Anthropologist usually do not share their research online. But mathematicians do. In fact open access is an important goal of the International Mathematical Union:
Endorsed by the IMU Executive Committee on May 15, 2001 in its 68th's session in Princeton, NJ.
Open access to the mathematical literature is an important goal. Each of us can contribute to that goal by making available electronically as much of our own work as feasible.
Our recent work is likely already in computer readable form and should be made available variously in TeX source, dvi, pdf (Adobe Acrobat), or PostScript form. Publications from the pre-TeX era can be scanned and/or digitally photographed. Retyping in TeX is not as unthinkable as first appears.
Our action will have greatly enlarged the reservoir of freely available primary mathematical material, particularly helping scientists working without adequate library access.
If you search for the "top mathematical journals" you will get that those journals are fully available online -- field medalists have published their work in most of these journals:
Not all of the math journals are open access but most of them are - even when commercial publishers like Springer manage the business. In fact, mathematicians use open access as a tool to attract the attention of their peers, which makes their research more robust and productive.
I wonder why some scientist such as anthropologist are so closed, and others, like mathematicians and economist are so open in this regard? This can partially explain the dynamism of some fields versus others.
I will post more on this debate.