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 paper-title first, then http url and at last author-name.

1. The Two Cultures of Mathematics
http://www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf
Timothy Gowers
2. What is Good Mathematics?
http://arxiv.org/abs/math.HO/0702396
Terence Tao
Terence Tao
4. For Potential Students
http://math.stanford.edu/~vakil/potentialstudents.html
Ravi Vakil
5. Advice to a Young Mathematician
http://press.princeton.edu/chapters/gowers/gowers_VIII_6.pdf Princeton Companion to Mathematics
6. Ten Signs a claimed Mathematical Breakthrough is wrong http://www.scottaaronson.com/blog/?p=304
Scott Aaronson
7. On Proof and Progress in Mathematics
http://arxiv.org/abs/math.HO/9404236
William Thurston
8. A Mathematician’s Lament
http://www.maa.org/devlin/LockhartsLament.pdf
Paul Lockhart
9. Truth as value of duty: Lessons of Mathematics http://arxiv.org/abs/0805.4057
Yuri I Mannin
10. Mathematical Knowledge: Internal Social And Agricultural Aspects http://arxiv.org/abs/math/0703427
Yuri I Mannin
11. The Cult of Genius
http://blogs.discovermagazine.com/cosmicvariance/2007/02/25/the-cult-of-genius/
Julianne Dalcanton
12. Take it to the Limit
http://opinionator.blogs.nytimes.com/2010/04/04/take-it-to-the-limit/
Opinionator on New York Times
13. How to Supervise a Ph.D.
http://ppss.ph.unimelb.edu.au/2520/node33.html
14. Essential Steps of Problem Solving
https://gauravtiwari.org/essential-steps/
Gaurav Tiwari
15. On the Electrodynamics of Moving Bodies
http://www.fermilab.ch/etexts/einstein/specrel/www/
Albert Einstein
16. Who can name the Bigger Number?
http://www.scottaaronson.com/writings/bignumbers.html
Scott Aaronson
17. Division by Three
http://arxiv.org/abs/math/0605779v1
Doyle and Conway
18. Birds and Frogs
http://www.ams.org/notices/200902/rtx090200212p.pdf
Freeman Dyson
19. A Mathematical Theory of Communication
http://math.harvard.edu/~ctm/home/text/others/shannon/entropy/entropy.pdf
Shannon Day
20. Missed Opportunities
http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.bams/1183533964&page=record Freeman Dyson
21. The Unreasonable Effectiveness of Mathematics in the Natural Sciences
Eugene Wigner
22. On Computable Numbers with an Application to the Entscheidungsproblem http://www.thocp.net/biographies/papers/turing_oncomputablenumbers_1936.pdf Alan Turing
23. Funny Problems
http://arxiv.org/abs/math/0010133v1
Florentin Smarandache
24. Life and Work of the Mathemagician Srinivasa Ramanujan
http://arxiv.org/abs/math/0003184v1
K Srinivasa Rao
25. Why Everyone Should Know Number Theory?
http://arxiv.org/abs/math/0210327v1
Minhyong Kim
26. Meta Math! The Quest for Omega
http://arxiv.org/abs/math/0404335v7
G J Chaitin
27. Vedic Mathematics
http://arxiv.org/pdf/math/math.GM/0611347
W B Vasantha Kandasamy & Florentin Smarandache
28. On Multiple Choice Questions in Mathematics
http://terrytao.wordpress.com/2008/12/14/on-multiple-choice-questions-in-mathematics/ Terence Tao
29. Ramnujan Type 1/pi Approximation Formulas
http://arxiv.org/abs/1111.3139v1
Nikos Bagis
30. Collatz’s 3x+1 Problem and iterative maps on Interval
http://arxiv.org/abs/math/0608708
Wang Liang
31. Proof of Riemann Hypothesis
http://arxiv.org/abs/0706.1929
Jinzhu Han
32. Solving Polynomial Equations from Complex Numbers
http://arxiv.org/abs/1112.5331v2
Ricardo S Vieira
33. Age of Einstein
Frank WK Firk
34. The Mysteries of Counting
http://math.ucr.edu/home/baez/counting
John Baez
35. Generalisation of Ramanujan Method of Approximating Root of an Equation http://arxiv.org/abs/1112.5092v1
R K Muthumalai
36. How to Gamble if You are in Hurry?
http://arxiv.org/abs/1112.1645v1
37. How to Survive a math class?
http://www.math.clemson.edu/~mjs/courses/misc/study.pdf
Matthew Saltzman & Marie Coffin
38. Is life Improbable?
http://math.ucr.edu/home/baez/improbable.pdf
John Baez
39. Remarks on Expository Writing in Mathematics http://www.math.uiuc.edu/~r-ash/Remarks.pdf
Robert B Ash
40. Success in Mathematics
Saint Louis University
41. Teaching and Learning Mathematics
http://www.k12.wa.us/research/pubdocs/pdf/MathBook.pdf
Terry Bergeson
42. Helping your child learn Mathematics
US Department of Education
43. Engaging Students in Meaningful Mathematics Learning: Different Perspectives, Complementary Goals
http://ed-osprey.gsu.edu/ojs/index.php/JUME/article/viewFile/115/58
Michael T. Battista

1. 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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2. Mayank says:

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.

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