Any surviving contemporary manuscripts by ancient mathematicians? As I understand it, most of what we know about ancient mathematics comes from copies, quotations, and summaries by later scribes and scholars.  Medieval Arab mathematicians in particular are given much credit for preserving the Greek classics:

In a general way it may be said that the Golden Age of Arabian
  mathematics was confined largely to the 9th and 10th centuries; that
  the world owes a great debt to Arab scholars for preserving and
  transmitting to posterity the classics of Greek mathematics; and that
  their work was chiefly that of transmission…  (David E. Smith,
  History of Mathematics, 1958)

Given that so many of the ancient texts appear to be lost (even in reproduction), I am curious about which original texts by known authors have actually survived.  And by "original texts", I mean the physical manuscripts that were dictated or handwritten by the authors themselves, or at least believed to be copied during their lifetimes rather than years or centuries later.
The earliest mathematical texts I know of don't fit these criteria.  For example, the Rhind Papyrus (from perhaps 2000 BCE) is itself a copy of a much older work, and while the scribe's name is known, he was not the author.  I'm not sure what the oldest surviving copy of the Zhou Bi Suan Jing (perhaps 1046 BCE) is, but in any case the identity of the author is unknown.
Do contemporary manuscripts exist for any named ancient mathematicians?  For example, do we have any autographs of Archimedes, Euclid, Diophantus, or Pappus, or copies that were produced during their respective lifetimes?
 A: I think that there are none.
Some data.
For Euclid, see: 


*

*Thomas Heath (editor), The Thirteen Books of Euclid's Elements. Volume 1 (1908, also Dover reprint), page 46-on, lists the Ms used for the modern edition of Euclid's Elements :



The MSS. used for Heiberg's edition of the Elements are the following:
(1) P = Vatican MS. numbered 190,4to, in two volumes (doubtless one originally); 10th century.
(2) F = MS.XXVIII, 3, in the Laurentian Library at Florence, 4to; 10th century.
(3) B = Bodleian MS., D'Orville X. I inf. 2, 30, 4te; A.D. 888.

and so on for MSS. of 11th and 12th centuries.
Also some extant fragments have been found on ancient papyri:

  
*
  
*Papyrus Herculanensis No. 1061 [the oldest of all sources].
  
*The Oxyrhynchus Papyri I. p. 58, No. XXIX. of the 3rd or 4th century.

For Archimedes, see:


*

*Thomas Heath (editor), The Works of Archimedes (1897, also Dover reprint), page xxiii:



The MSS. of the best class all had a common origin in a MS. which, so far as is known, is no longer extant. It is described in one of the copies made from it (to be mentioned later and dating from some time between A.D. 1499 and 1531) as 'most ancient', and all the evidence goes to show that it was written as early as the 9th or 10th century. At one time it was in the possession of George Valla, who taught at Venice between the years 1486 and 1499.
The three most important MSS. extant are:
F (= Codex Florentinus bibliothecae Laurentianae Mediceae
  plutei xxvm. 4to.) [copied from Valla's MS. in 1491 or soon after].
B (= Codex Parisinus 2360, olim Mediceus) [copied from the Valla MS.]
C (= Codex Parisinus 2361, Fouteblandensis) [written by one Christophorus Auverus at Rome in 1544].

The recently discovered  ancient Archimedes Palimpsest is a 10th-century Byzantine copy of an otherwise unknown work of Archimedes.
A: I know that this might be disappointing, but in general it's utopistic to hope having the original handwritten work of an author who lived before the XIV century. This for multiple reason (one being -among other things- that even if you could state that the document was of the age of the author, it could be impossible to prove that the one who wrote was effectively the mathematical author of the work).
Actually what the History of Science is concern about is to reconstruct the "Archetype" of the manuscript, which means to reconstruct how the original copy should have been, just looking at the copies we have. Notice that this process is conceivable in History of Mathematics only because generally there have been really little copies of manuscripts and made by persons who generally didn't understand much of what they were copying. So that alterations are few and simple and it is quite easy to understand who copied from who. In others sector like philosophy or others is generally impossible to even hope reaching something near an archetype of a text.
A clear example is Archimidean texts which arrived if I rember correctly in 4 copies in Europe, one being the Codex C which was discovered quite recently and which is quite different from the other three sources.
So to answer to your question, maybe you should ask which are the work of ancient mathematicians that we have in a form that is near to the original form.
A: The oldest Latin manuscript I know of involving mathematics is the Codex Arcerianus, a treatise on surveying and civil engineering. Some of the writings in this complex collection are probably original and date to the 6th century AD.
The oldest Greek manuscripts are extremely fragmentary and tend to be elementary calculations, not advanced mathematics. Perhaps the most interesting is a single page of papyrus known as PSI VII 763 which is from an elementary manual on arithmetic.
There are hundreds of Babylonian and Sumerian clay tablets with mathematical content, many of which have not even been analyzed. One of the better known of these is is British Museum tablet #40054 which computes the position of Juppiter in the night sky and appears to be a relatively sophisticated integration and may be as old as 300 BC.
