UGC draft math curriculum obsolete and retrograde: Prof Amber Habib

The University Grants Commission (UGC) has recently released draft curricula for nine subjects under the Learning Outcome Based Curriculum Framework (LOCF). While the stated aim is to promote flexibility and innovation in syllabus development, the drafts have drawn criticism for what many see as an attempt at saffronisation.

Courses now include materials on sustainability themes in the Ramayana in political science, Vastu and Ayurveda in anthropology, and Bharatiya philosophy in commerce.

In mathematics too, there is mention of mandala, geometry, yantras, and the need to know the subject’s Bharatiya perspective. Amber Habib, a professor of mathematics at Shiv Nadar University, helps us unpack what this means.

From your perspective, what do you think the LOCF is really trying to do?

Essentially, I have multiple concerns. Saffronisation is one of them, but there is also a great loss of standard mathematics itself. What passes for a good undergraduate education in mathematics changes with time, and what I would say about the current mathematics curriculum is that it would have been considered obsolete when I was in college.

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When I first started teaching at the college level in India about 25 years ago, the syllabus in universities looked a little like this. In IITs, it was quite different, as it was in other research institutions. But the curriculum had been changing everywhere and improving with time.

A lot of improvement happened over the next 10-15 years, and what I see recently, especially in this curriculum, is that all that was gained has been thrown away. We are back to a curriculum of mechanical mathematics, one that rewards memorising formulas.

It feels as if the people designing this curriculum are not aware of what has been happening in math education at both school and college levels in recent years.

Some of the books I saw listed are 100 years old, by British authors writing in 1910, 1922, and 1924. These courses—analytic geometry, old-fashioned mechanics—were thought to be gone for good. Better courses had come in their place, but suddenly they are back, and in the core compulsory courses that no student can avoid.

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The curriculum is also supposed to serve various needs. One is: What are students learning in school? School education has changed a lot over the last 30-40 years. A curriculum that was obsolete 30-40 years ago was at least in sync with the school education of that time. Now it is not even in sync. It feels as if the people designing this curriculum are not aware of what has been happening in math education at both school and college levels in recent years.

The other thing is the output. The students coming out of your programme. What are they likely to do? What would they want to do in the future? You could split this into three. Some just want to do mathematics, so they need courses that will make them experts as mathematicians.

Others want to do math but also look at applications. And finally, there are those not interested in math beyond the degree, but who will still enter careers—finance, insurance, modelling, other sciences—where mathematical knowledge is relevant.

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The National Educational Policy (NEP) has promised that after the four-year programme, a student will be fit to go directly to a PhD programme without doing a master’s in between. That means the four years should cover what was in the earlier three-year programme, plus some master’s level courses. Only then can students hope to enter a PhD programme in modern mathematics. But what is happening now is that after four years, students do not know more than they used to under the three-year programme. They are certainly not fit for direct PhD admission.

This is a general problem with NEP curricula, but in mathematics, it is worse. Compared to other disciplines, the mathematics curriculum seems to have simply cut and pasted old materials from 30-40 years ago, recommending books that are 100 years old.

Obsolete is one thing, but concepts like mandala geometry, yantras, sutra-based methods—are they even factually correct? Do they fit into a modern-day mathematics course?

The obsolete part is still what counts for these people as Western mathematics, and even from that, they have taken the obsolete parts. Mathematics has changed a lot over the last 50-100 years. If a student wants to go into research, there are key topics they must know to do anything meaningful. These used to be present in the older three-year curriculum: advanced algebra, real analysis.

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Without these, you cannot do good master’s courses, let alone a PhD. These are gone in the current programme. That is what I meant by obsolete, incomplete, and even retrograde. Students will know less than before.

About ancient Indian mathematics: I myself have an affection for it. I have taught a course in it several times. It is very interesting to see how people developed concepts one or two thousand years ago, often without the language or symbolism we have today.

Some students will leave after three years without ever doing real analysis. That is a serious problem. In India, they may still be considered graduates, but if they apply abroad with a degree lacking real analysis, they will not be taken seriously.

