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 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 and you may find several research papers on ArXiv by visiting http://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 paper-title first, then http url and at last author-name.

[It is better adviced to open these links to a new tab/window for smooth reading. ]

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/career-advice/
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/the-cult-of-genius/
Julianne Dalcanton

Take it to the Limit
http://opinionator.blogs.nytimes.com/2010/04/04/take-it-to-the-limit/
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/essential/
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.bell-labs.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/on-multiple-choice-questions-in-mathematics/ Terence Tao

The Fear and The Use Of Mathematics and Physics http://gauravtiwari.org/the-fear/
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/~r-ash/Remarks.pdf
Robert B Ash

Success in Mathematics
http://mathcs.slu.edu/undergrad-math/SuccessinMath.pdf
Saint Louis University