Firoozbakht's conjecture, BDS conjecture & deep learning, Lie Groups, Statistical Riemannian Framework, Ramanujan Machine..

Hey Readers,

It's 4:30 AM Saturday night. And I am at it again. A blog I restarted which I used to write 12 years back to motivate new thinking in data, math and AI. The paper I like the most these days is Job Postings and Aggregate Stock Returns - https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3223141

1. If I ever write my next book, there will be special mention of Iranian mathematician Farideh Firoozbakht - almost an unsung hero of math - She studied pharmacology and later mathematics at the University of Isfahan, and later taught mathematics at that university (Talk about reinventing the career). 

Extremely famous for her Firoozbakht's conjecture (pattern in prime numbers in simple words) which was stated in 1982 - this conjecture achieved some fame 

- in 2011 when I wrote about it along with new orchestrations on dynamical systems (Naive Entropy, Nash Entropy etc), 

- also on Maryam Mirzakhani's work on topology, geometry and dynamical systems (specially her work on Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces - https://www.math.stonybrook.edu/~mlyubich/Archive/Geometry/Teichmuller%20Space/Mirz3.pdf And when I also wrote about possibility of GeoDesic Convolutional Neural Networks - Geodesic CNNs & 

- & on Laura De Marco's work on dynamical systems my datahulk blog & 

in 2015 when Alexei Kourbatov published a paper on it in International Mathematical Forum 10 (2015), 283–288. Verification of the Firoozbakht conjecture for primes up to four quintillion, (unproven till now and has a very strong affiliation with Riemann Hypothesis).

I have a very strong viewpoint that Andrica's conjecture & Firoozbakht's conjecture and how looking at prime numbers as a dynamical system can have a smarter way to solve this. I also have a way to look at it further in terms of How To use GANs - Generative Adversarial Networks (with optimum convergence while leveraging Nash entropy) to solve PDEs in Dynamical & Chaotic systems generated through prime numbers. Anyway, more to come later... some surprises in store along with my Ricci Flow Video..  

Firoozbakht passed away in 2019 without many people knowing it... Almost an unsung hero who could have been celebrated everywhere. I always found it bit disappointing that Terence Tao mentioned Cramér conjecture in his blog but not Firoozbakht's conjecture. But, hey, everyone makes their own choice (that's why Thaler's choice architecture right??? right????) 

2. Another person who is doing some cool work is Nina Miolane - Amazing work on Statistics on Lie groups (& abelian groups): A need to go beyond the pseudo-Riemannian framework - https://aip.scitation.org/doi/abs/10.1063/1.4905963

Again, I want to highlight 1984 paper by Sir Atiyah, TIFR and Sir Atiyah's Student George Lusztig and his work on Quantum Groups. I know Nina's GeomStats is focus on Biomedical Topology but there is one more way to grow GeomStats in topology

i.e. growing GeomStats like Ramanujan Machine where AI would solve complex group theory problems trained on Lusztig's group theory paper including lie groups, abelian groups, Weyl groups, Chevalley groups, semisimple p-adic groups, quantum groups etc..

Btw, The first suggestion I gave to Ramanujan Machine when I became their advisor was this paper on BDS conjecture & deep learning by Laura Alessandretti - Machine Learning meets Number Theory: The Data Science of Birch-Swinnerton-Dyer - https://arxiv.org/abs/1911.02008