Mathematics is beautiful and there is no place of ugly mathematics in this world. Mathematics is originated from creativity and it develops with research papers. Research Papers aren’t only very detailed and tough to understand for a general student, but also interesting. Here, I have collected the list of some excellent articles and research papers (belong mainly to Math) which I have read and are easily available online. The main source of this list is ArXiv.org.
If you know any other paper/article which you find extremely interesting and that is not listed here, then please do comment mentioning the article name and URL. Papers/articles are cited as papertitle first, then http url and at last authorname.

The Two Cultures of Mathematics
http://www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf
Timothy Gowers 
What is Good Mathematics?
http://arxiv.org/abs/math.HO/0702396
Terence Tao 
Career Advice (A Collection of Some very good advices) http://terrytao.wordpress.com/careeradvice/
Terence Tao 
For Potential Students
http://math.stanford.edu/~vakil/potentialstudents.html
Ravi Vakil 
Advice to a Young Mathematician
http://press.princeton.edu/chapters/gowers/gowers_VIII_6.pdf Princeton Companion to Mathematics 
Ten Signs a claimed Mathematical Breakthrough is wrong http://www.scottaaronson.com/blog/?p=304
Scott Aaronson 
On Proof and Progress in Mathematics
http://arxiv.org/abs/math.HO/9404236
William Thurston 
A Mathematician’s Lament
http://www.maa.org/devlin/LockhartsLament.pdf
Paul Lockhart 
Truth as value of duty: Lessons of Mathematics http://arxiv.org/abs/0805.4057
Yuri I Mannin 
Mathematical Knowledge: Internal Social And Agricultural Aspects http://arxiv.org/abs/math/0703427
Yuri I Mannin 
The Cult of Genius
http://blogs.discovermagazine.com/cosmicvariance/2007/02/25/thecultofgenius/
Julianne Dalcanton 
Take it to the Limit
http://opinionator.blogs.nytimes.com/2010/04/04/takeittothelimit/
Opinionator on New York Times 
How to Supervise a Ph.D.
http://ppss.ph.unimelb.edu.au/2520/node33.html 
Essential Steps of Problem Solving
http://gauravtiwari.org/essentialsteps/
Gaurav Tiwari 
On the Electrodynamics of Moving Bodies
http://www.fermilab.ch/etexts/einstein/specrel/www/
Albert Einstein 
Who can name the Bigger Number?
http://www.scottaaronson.com/writings/bignumbers.html
Scott Aaronson 
Division by Three
http://arxiv.org/abs/math/0605779v1
Doyle and Conway 
Birds and Frogs
http://www.ams.org/notices/200902/rtx090200212p.pdf
Freeman Dyson 
A Mathematical Theory of Communication
http://cm.belllabs.com/cm/ms/what/shannonday/paper.html
Shannon Day 
Missed Opportunities
http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.bams/1183533964&page=record Freeman Dyson 
The Unreasonable Effectiveness of Mathematics in the Natural Sciences http://www.ipod.org.uk/reality/reality_wigner.pdf
Eugene Wigner  On Computable Numbers with an Application to the Entscheidungsproblem http://www.thocp.net/biographies/papers/turing_oncomputablenumbers_1936.pdf Alan Turing

Funny Problems
http://arxiv.org/abs/math/0010133v1
Florentin Smarandache  Life and Work of the Mathemagician Srinivasa Ramanujan

http://arxiv.org/abs/math/0003184v1
K Srinivasa Rao 
Why Everyone Should Know Number Theory?
http://arxiv.org/abs/math/0210327v1
Minhyong Kim 
Meta Math! The Quest for Omega
http://arxiv.org/abs/math/0404335v7
G J Chaitin 
Vedic Mathematics
http://arxiv.org/pdf/math/math.GM/0611347
W B Vasantha Kandasamy & Florentin Smarandache 
On Multiple Choice Questions in Mathematics
http://terrytao.wordpress.com/2008/12/14/onmultiplechoicequestionsinmathematics/ Terence Tao 
The Fear and The Use Of Mathematics and Physics http://gauravtiwari.org/thefear/
Dr. Bikram Phookun 
Ramnujan Type 1/pi Approximation Formulas
http://arxiv.org/abs/1111.3139v1
Nikos Bagis 
Collatz’s 3x+1 Problem and iterative maps on Interval http://arxiv.org/abs/math/0608708
Wang Liang 
Proof of Riemann Hypothesis
http://arxiv.org/abs/0706.1929
Jinzhu Han 
Solving Polynomial Equations from Complex Numbers http://arxiv.org/abs/1112.5331v2
Ricardo S Vieira 
Age of Einstein
http://www.physicsforfree.com/ageofeinstein.pdf
Frank WK Firk 
The Mysteries of Counting
http://math.ucr.edu/home/baez/counting
John Baez 
Generalisation of Ramanujan Method of Approximating Root of an Equation http://arxiv.org/abs/1112.5092v1
R K Muthumalai 
How to Gamble if You are in Hurry?
http://arxiv.org/abs/1112.1645v1
Ekhad, Georgiadis & Zeilberger 
How to Survive a math class?
http://www.math.clemson.edu/~mjs/courses/misc/study.pdf
Matthew Saltzman & Marie Coffin 
Is life Improbable?
http://math.ucr.edu/home/baez/improbable.pdf
John Baez 
Remarks on Expository Writing in Mathematics http://www.math.uiuc.edu/~rash/Remarks.pdf
Robert B Ash 
Success in Mathematics
http://mathcs.slu.edu/undergradmath/SuccessinMath.pdf
Saint Louis University
Interesting to see your name just above Albert Einstein
Eww!! I didn’t notice that. 😉
All the contents you mentioned in post is too good and can be very useful. I will keep it in mind, thanks for sharing the information
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Not that I am seeing this kind of list for the first time. In fact, I myself have prepared an (unpublished) list of such articles and (published) list of mathematical resources/websites.
But it is heartening to have stumbled upon on your page. I actually found out that many of the link listed above were unknown to me. I have bookmarked your page hoping that you would keep this list updated.
Cheers.