Prakhar Pratyush 🇮🇳

यथा शिखा मयूराणां , नागानां मणयो यथा ।
तद् वेदांगशास्त्राणां , गणितं मूर्ध्नि वर्तते ॥

[Prakhar Pratyush 🇮🇳 @pursuingstacks]

When an Elliptic Curve met a Modular form - A short tale on Reciprocity laws in Number Theory

[Math, Inc. @mathematics_inc]

Math, Inc. is proud to announce an all-star group of Veritas Fellows:

Renowned professor Kevin Buzzard, alongside Fields Medalists Maryna Viazovska and Terence Tao.

They will lead teams to build formal mathematics at unprecedented scale. 🧵

[Emily Riehl @emilyriehl]

In a talk called "A reintroduction to proofs"

https://t.co/Rub7iN8fhS

I've speculated about teaching an undergraduate level introduction to proofs course but using dependent type theory as the implicit formal system in place of set theory and first order logic.

[Bhāvanā Magazine @BhavanaMagazine]

1972: The Montgomery–Dyson Meeting

The interface between number theory and random matrix theory can be traced to a moment of pure enthusiasm. In 1972, Sarvadaman Chowla insisted that Hugh Montgomery meet Freeman Dyson over tea. Decades later, Montgomery described the episode as follows:

“Here’s a thing about Chowla: when he got a bee in his bonnet, he was unstoppable.

Chowla won and dragged me over to meet Dyson. Dyson was listening attentively to everything that Chowla was saying, and I was uncomfortable. I had expected Dyson to shake my hand and say, ‘I am glad to meet you’, and reminisce about how he had worked with Davenport and so on.

But he just turned and asked what I was thinking about. I said: I think that the differences between the zeros of the zeta function are distributed with the density [shown in the image below].

Instantly, Dyson said, ‘That’s the pair correlation of the eigenvalues of a random Hermitian matrix’. To say I was stunned would be an understatement. It blew my mind.”

For more on Sarvadaman Chowla, read the article by @kaneenikasinha at: https://t.co/gmwAgCKoyV.

[Scott Kominers @skominers]

Epic. I think we're going to see a ton of this type of work in the next year, as more and more mathematicians start asking models about the questions they've puzzled over repeatedly and/or gotten close to solving.

That's certainly been my experience thus far -- already finished two papers this way and on my way to a third, respectively based around ideas I first thought about in 2022, 2009, and 2004(!).

(h/t @ben_golub)

[adithya @00aleph00]

A few months ago, I learned about an amazing theorem which gave me pause:

The sum of the reciprocals of twin primes CONVERGES!

i.e: the sum (1/3 + 1/5) + (1/5 + 1/7) + (1/11 + 1/13) + ... converges.

This is amazing because the sum of reciprocals of all the primes DIVERGES! So this roughly means that "there are much more primes than twin primes".

I was enamored by this statement. How would you even begin proving it? How is it related to the twin prime conjecture? I decided that I would make a short 5 min video on it.

3 months later ... and the video ended up being 30 minutes long. But it should be out in a few days and I'm so excited for you see it. Keep your eyes peeled 👀

[Aryeh Kontorovich @aryehazan]

my aspiring mathematician nephew is concerned that maybe someday we'll run out of nontrivial theorems to prove

he knows there are infinitely many *theorems* but worries that there might only be many finitely interesting ones

I told him that all the mathematicians I know think otherwise

what argument would put him at ease?

[Prakhar Pratyush 🇮🇳 @pursuingstacks]

@Takuiten @wojakcodes Yes bhai. This is me ✋🏽

[taku (builder arc) @Takuiten]

"An equation means nothing to me unless it expresses a thought of God." — Srinivasa Ramanujan

[THE SKIN DOCTOR @theskindoctor13]

Two private AC buses caught fire within 10 days, the first in Jaisalmer on 14 Oct and the second in Kurnool today, killing 20 and 19 passengers, respectively.

Time to learn one more survival skill in India. Private AC buses usually have only one door, I think the law mandates for one only. The emergency exit is supposed to be there, but in most cases, it’s non-functional. These buses have poor wiring, unauthorized modifications, and plenty of flammable material, enough to give you one of the worst possible deaths.

So think before you travel in an AC bus in India. If you have to, check the emergency exits, are they functional or not? Don’t bother asking the govt for better regulations. Itna bada desh, roz hazaaro log marte rehte hain. Who cares if a few more die? Apna bachaav khud karo.

[Narendra Modi @narendramodi]

Had a great interaction with Shubhanshu Shukla. We discussed a wide range of subjects including his experiences in space, progress in science & technology as well as India's ambitious Gaganyaan mission. India is proud of his feat.

@gagan_shux

[Narendra Modi @narendramodi]

We welcome the successful launch of the Space Mission carrying astronauts from India, Hungary, Poland and the US.

The Indian Astronaut, Group Captain Shubhanshu Shukla is on the way to become the first Indian to go to International Space Station. He carries with him the wishes, hopes and aspirations of 1.4 billion Indians.

Wish him and other astronauts all the success!

[Bhāvanā Magazine @BhavanaMagazine]

Mathematicians are of two kinds:

There are birds like eagles who have a panoramic view of deep mathematical structures and then there are frogs, who love the specific mathematical details.

(1/2)

[Didier 'Dirac's ghost' Gaulin @DiracGhost]

If you have an interest in number theory, this Fermat's last theorem conference is one of high quality, as it contains rare lectures by John Tate, Barry Mazur, Joe Silverman, Jaap Top and many more.

Check out the quoted link.

[Didier 'Dirac's ghost' Gaulin @DiracGhost]

Thank you Noam Elkies, now I know.

[Bhāvanā Magazine @BhavanaMagazine]

André Weil was born today on 6th May, 1906. He was one of the most influential pure mathematicians of the twentieth century, especially known for his contributions to Number Theory and Algebraic Geometry, and had a lifelong interest in the history of mathematics.
(1/5)

[Joel David Hamkins @JDHamkins]

I shall be giving a series of advanced set theory lectures at Peking University in June for the summer session. Lectures on set theory and the foundations of mathematics. Topics will include forcing, independence, definability, truth, set-theoretic geology, the modal logic of forcing, set-theoretic potentialism, and more. Currently preparing the detailed notes... Stay tuned for more information.

[NASA's Johnson Space Center @NASAJohnson]

The @Axiom_Space Mission 4 (Ax-4) crew has completed their @NASA training ahead of their mission to the @Space_Station! In Houston, the crew’s training teams celebrated this milestone with a mission plaque hanging and cake cutting ceremony – a NASA tradition. 💫

[Niko McCarty. @NikoMcCarty]

Indian gov't is buying a subscription to 13,000 academic journals, and then making them all available to "18 million students, faculty, and researchers" for free.

The cost is $715 million over 3 years. It includes Elsevier, Nature, and AAAS.

Have any other countries done this?

[Narendra Modi @narendramodi]

It’s a matter of immense joy and pride that India has come 4th in its best-ever performance in the International Maths Olympiad. Our contingent has brought home 4 Golds and one Silver Medal. This feat will inspire several other youngsters and help make mathematics even more popular.

[Edward Frenkel @edfrenkel]

It's been a long time coming... and here it is. Thank you, @BradyHaran! If you are curious about the Langlands Program, this is your portal:
https://t.co/TRyJ22Q3Fv