Sagar Shrivastava

Origami enthusiast who is a Visiting Professor in the Mathematics department of Ashoka University.

[levent @__alpoge__]

hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final

((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3, has jacobian determinant -2, and sends (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0)

[Sagar Shrivastava @ntsesagar]

Everyday we're learning what more AI can do in Math. Some mathematicians told me ,they are scared of loosing their edge to AI, I feel that we're in an era where we have the smartest helpers who definitely know a lot more than we do, and are just waiting for the right prompt.

[Jared Duker Lichtman @jdlichtman]

This is quite a remarkable result:

Posed in 1939, the Jacobian conjecture is one of the central open problems in algebraic geometry, but was just disproved by Alpoge, Matthew, and Claude Fable 5.

The Jacobian conjecture roughly says that a multivariable polynomial F has an inverse function (made out of polynomials) provided the Jacobian is non-singular (i.e. matrix of partial derivatives has non-zero determinant). This condition is neccessary by the Inverse Function Theorem from multivariable calculus. The hard question is whether it is also sufficient.

Evidently, Fable found that

F(x,y,z) = ((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z)

has det(J_F) = -2 non-zero. However F is not invertible, since F sends three different pts (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to the same image (-1/4, 0, 0).

Beyond the disproof itself, it would be value to know if a suitably refined conjecture is recoverable. Per @Acer, GPT5.6 has proposed:
"A constant-Jacobian polynomial local biholomorphism with no loss of sheets at infinity—e.g. a proper Keller map—is an automorphism."
I would be interested to know if any algebraists (e.g. @levent @littmath) have a reaction to this...

A further twist to the story:
Not only was the Jacobian conjecture one of the central open problems in algebraic geometry, it was (a special case of) Yitang Zhang's PhD problem!

The catch was that Zhang's advisor had him solve it, assuming a lemma of his advisor. But that lemma turned out to be false! As a result, Zhang's thesis crumbled and he then struggled to get recommendation letters and a permanent academic position. Despite all this, Zhang went on to prove bounded gaps between primes!

This is one of the most inspiring stories in modern mathematics, and was a motivation for me to work in the same area for my doctorate.

[Sagar Shrivastava @ntsesagar]

To know more, check out this link- https://t.co/IAnuMM6dGs

[Sagar Shrivastava @ntsesagar]

Applications open for *Math Apprenticeship Programme* under the *Lodha Genius – Ashoka University Programme (LG-AUP)* .

This is a 5-week dual internship at Ashoka University from 15 May to 20 June 2026, combining teaching assistance and project work in mathematics.

[Sagar Shrivastava @ntsesagar]

Key details:
⦁Role: Teaching Assistant
⦁Location: Ashoka University, Sonipat
⦁Eligibility: UG/PG students with strong background in Mathematics
⦁Accommodation & meals provided

Application deadline: *28 February 2026 (Saturday)
*Apply here:*
https://t.co/qyw5EGU18G

[Sagar Shrivastava @ntsesagar]

Applications open for Math Apprenticeship Programme under the Lodha Genius – Ashoka University Programme

This is a 5-week dual internship at Ashoka University from 15 May to 20 June 2026, combining teaching assistance and project work in mathematics.

[Sagar Shrivastava @ntsesagar]

To all the math nerds celebrating kiss day, what is the equation of a kiss?

It's "a lip tickle"!!!

Retweet if you get it, but don't comment it out loud.

#KissDay #math #nerdcore

[Sandeep Juneja @sandeepjuneja66]

eXSPLOre 26. The registration deadline is approaching. Please inform interested students and researchers. We have an exciting line up of speakers and a great mix of academic and industry oriented activities.

[Tata Institute of Fundamental Research @TIFRScience]

TIFR faculty have been honored with the #RashtriyaVigyanPuraskar, India’s highest recognition for excellence in science & innovation.
🔹Jayant Narlikar (Vigyan Ratna,posthumously)
🔹Mahan Mj (Vigyan Shri)
🔹Deepa Agashe & Sabyasachi Mukherjee (Vigyan Yuva-Shanti Swarup Bhatnagar)

[Sagar Shrivastava @ntsesagar]

For those undergraduate students in or around Delhi and interested in mathematics, do apply and challenge yourself!!
#madhavamath #ugmath #maths

[Sagar Shrivastava @ntsesagar]

@H0H0v 216

[Sagar Shrivastava @ntsesagar]

@kartanekaramko Really none

[Howie Hua @howie_hua]

We are a month away from one of the coolest mathematical dates of our lifetime!

[adithya @00aleph00]

some tips on how to read math textbooks:

[Anthony Bonato @Anthony_Bonato]

Astronomers spot possible biggest black hole in the universe

[Philosophy Of Physics @PhilosophyOfPhy]

"Students don't need a perfect teacher.Students need a happy teacher, who's gonna make them excited to come to school and grow a love for learning."

- Richard Feynman

[Sagar Shrivastava @ntsesagar]

I don't know about yours, but my @YouTube updates is going to repair the space-time continuun!!!

#relativity #spacetime #updates #YouTube

[HBCSE @HBCSE_TIFR]

Kanishk Jain (GOLD) Pune, Maharashtra;
Snehil Jha (GOLD) Jabalpur, Madhya Pradesh
Riddhesh Anant Bedale (GOLD) Indore, Madhya Pradesh
Aagam Jignesh Shah (SILVER) Surat, Gujarat
Rajit Gupta (SILVER) Kota, Rajasthan

[Sagar Shrivastava @ntsesagar]

Hurry up fellas, and communicate this to as many school students as possible!!

[HBCSE @HBCSE_TIFR]

Hurry Up! Only few days left for IOQM registrations!
Don't miss your chance to take the first step towards representing India at the International Mathematical Olympiad. Eligible students enroll now and challenge yourself with the best minds in Mathematics. #IOQM2025