Perhaps not really a paper, but i think a "must-read" is A Mathematician's Lament by Paul Lockhart.

"God exists since mathematics is consistent, and the Devil exists since we cannot prove it."- André Weil

Sir Michael Atiyah. Besides his great technical work (his collected papers are absolutely magnificent!) especially his great interview "Beauty in Mathematics" was very inspiring to me. Another ...

" Last time, I asked: "What does mathematics mean to you?" And some people answered: "The manipulation of numbers, the manipulation of structures." And if I had asked what music means to you, would ...

"Why are numbers beautiful? It's like asking why is Beethoven's Ninth Symphony beautiful. If you don't see why, someone can't tell you. I know numbers are beautiful. If they aren't beautiful, nothing ...

"classic" Title: Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem (US) Fermat's Last Theorem: The story of a riddle that confounded the world's greatest minds for ...

Birds and Frogs by Freeman Dyson, which explains nicely that the world of mathematics is both , broad and deep.

"A mathematician who is not also something of a poet will never be a perfect mathematician"- Karl Weierstraß

The answer is yes!(at least if quaternionic holomorphic geometry counts) "Qauternionic holomorphic geometry" provides a very elegant description of surfaces in 3- and 4-dimensional space. The first ...

“The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colors or the words must fit together in a harmonious way. Beauty is the first test: there is no ...

"The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful." - Henry Poincaré

Jürgen Moser (1965), On the Volume Elements on a Manifold , Transactions of the American Mathematical Society, Vol. 120, No. 2 (Nov., 1965), pp. 286-294 http://www.jstor.org/stable/1994022 Besides ...

"My work always tried to unite the true with the beautiful; but when I had to choose one or the other, I usually chose the beautiful."- Herman Weyl

A simple application is the following: Every sequence of $n^2 +1$ distinct real numbers contains a subsequence of length $n +1$ that is either strictly increasing or strictly decreasing. (Other ...

The answer is no. Take the "classical" example of the line with two origins. This space is non-Hausdorff, paracompact and doesn't admit partitions of unity. EDIT: I think the question is a kind of "...

You might also find the work of Joyce useful, which builds upon the work of Dubuc (E. J. Dubuc. C∞-schemes. Amer. J. Math., 103(4):683–690, 1981) and Moerdijk and Reyes (I. Moerdijk and G. E. Reyes. ...

It seems to me that you could be interested in the following (I haven't checked the paper in detail, but I think theorems of this "style" could be helpful for you): Dieter Kotschick, Orientations ...

I think this "well known fact" was proved first by Borel and Serre, Borel, A., Serre, J. P.: Groupes de Lie et puissances réduites de Steenrod. Amer. J. Math.75, 409–448 (1953) For a more detailed ...

Perhaps you will also find the following interesting: V. Braungardt und D. Kotschick: “The classification of football patterns”, 2006. (for a popular Summary see: D. Kotschick: „The Topology and ...

I think you are searching for the following: An exotic {4}-manifold by Selman Akbulut We construct two compact smooth 4-manifolds $Q_1, Q_2$ which are homeomorphic but not diffeomorphic to each ...

Riemann-Roch in the version I know it: Let $(E,\bar{\partial})$ be a holomorphic bundle over a compact Riemann surface $M$. Then $$\operatorname{index}(\bar{\partial}) = \deg E -(g-1)\operatorname{...

I am not sure whether this answers your question, but you should perahps have a look at Faber, Pandharipande: Relative Maps and Tautological Classes "The push-forwards of all Gromov-Witten ...

"A mathematical truth is neither simple nor complicated in itself, it is." - Émile Lemoine

Perhaps you will also like "Heat kernels and Dirac operators" by Nicole Berline,Ezra Getzler,Michèle Vergne (see the google books link here) Perhaps not the "full" Atiyah-Singer index theorem, but ...

Just to add some things to Igor Belegradek's post: "1.That the isometry group of a Riemannian manifold is always a lie group." This is the famous Myers-Steenrod theorem, proven in 1939 (Myers, S.B. ...

First of all: this is from the "differential-geometric point of view" If you want to "classify" vector bundles chern classes are a very helpful tool. Well, it can happen that two bundles are "...

Since a $\bar{\partial}$-Operator is an elliptic Operator, you can use elliptic theory in order to prove the Serre duality. In fact the Serre duality is a kind of corollary of the"fundamental theorem" ...

(3) Yes, this is exactly the differential bordism groups $D_k(Y)$ of Conner (see §1.9 in P.E. Conner, Differentiable Periodic Maps, second edition, Springer Lecture Notes in Mathematics 738, Springer-...