Shiva Kintali

Senior AI Architect at Nvidia, Mathematician, Cryptographer, Ex Princeton Lecturer, Artist, Writer, GeorgiaTech (PhD), USC (MS), IIT Kharagpur (B-Tech)

[Shiva Kintali @ShivaKintali]

Here is a Short Proof of the Quasi-Riemann Hypothesis.

My goal here is to substantially simplify OpenAI’s proof and focus only on proving the Quasi-Riemann Hypothesis for some 1-c, without worrying about maximizing the value of the c.

I obtained a much shorter proof for c=1/48. This proof is easy to understand and it can be taught in math courses in one lecture.

It is self-contained. It is only 21 pages including abstract, proof overview, all proof details and references.

Paper is on my homepage: https://t.co/IIjOhmNDjU

PDF file: https://t.co/UwN9nn6mAv

CC: @AlexKontorovich @__alpoge__ @jdlichtman @cremieuxrecueil @danielmarinq @stevenstrogatz @kenono691 @littmath @nasqret @PI010101 @nechita_ion @Isaac__kim @FryRsquared @wtgowers @MarcusduSautoy @DrEugeniaCheng @JSEllenberg @JohnDCook @JDHamkins @AxlerLinear @emilyriehl @hollykrieger @Kit_Yates_Maths @PoShenLoh @robertghrist @AlexKontorovich @kenono691 @ch_nira @rrwilliams @lreyzin @ChrisPeikert @fortnow @RadishHarmers @thomasfbloom @abhatt2 @mahdi_tcs_ @octonion @prz_chojecki @thegautamkamath

[OpenAI @OpenAI]

We’re releasing a broad range of new mathematical results produced by an internal frontier model.

We’ve been consulting with the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study, and we have drawn on their advice and public recommendations to inform how we release these results.

https://t.co/7N6TPlft1P

[Shiva Kintali @ShivaKintali]

One of my favorite open problems from 2004 is now resolved. 🥳🕺💃🎉🎈🤖🦾

An Optimal Quantum Query Lower Bound for Matrix-Product Verification

Paper is on my homepage: https://t.co/4tt0O2hg0N

PDF file: https://t.co/2Ohj5p8UJv

[Shiva Kintali @ShivaKintali]

Fixed-Order Strong Komlos Conjecture is false.

Paper is on my homepage: https://t.co/4tt0O2hg0N

PDF file: https://t.co/MRS4VXkw5y

CC: @AlgoSvensson @sahilsingla81 @ShacharLovett @MCombinatorics @kiragoldner @PI010101 @thomasfbloom @rrwilliams @DmitryRybin1 @lreyzin

[Shiva Kintali @ShivaKintali]

I have two new results on approximating Graphic TSP. Breaking the 7/5 Barrier for special cases.

Posted on my homepage: https://t.co/IIjOhmNDjU

101/73 for Graphic TSP on Graphs of Girth at Least Five: https://t.co/hzwqCl4tph

53/38 for Graphic TSP on Bipartite Graphs: https://t.co/7bRhq9ZtQX

CC: @AlgoSvensson

[Shiva Kintali @ShivaKintali]

An optimal 1/e guarantee for rank-two matroid secretary.

Paper is on my homepage: https://t.co/rMP0w3JQPd

PDF file: https://t.co/02kMRiK57S

CC: @AlgoSvensson @sahilsingla81 @MTHajiaghayi

[Shiva Kintali @ShivaKintali]

I am very excited to announced an exponential lower bound for exact parity in depth-four QAC circuits.

My paper is on my homepage: https://t.co/4tt0O2hg0N

PDF file: https://t.co/GV0HTsFhJG

[Shiva Kintali @ShivaKintali]

I have extended the recent Lamzouri’s method to fixed Dedekind zeta functions.

My paper is on my homepage: https://t.co/4tt0O2hg0N

PDF file: https://t.co/iti6lrcKme

[Shiva Kintali @ShivaKintali]

I held the world record for the Bounded gaps between primes for just two days. 🤣

Today Sep 3rd, 2026: @axiommathai announced H1 <= 212.

Sep 1, 2026: I showed that H1 <= 236 with the help of AI, building on Julia’s Stadlmann’s work.

I had announced H1 <= 236 in my tweet: https://t.co/8YU3MLlJ5S

Posted my paper on my homepage: https://t.co/iKK6tFbuVH

Aug 31, 2026: H1 <= 240 by Julia Stadlmann (without using AI). This is an awesome paper with new insights and progress in more than a decade. https://t.co/JSL3wyFGST Congratulations to Julia Stadlemann 👏👏👏

Year 2014: H1 <= 246 by Maynard and Polymath Project.

