Essays & Notes

OpenAI recently announced that its generative AI model had achieved a Gold medal performance in the International Mathematical Olympiad (IMO). Shortly thereafter, Demis Hassabis—CEO of Google DeepMind and Nobel laureate—announced that their model has achieved the same performance. Last year, their specialized model called AlphaProof and AlphaGeometry could only manage a Silver.

This isn’t just another benchmark. The IMO fiercely tests pre-university students’ mathematical creativity, problem-solving skills, and logical depth. It does not test routine calculations; instead, it demands original, often elegant, ideas. The problems are notoriously hard even for some mathematicians, let alone machines.

The exam typically consists of six problems spread over two days, and examiners score each contestant out of 42 points. Achieving a Gold usually requires 30+ points, depending on that year’s difficulty. India has had an impressive history at the IMO, with students consistently ranking in the top 20 countries globally and winning Golds and Silvers several times..

So, what does it mean when an AI model secures a Gold in such a competition? It’s exciting news for more than one reason. It signals that generative AI—originally embraced for tasks like writing emails, generating code snippets, or searching resources online—can now solve some of the hardest intellectual problems, which everyone once believed required deep human intuition and creativity.

This doesn’t mean AI has become sentient, though that misunderstanding persists. What it does mean is that these models are now robust tools capable of complex reasoning, mathematical insight, and strategic problem-solving—far beyond their initial design goals.

What makes this even more remarkable is that these AI systems are general-purpose large language models (LLMs). Unlike AlphaGo or AlphaFold, which were trained with the explicit purpose of mastering Go or protein folding, these models were not specialised for maths. These models—trained on vast amounts of general text and code rather than specialized mathematical datasets—nevertheless solved the Olympiad problems without any internet access or human intervention.

Apart from proving theorems and occasionally experiencing those Eureka moments, travelling and exploring new places is one of the satisfying perks of being in academia. I’m not going to deny that I was looking forward to it when I started my PhD in 2018 - and then we had the pandemic. After a long wait, I finally had a chance to attend a Theory Winter School in Zinal, Switzerland, in January. It was undoubtedly the most surreal experience of my life, and I couldn’t have expected it to be any better. I am blogging about it to preserve my experience, mostly the parts that cannot be captured in any other way.

Theory Winter School - Switzerland

It was the second edition of the winter school on theoretical computer science co-organised by EPFL and ETH Zurich in the foothills of the Swiss Alps. Five days, three courses, twelve lectures, and ample time for leisure activities and discussion - the program perhaps has the most attractive schedule of the workshops I have encountered. The workshop is particularly exclusive since invitations are extended after some profile evaluation of applicants - I couldn’t get it in the first edition even though it had lectures much closer to my research interests. Nonetheless, I got the invitation this time, and it was time to fly to Switzerland.

I started my fifth year of PhD last year in August, and with that, I entered that phase where new graduate students would look up to me seeking guidance. I was invited to a panel discussion as a panelist to share my advice with a wider audience. I realised that nothing new could have been said to them which they already don’t know, but re-emphasising the same points brought reassurance that it will all turn out well. However, sometimes conversation among panelist take unexpected turn that, upon reflection, are immensely valuable. One such issue brought up was on financial challenges during PhD.

Monetary challenges during graduate studies are one of the primary deterrents to pursuing studies after undergrad. In Indian academia, PhD students get ₹35T (₹31T for the first two years), which is significantly less compared to other countries, even after considering the purchase power parity. It forces us to reprioritise ambitions, bringing in readjustments which could be hard to accept but needed nevertheless.

It certainly helps if one has the necessary financial awareness, which develops with experience, and is not discussed at a young age. This is why those joining after spending some years in the industry don’t sweat from it. I wanted to write my thoughts on it, as for some it may be “emphasis” though for others it could be “re-emphasis”, either way I hope it brings “reassurance”. The suggestions I want to make are unusual and are seldom discussed, but after receiving occasional appreciation for peers, I was motivated to turn them into a more permanent form. They may not fit everyone, but it isn’t meant to be, as they only intend to light the spark for thinking about it.

Every year in January, I like to spend some time contemplating the books I have read in the past year. It started with an exercise where I would keep a count of books I have read and challenge myself to improve in the upcoming year. The purpose was to develop a habit of reading, a hobby I admire the most. In a world that is evolving towards consuming shorter content, micro-blogging, reels etc., book reading is a way of preserving my attention span. In 2023, I thought of sharing some of my reads with brief thoughts to give my exercise a more permanent form. The purpose of the article could be a simple recommendation list or a peak through a slit into my psyche. Either way, it is just a note of admiration for the authors of books in this list.

The Finale Empire

In many years of my book reading expedition, I have read very few fantasy novels or, more honestly, avoided them. I wanted that to change last year, so I picked up the Mistborn series on Bhargav’s recommendation. The book’s title was fascinating, and so was the setup, a trilogy (later extended) which begins with the end of an empire. It was extraordinarily fast and a page-turner, which I couldn’t put down once I started. Later in the year, before I picked the second book of the series, I learned that Sanderson is known for its distinctive style in story development. Overall, I felt elated to have chosen a great book to start my growing interest in the fantasy genre.