Why do mathematics in the age of AI

Srivatsav Kunnawalkam Elayavalli, Assistant Professor, UC Berkeley

I am a mathematician. I like to think deeply. But why? It is not because I get a paycheck. Sometimes I wonder if it is because I am good at it and want to prove something to the people around me. It is not. Ultimately it is because of a fundamentally cultural craving and a desire to uphold ‘manōdharma’. This roughly translates to ‘moral duty to the mind’. But to truly explain what this means for me, I must take you on a detour into the world of Indian classical music.

If you have ever been to a classical carnatic concert, you will routinely see people in the audience doing any or all of the following: weaving gestures with their hands, screaming out “sabhash!” or “aaha!” or “ayyo!”, shedding a tear, and perhaps even stand up and clap in the middle of the piece. These are indications of a hidden connection formed between the musician and listener. This connection is built on the vehicle of ‘bhāva’, an important feature of musical manōdharma. It is crucial to note that manōdharma in this context is organized centrally as a spontaneous creative exploration, a feature that is quite unique among other forms of classical music in the performance space. There is however a tradeoff with central values notably around perfection of delivery, measured structural themes and a focus on optimization and precision. We will return to this in a moment.

It is hard and perhaps futile to translate ‘bhāva’ accurately, but I could say that it is an indicator of an emotional experience that opens your core to new depths of appreciation. At the same time, it is quite elusive: not something to be codified or measured. Although I am not an expert in buddhist philosphy, a colleague (Mahan Mj) told me something about the roots of advaita that resonates with my understanding of bhāva: “any real piece of knowledge is acausal, in the sense that a flash of understanding is not something for which you have proper cause-effect chains”. Bhāva underpins multiple millennia of civilizational growth inside India. For instance, the Bhakti (the bhāva involved in the surrender of oneself to God) movement produced phenomenal bodies of creative outbursts, notably including the formation and organization of carnatic classical music by the trinity Tyagaraja, Muthuswami Dikshitar, and Syama Sastri. Another fascinating example of the manifestation of bhāva in creative output is the story of the legendary Srinivasa Ramanujan. Ramanujan largely attributed his creative findings to the Goddess Namagiri Thayar. To this day it is not clear within mathematical circles how exactly he discovered theorems that were decades ahead of his time, without proof or explanation.

It is perhaps helpful to consider manōdharma in simplistic terms: as simple as a conscious quest for an ‘aha moment’. This is for instance what drew me to mathematics, which to me is a several centuries old industry of systematic ‘aha moment’ production. At the very core of cultivating these ‘aha moments’ is indeed bhāva, perhaps in a form one often refers to as mathematical taste. This aspect of ones intimate relationship with mathematics, and even with their own mind at large, is completely independent of the ideals from before of perfection, optimization, measurement and precision (which I will denote by POMP). I argue that the conscious inculcation of bhāva is the source and also the pinnacle of human achievement, and by design is independent of anything to do with artificial intelligence.

I consider the recent emergence and impact of large language models (LLMs) as a step towards the culmination of our long standing obsession on POMP, perhaps starting from the industrial revolution. What is rather ironical is that this obsession has already to a large extent and eventually will render all human enterprise in activities centered around POMP completely obsolete. While I do not know if LLMs as they are currently designed will surpass human beings in all possible avenues, it is entirely possible that some day soon it might. In fact in my own case, I completely recognize the power and beauty of AI, and am ready to accept that it probably already is ‘better’ than me at math. But I simply do not care about this. Knowing this contributes nothing to my own journey of manōdharma. Every human being has such a journey, and mathematics is one prominent route to travel that I believe will always exist and be available for everyone until humanity exists. I will not disregard the existence, progress and impact of AI tools, I will use them and appreciate them insofar as it invokes bhāva and enriches me. I think this is not a time for mathematicians to panic, but it is a time for us to be honest with ourselves and work to make our mathematical experience richer. We do, however, need to be conscious about the fact that our profession will certainly change a lot in the coming years. It seems rather self defeating to continue operating on the status quo which remains oblivious to AI. Ultimately, we work in one of the greatest ‘aha factories’ of all time, and I think these factories are only going to be more and more important for humanity in the future.

Acknowledgements. I am grateful to the following people for helpful conversations that motivated me to write this: Uri Bader, Milind Hegde, Mahan Mj, Forte Shinko, Thomas Sinclair and Jennifer Zhu.


Received 8 August 2026.

5 responses to “Why do mathematics in the age of AI”

  1. Rafael Avatar
    Rafael

    Thanks so much for this! It is immensely insightful and maybe hopeful of the future that may come to math.

  2. Venkatkrishna Karumanchi Avatar
    Venkatkrishna Karumanchi

    thank you for the article, would like to clarify that buddhist philosophy and advaita are not the same. Advaita is a monist hindu philosophy.

  3. Stefan Avatar
    Stefan

    I think most of us agree on why we are doing math (perhaps in different words) and that this motivation is only mildly affected by AI. But a different question is why should society pay us to do it? For instance it does not pay us to pursue our favorite sport, which can also be a source of satisfaction (though perhaps of a more mundane kind, excuse my ignorance of Indian philosophy).

    1. Srivatsav Kunnawalkam Elayavalli Avatar
      Srivatsav Kunnawalkam Elayavalli

      My point is that what I call “manodharma” is part of the ultimate purpose of humanity and our profession offers people a well established path towards it for people of the world. These people could include for example the people we educate in our courses, or those with whom we develop mathematics together. The society pays for many things, and I personally think that the very very minor fraction that goes to the mathematical profession is justified. Of course these questions will be evaluated from time to time, and trends may change.

      On a basic level, many societies do pay for college education that is for the most part comprised of opportunities that allow young people to pursue sources of enrichment and satisfaction, including one’s favorite sport. Strictly speaking, if one only wants to train people for the workforce, large portions of schooling and college education seem completely futile and unnecessary. I view public education as an early example of the society paying for uplifting the collective manodharma of humanity.

      Regarding your last point, of course there is a distinction to made between mere hobbies and deeper and sustained interests. It is perhaps unlikely that society would pay one for pursuing his own hobbies. However, if there is a substantial volume of people who collectively want to pursue something in a systematic manner, I think it will organically derive a strong enough pull for support from the society, both financial and moral. Mathematics gave me a life, and I know many extremely talented young people growing up and especially also right now (including students of my own) who derive existential purpose and security from the world of mathematics.

  4. Sahana HB Avatar

    As a mathematician and Indian classical dancer, I have to say this resonates with me. What the author is referring to is the core of why many people (I think) pursue research in mathematics. It is a search for “truth” which is so fundamental that it seems “natural” once you’ve worked hard to understand it. Somehow the subject combines deep reality with an elegance that no other language manages to achieve. Further, that sense of satisfaction and achievement when we make mental breakthroughs is its own reward. Most of us do not pursue this field to “show off”, but rather because we are on our own internal pathways of discovery.

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