How I Got Accepted into Stanford's AI & Deep Mathematics Research Program

Rajnikant Dhar Dwivedi — Wed, 17 Jun 2026 00:00:00 +0000

I’m going to be honest — when the email arrived on June 15 at 7:30 in the morning, I had just woken up. Still groggy, phone in hand, I almost scrolled past it. The subject line read: “Congratulations! You’ve been selected for the Stanford AI & Deep Mathematics Research Program.”</em> I read it three times before it actually registered.</p>

This post is for everyone who asked me “how?” — for every student from a small town who wondered if the big doors were actually open for them, and honestly, for myself. Writing this down makes it feel real.</p>

Where It All Started</h2>
I grew up in Siddharth Nagar, Uttar Pradesh. Not exactly a city people associate with Stanford. My parents aren’t researchers or professors — my father runs a small business, and my mother has always been my loudest supporter. Internet was patchy, opportunities were few, but curiosity was something nobody could take away from me.</p>
I got hooked on computers early. By the time I was 16, I was writing scripts to automate things at home just for fun. At 17, I cleared TCS CodeVita and landed a DevOps engineer role at TCS — something I never really shouted about, but it validated something deep inside me: the work was real, and I was capable of it.</p>

“If you’re from a place people have never heard of, your job isn’t to apologize for it. It’s to make them remember it.”</p> </blockquote>
Fast forward: Chandigarh University for my B.Tech, the MIT Professional Education Applied Data Science Program, a HackMIT finalist badge, and winning the Qualcomm ArkLOL Hackathon 2025 as Lead Developer of Team Invincibles with our AI-powered AR education platform ArkEDU. Each of these built the profile — but more importantly, each of them built the conviction.</p>

Finding the Program</h2>
I first came across the Stanford AI & Deep Mathematics Research Program in late March 2026, deep in a research rabbit hole. I was reading about the mathematical foundations of neural networks — specifically geometric deep learning and how Riemannian manifolds show up in transformer architectures. One of the papers I found was co-authored by faculty running this exact program.</p>
The program runs July 1 through August 30, 2026, at Stanford University in California. It’s intensive: actual research, not coursework. The intersection of AI and deep mathematics was precisely what I had been gravitating toward in my own side projects.</p>
I almost didn’t apply. The imposter syndrome was loud that week. I texted Shikha about it. She said, in her characteristically no-nonsense way: “Apply first. Spiral later.”</em> So I did.</p>

The Application</h2>
The application had three main components: a statement of purpose, a technical portfolio, and two recommendation letters. There was also a short research proposal describing a problem you’d want to work on during the program.</p>
Statement of Purpose</h3>
I spent nearly two weeks on mine. The first draft was too formal, trying too hard to sound “Stanford-worthy.” My mentor read it and said it didn’t sound like me. So I scrapped it and started over — writing about the night I stayed up until 4 AM debugging an edge case in ArkEDU’s spatial mapping algorithm, and how that frustration turned into a genuine question about whether our mathematical tools for representing 3D space were even the right ones.</p>
Technical Portfolio</h3>
I submitted a curated selection: ArkEDU (Qualcomm Hackathon), HeroTrack — a full-stack AI productivity app built with React, TypeScript, Express.js, PostgreSQL, and GPT-4o — plus CTF and web security research, including my top-3 finish in the openECSC write-up competition.</p>
Research Proposal</h3>
“Towards Topology-Aware Attention: Applying Persistent Homology to Transformer Self-Attention Patterns.”</em> The core idea: attention heads seem to learn latent geometric structure that classical linear algebra doesn’t fully describe — and tools from algebraic topology might give us a better lens. Speculative, yes. But genuinely mine.</p>

14</div>
days writing the SOP</div></div>
3</div>
full drafts scrapped</div></div>
~40h</div>
spent on the proposal</div></div>
2</div>
recommendation letters</div></div> </div>

The Interview</h2>
About three weeks after submitting, I got a calendar invite for a 45-minute video interview with two faculty members.</p>
The interview was nothing like I expected. No quiz, no gotcha questions. The first 10 minutes were almost conversational. Then one faculty member pushed back hard on a claim I made about persistent homology being “computationally tractable” for large-scale transformers. He was right. Instead of crumbling, I acknowledged the gap, proposed a workaround involving approximation schemes, and said: “This is exactly why I want to be in a research environment — to stress-test ideas with people who can see the holes I can’t.”</em></p>

Knowing what you don’t know — and being unafraid of it — might be the most important thing you can demonstrate in a research interview.</p> </blockquote>
They ended with a beautiful question: “If you could change one thing about how machine learning is currently taught, what would it be?”</em></p>
I said we teach optimization before intuition — we teach people to minimize loss functions before they understand what loss actually means in the real world. They smiled. That felt good.</p>

The Wait, and the Morning Everything Changed</h2>
Two and a half weeks of checking email compulsively. I kept working. Late-night calls with Shikha about everything except</em> Stanford, because talking about it too much felt like tempting fate.</p>
Then June 15 arrived.</p>

Received — June 15, 2026 · 7:30 AM</p>

Rajnikant Dhar Dwivedi - research

How I Got Accepted into Stanford's AI & Deep Mathematics Research Program

The Application</h2> The application had three main components: a statement of purpose, a technical portfolio, and two recommendation letters. There was also a short research proposal describing a problem you’d want to work on during the program.</p>

The Application</h2>
The application had three main components: a statement of purpose, a technical portfolio, and two recommendation letters. There was also a short research proposal describing a problem you’d want to work on during the program.</p>