements into their midst only weakens them from within.
Further, vernacularisation (or Indianisation) of not just mathematics but any form of knowledge, if pushed from above, ends up being hegemonic in its own way. Firstly, discourses are never wholly traditional or modern, vernacular or standard, but somewhere in between and inextricably entangled. Secondly, practices generate their own context such that forcibly "contextualising" through recourse to extraneous factors of "culture" or "civilisation" repeats an epistemic violence, this time not because of mindless abstraction, but in the name of the rapidly wearing-out bogey of decolonisation. And lastly, historians such as Senthil Babu D have, through meticulous historical research, pointed out that traditions of vernacular mathematics in socially fragmented societies are as much about division of labour and caste as about mathematical ingenuity and have to be revisited as such without exonerating them of histories of exploitation and manipulation. For example, in exploring the narratives around the figure of the accountant during the pre-colonial period and with the onset of company rule, Babu D's work traces the complex connection between computational practices and their consequences for the public at large. Such narratives show that vernacularisation cannot hope to proceed simply as a way of restoring past glory, but will have to seriously contend with granular material histories of different professions, and more broadly with the meaning that mathematical knowledge has held for labouring and working people of the subcontinent over the ages.
This implies that cherry-picking elements which are deeply woven into such fabric of the "social" for the purpose of national or civilisational resurgence and to place them in textbooks as neutral and consistent pieces of knowledge does a disservice both to history and mathematics. No doubt more informed conversations are required around vernacular traditions of mathematics, but to confuse the demands of historical work with mathematics is to make a category error, and in the case of UGC's draft curriculum also reflects sheer thoughtless haste.
The last principle I must mention is that of the heterogeneity of forms which constitute mathematics and the problem of translatability. Take an example: Algebra and geometry in their potential are two very different forms, such that Descartes's attempt to bring them together was occasioned by the attempt to solve a problem (Pappus's locus problem). But as the American poet and philosopher of mathematics Emily Grosholz shows, whatever impressive gains the resulting analytic geometry made in terms of addressing a certain class of problems, it also lost specific potentialities associated with algebra and geometry. There's nothing particularly concerning about this; it is inevitable with any creative practice (whether mathematical or literary), and it further demonstrates how mathematical practice grows by translating forms into one another in order to tackle problems that would not yield under a straightforward approach. This also attests to the erroneous nature of the foundationalist vision of mathematics (that mathematics is either all sets or logic), bringing to the fore more relevant philosophical notions such as "convention" and "modularity".
To cut to the chase, given this view, it would make more sense to introduce "Indian" concepts and styles of thought at the cutting edge of the discipline to see how helpful they are in devising solutions to emergent issues. So, for example, it might be assessed how effective computational or experimental approaches are in understanding the challenges posed by AI; to see if contemporary mathematicians can look for resources in Buddhist or Jain logic to navigate problems in multimodal or fuzzy logics, and so on. In short, it is better to test the robustness of a system in the "field" rather than letting it in through the backdoor. This not only respects the integrity of the discipline but also sets the ball rolling for critical and meaningful conversations with different traditions. The insights gained from such conversations can then suitably be incorporated into teaching and pedagogy as well.
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At the end it must be clarified that the intention of this article is not to side with the status quo, but to critically interrogate the will to reform. To ask, who leads the reform and towards what end? Where are the stakeholders (mathematicians-teachers, students etc.) in all this? And what is their view of the contemporary demands of mathematics and its learning? In other words, if there is a "community" around mathematics, what does it agree or disagree about, and where do members of this community place their hopes and aspirations?
It is heartening that in this case, the mobilisation has been led by the mathematicians themselves. I suggest that this be seen as an opportunity to keep the flame of debate alive over mathematics in India -- a debate which has never really taken place in the public domain since Independence. In a diverse and multilingual country like India, there are far more pressing and "nationally" important concerns regarding the making and teaching of mathematics. Linguistic plurality, lack of quality Indian texts at the undergraduate level, disconnect with cutting-edge advances in the field, and short training duration for school teachers are only some of them. Simply nationalising the curriculum will give a short shrift to these. The need of the hour is a closer engagement with mathematical practice and its remarkable heterogeneity, and to act cautiously and critically, instead of entertaining the feeling of some imaginary ascent with an arbitrarily refurbished curriculum, for an ascent can also become a slide without the right steps being carved in. And as they say in mathematics, steps matter, often even more than the solutions!
The writer is a Hindi poet and assistant professor (Sociology) at the School of Humanities and Social Sciences, IIT Mandi