MATHEMATICAL LINKS :
Quizzes in basic UG and PG mathematics (mainly created by Terrence Tao).
Suggested readings for students in Probability (written by Manjunath Krishnapur ).
A site with a collection of Open Problems
Problems and Riddles in Analysis, Probability and Theoretical Computer Science.
Some links for online notes 1 , 2
Tricki - 'a Wiki-style site that is intended to develop into a large store of useful mathematical problem-solving techniques'.
For papers in mathematical journals : mathscinet
For mathematical dicussions and questions : mathoverflow
On history of Mathematics : http://www-history.mcs.st-andrews.ac.uk/
An online mathematics encyclopedia : mathworld
Online courses in mathematics in india : NPTEL
open courseware of MIT, USA : OCW# For pre-prints on various subjects : http://www.arxiv.org
Online Courses with certificates : Coursera
ADVICE ON TALKS, WRITING, MATHEMATICS ET AL.
Ten Lessons I wish I had been taught – Gian Carlo Rota. An educative read.
How to write Mathematics - Paul Halmos. Hear it from the horse's mouth.
How to talk Mathematics - Paul Halmos.
How to give a good colloqium - John E. McCarthy
Do not remain nameless to yourself - R. Feynman on solving trivial problems.
What to know before starting Grad school.
Advice for Probability graduate students (by Carl Mueller)
What's a mathematician to do ? An existential question that troubles the best of minds at various times.
Speaking and Listening - A Univ. Michigan resource page for talks.
POPULAR ARTICLES :
On A. N. Kolmogorov - by K. R. Parthasarathy
Numberplay - An interesting NY Times blog on Math puzzles.
Me, Myself and Math - A six-part series in NY Times by Steve Strogatz that looks us through the lens of maths.
A Popular Math Blog on NY Times by Steve Strogatz.
Lifelong debunker takes on arbiter of neutral choices. An interesting article on an interesting mathematician.
Within every Math problem, For this Mathematician lurks a card-shuffling problem Another article on the same interersting mathematician.
The magical mind of Persi Diaconis.
In shuffling, 7 is a winning number.More on card-shuffling and its mathematical side.
India in the world of Mathematics by M.S. Raghunathan.
The coming of age of Mathematics in India. by Raghavan Narasimhan.
Mathematics in ancient India - J. L. Nehru
Understanding Ancient Indian Mathematics - S. G. Dani. A crisp and clear introduction.
The Mathematics of election forecasting - R. L. Karandikar.
Dangerous Knowledge - A BBC documentary on the lives of four of the finest scientists - Cantor, Boltzmann,Godel,Turing - who ended their own lives.
The legacy of Srinivasa Ramanujan - M. Ram Murty and V. Kumar Murty.
The Singular Mind of Terry Tao - A wonderful article on Tao and mathematical research.
Will Computers Redefine the Roots of Math? - On Voevodsky and proof automation.
The impenetrable proof : Shinichi Mochizuki and the impenetrable proof of the abc conjecture.
Bayesian principles and neuroscience
The fun is in the struggle with a problem that resists. - Interview with Syliva Serfaty.
A path less taken to the peak of the math world. On the unusual path of Huh to Rota's conjecture.
On surprising usefulness of basic science research.
On Ayurveda, nobel prize and false-pursuits of glory.
A bird's eye-view of hyperuniformity - On mathematics behind patterns found in nature.
On Donna Strickland, Alison Haracourt
Sealing backdoor entry to breaking RSA : How the recent results on 'virtually' all higher-degree polynomials of a certain type being prime makes it harder to break RSA encryption.
A conversation with Venki Ramakrishnan.
A Math teacher's life summed up by the gifted students he mentored.
Sphere packing in 8 and 24 dimensions
An interview with Gagandeep Kang.
Karen Uhlenbeck on gender politics of mathematics.
Interview with V. S. Varadarajan
Interview with K. R. Parthasarathy
Interviews with Statisticians and Probabilists.
Random search wired into Animals
Autoiographical sketch of Talagrand
Autobiographical sketch , Interview of Kallenberg and questions by colleagues.