Congrats to @axiommathai 👏

I will stop my AI agents now and move on to another math open problem from my favorites list. 🙂

Previously, I held the world record for the percentage of zeros of the Riemann zeta function on the critical line for just two days 🤣 See the timeline here: https://t.co/B8Kni0B7x8

[Axiom @axiommathai]

1/ ✨ World record today on bounded gaps between primes, one of number theory’s oldest open conjectures. 

We show that infinitely many pairs of prime numbers are separated by 212 or less.

[Shiva Kintali @ShivaKintali]

I just achieved a new bound on H1 using AI. 🥳🕺💃🎉🎈🤖🦾

H1 = Bounded gaps between primes.

Today (Sept 1, 2026): H1 <= 236 by Human+AI.

Yesterday (Aug 31, 2026): H1 <= 240 by Julia Stadlmann (only human).

Year 2014: H1 <= 246 by Maynard+Polymath.

I was trying to improve H1 for more than 2 years now. The new insights in yesterday's paper by Julia Stadlmann are awesome.

My agents are still running. I am expecting a bound below 236.

My paper is available on my homepage: https://t.co/iKK6tFbuVH

PDF file: https://t.co/ZSTyhqBaGr

[Thomas Bloom @thomasfbloom]

A great new result on gaps between primes (by a human!) - Julia Stadlmann has shown there are infinitely many pairs of primes at most 240 apart.

(The previous record by Maynard+Polymath was 246.)

https://t.co/FE5MvSRr1m

[Shiva Kintali @ShivaKintali]

@slimer48484 I had the proof of "Irrationality of the 5-adic zeta value zeta_5(3)" one week ago and uploaded it on my homepage: https://t.co/rMP0w3JQPd

Most of the work in my paper is done by ChatGPT.

PDF file: https://t.co/oWU6BVbYAW

[deckard @slimer48484]

Exciting new mathematical results by Fable: The p-adic zeta_5(3) value was proven irrational!

This was done using an extension of methods by Calegari Dimitrov and Tang, whose method proved L(2,χ−3) irrational.

[Circumjovial @CircumjovialLLC]

🧵4. Two days prior to Anthropic's announcement, @ShivaKintali improved the unconditional lower bound from 41.6% to 42.1%. I&amp;AI improved on that by whopping 0.000155458. Kintali held the world record for two days! A mathematics world record laureate nonetheless!

[Circumjovial @CircumjovialLLC]

@ShivaKintali Hi Shiva! Here is a very small improvement on your 41.108217 to 41.108372. Cheers!

[Shiva Kintali @ShivaKintali]

A cubic lower bound for Electrostatic Equilibria: Failure of Maxwell's conjecture for infinitely many n.

My paper proving M(n) = Omega(n^3) is on my homepage: https://t.co/4tt0O2hg0N

PDF file: https://t.co/qBhp7IisTs

[Shiva Kintali @ShivaKintali]

A Quadratic Lower Bound for Maxwell’s Equilibrium Problem

My paper proving M(n) = Omega(n^2) is on my homepage: https://t.co/4tt0O2hg0N

PDF file: https://t.co/muuNG1NTnD

[Shiva Kintali @ShivaKintali]

Maxwell conjecture is false for four point charges.

Here is my paper proving M(4) &gt;= 11: https://t.co/wgGNDo0Oce

This is the smallest counterexample, because I proved M(3)=4 in my previous paper: https://t.co/2Z0KVEV31A

All papers are on my homepage: https://t.co/4tt0O2hg0N

[Shiva Kintali @ShivaKintali]

Just two days ago (on Aug 8th 2026), I have increased the percentage of zeros of the Riemann Zeta Function on the critical line from 41.6% to 42.1%

Today Anthropic announced 67.2% 👏👏👏

My paper is on my homepage: https://t.co/4tt0O2hg0N

PDF file: https://t.co/OjZ1MTXQr6

[Anthropic @AnthropicAI]

We asked an unreleased research version of Claude to take a stab at the Riemann hypothesis.

It didn’t solve it, but it did make strides on a related problem: it increased the lower bound for the fraction of zeros of the Riemann zeta function that satisfy the hypothesis from 41.6% to 67.2%.

https://t.co/aZDvqqhHRi

[Chris Peikert @ChrisPeikert]

Oh my goodness…

https://t.co/AmZ2Tl12th

[Shiva Kintali @ShivaKintali]

A Superlinear Lower Bound in Maxwell’s Equilibrium Problem.

Paper is available on my homepage: https://t.co/h6zUXKEkl3

[Fermat's Library @fermatslibrary]

Niels Abel, born exactly 224 years ago today, proved at 21 that there is no algebraic formula to solve equations of degree 5, settling a 250-year-old problem.

He paid the printer himself and compressed the proof to 6 pages to cut costs. He sent a copy to Gauss, who never responded. Abel died of tuberculosis at 26. Two days later, a letter arrived announcing he'd been appointed professor in Berlin.