From the viewpoint of history, it is valuable and enjoyable. It is also interesting to study how cultures interacted and exchanged knowledge. Ancient Indian mathematicians explicitly said they learned from the Greeks. They mentioned Greek texts and authors by name. They acknowledged learning from others, then built their own insights.

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There is no mention of this in the current curriculum. Instead, it is written as if foreigners suppressed our contributions, and as if we never learned from anyone. That is not something to be proud of. Our ancestors themselves openly said they learned from the Greeks and Romans. To ignore that is dishonesty.

Even internally, the syllabus focuses only on elite figures like Aryabhata, Brahmagupta, Bhaskara—upper-class men of privilege. We do not ask what others in society were doing with mathematics, even though mathematics is everywhere in life. This narrow view may be one reason why Indian mathematics peaked and then came to a dead end.

I would not mind a couple of elective courses in ancient Indian mathematics, if done well. But here, many things that should be compulsory—basic programming, numerical methods—have been shifted to electives. Meanwhile, electives are flooded with ancient Indian mathematics. Some colleges may only offer those, meaning a student may end up learning little modern mathematics beyond the early 20th century.

For non-math students, the situation is worse. General electives and value-added courses are almost all about ancient Indian mathematics—Aryabhata, Brahmagupta, Bhaskara. There are about a dozen such courses. So, a non-math student wanting useful mathematical knowledge will only find these. It is a disaster for the promotion of mathematics among non-mathematicians and the educated public. They will not learn any interesting or useful mathematics here.

Could you give an example of key concepts of modern mathematics that are missing?

Take calculus. It is central to engineering, physics, economics—anywhere you study change. Students learn some calculus in school, but only basic calculations. At university, it is expanded and justified through real analysis. Typically, there are two real analysis courses plus a follow-up, such as metric spaces. In this curriculum, there is only one basic real analysis course, and it comes very late, in the seventh semester.

Real analysis is foundational. It should come early, so its methods feed into differential equations, optimisation, and other courses. Here, students do those courses first, without the foundation. That makes the courses mechanical—rote formulas—because the reasoning base is missing.

Some students will leave after three years without ever doing real analysis. That is a serious problem. In India, they may still be considered graduates, but if they apply abroad with a degree lacking real analysis, they will not be taken seriously. They will be unable to cope with advanced courses. This is a major flaw.

You mentioned you have taught ancient Indian mathematics. How do we incorporate traditional Indian knowledge into our courses without crossing into saffronisation?

There is a global idea that using the history of mathematics in teaching is valuable. It helps students ask basic questions—why frame a problem in a certain way, and how did people begin thinking about it? When I teach ancient Indian mathematics, I ask students to imagine themselves a thousand years ago, without today’s formulas and symbols. How might they have thought about a problem? That act of imagination can be enriching, and non-math students often do as well as math students in it.

If used like this, history adds depth. But if you just say, “Aryabhata had so many shlokas, memorise them; Brahmagupta had 20 techniques, memorise them,” and then test students on them, it is pointless. That is what this curriculum does. Whatever opportunity there was to appreciate our ancestors’ achievements is lost in this approach.

Is there anything else you think is important in this discussion around the LOCF?

Yes. The term “Vedic mathematics” appears in the curriculum. What is called Vedic mathematics is actually a collection of calculation tricks from a book written in the 20th century. The author claimed inspiration from undiscovered shlokas, but no one else has seen them. It is a modern technique, with some cleverness, but it has nothing to do with the Vedas or with ancient Indian mathematics.

It has become a commercial enterprise—you can make money running courses that promise quick calculation methods “based on the Vedas.” People pay for it, but it exploits their ignorance. Unfortunately, this has made it into the curriculum, presented as genuine ancient Indian mathematics.

One of India’s eminent mathematicians, Prof. SG Dani, studied ancient Indian mathematics seriously. He wrote about the Shulba Sutras. He also wrote about Vedic mathematics, concluding that, in view of what mathematics is today, it is neither mathematics nor Vedic. It is a fun calculation trick, but not something to spend school time on, and certainly not something to mislead people with.