Quasi-crystal not quasi-scientist - Dan Shechtman on his nobel-prize winning discovery.
Interview with David Aldous
HISTORY & RELATED :
The Lost Cafe : Gian Carlo Rota. A Beautiful article on Stanislaw Ulam and cafe mathematics in the Europe of pre-WW2.
Birds and Frogs of Mathematics – Dyson Freedman. My favourite is the part on the historical tendency of England to lean towards experimental sciences and France towards abstract sciences
The origins and legacy of Kolmogorov's Grundbegriffe - G Shafer & V. Vovok. The intricate development of axiomatic foundations of probability from measure theory.
Hyderabad Intelligencer Published by Springer for ICM 2010 with articles on ICM, Indian mathematics and Hyderabad. A very good introduction to ICMs and Indian Mathematics.
The beginning of the Monte Carlo method – N. Metropolis.
Metropolis, Monte Carlo and Maniac. More on Metropolis and Monte Carlo
Indian Mathematics : Redressing the Balance - Ian G Pearce.
My friendship with Ramanujan in England - P. C. Mahalanobis.
The Quest to Solve the Hardest Math Problem in History (and the Minds that were Lost Along the Way). On Poincare' Conjecture.
My life with the physics dream team - Freeman Dyson on working with the greatest physicists of the 20th century.
Interview with C. R. Rao on his life and work.
The strange topology that is reshaping physics.
The forgotten life of Einstein's first wife.
Ten breakthroughs that made India proud.
When did modern science emerge in India ?
William Feller - by Gian-Carlo Rota.
Probability theory, Gambling and Mahabharata
Har Gobind Khorana and other scientists from Lahore
OTHERS :
Benford's Law and the Decreasing Reliability of Accounting Data for US Firms An interesting Mathematical law and its consequences for accounting.
Benford's Law and some Testing of Benford's Law
The Secret of the Fibonacci sequence in Trees. An article by a teenager on designing optimal solar panels.
A Report on Citation Statistics - Here is a report explaining why you should retain a healthy level of skepticism when it comes to evaluation methods based on journal impact factors, individual citation counts, h-factors and related creatures.
Rise of the Machines - L. Wasserman (on Machine learning and statistics - The introduction and the conclusion are worth reading even if not the technical details in between).
The moving Sofa problem. What is the largest sofa that can be moved across a L-shaped hallway of unit width ?
AMS Posters on Role of Mathematics
A visual introduction to probability and statistics
Combinatorial and other Mathematical Problems
A Mathematician's Lament - Paul Lockhart. An essay on pedagogy and philosophy of Mathematics. Highly recommended.
Abel prize Interview of Yves Meyer A fascinating interview touching upon his work in number theory, harmonic analysis, wavelets, Navier-Stokes and their connections to quasi-crystals, signal processing and gravitational waves.
Probability on Medium - Some interesting articles explaining concepts in probability, statistics and data science.
Cantor's paradise - A website with numerous popular math articles.
BOOKS :
Mathematics : A Very Short Introduction. - Timothy Gowers.
A Beautiful Mind - Sylvia Nasar.
Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem - Simon Singh.
Indiscrete Thoughts - Gian-Carlo Rota.
Surely, you can't be joking Mr. Feynman. - Richard Feynman.
Six Easy Pieces - Richard Feynman.
The improbability principle - David Hand ( on why incredibly unlikely things keep happening).
A short history of nearly everything - Bill Bryson. One of the best popular science books that I have read. Entertaining and Informative.
SOME MATHEMATICAL BLOGS / WEBSITES :
Bhavana - An Indian mathematics magazine.
Quanta Magazine : Cannot recommend this enough. A magazine by Simon's foundation reporting developments in mathematics, theoretical physics, theoretical computer science and the basic life sciences.
Nautilus - Another magazine with some good science related articles.
Gower's weblog - A blog of the mathematician Timothy Gowers.
What's new - A blog of mathematician Terence Tao.
And a non-blog by David Aldous
Djalil Chafai's blog.
A blog on probability and statistics
Institute of Mathematical Statistics - Has useful information on probability and statistics conferences, interesting articles and free membership for graduate students.