We have a webpage with links to 1000 internal pages (scientific paper abstracts). Google indexed the site as can be verified by their Webmaster Tools but the site is practically non-visible if you query for terms inside the pages. I read that Googlebot doesn't like to see pages with many links listed but would it make a difference if I split it up by subject so instead of 1K links we have 10 pages linked with 100 links each?
If you want the page to rank and be returned for queries relevant to the scientific papers within it, you will have to change the page structure.
Right now, it's a list of 1000 links. That's a useful resource to Googlebot for discovering all the papers you link to, but not a useful page for human visitors. The New York Times has a similar approach for trying to make their MASSIVE 150-year backlog of content discoverable: http: //spiderbites.nytimes.com/pay_1986/articles_1986_06_00000.html
If you want the link page to rank, you will have to figure out a way to break those 1000 links down into smaller conceptual bundles - let's call them category pages. Each category page needs an introductory paragraph around what's in that bundle, why you think the resources are valuable, how you curated the list, what visitors can expect to learn, etc.
You will then have to figure a way to get more link authority flowing into these pages so they can rank and earn traffic. The easiest way is to move them up in your information architecture, so they're within 1 to 2 clicks of your home page.
A harder (but more beneficial) approach would be to create category pages that are so uniquely valuable that other people would want to link to them, and then proactively reach out to others in your scientific community, asking them to link to these pages from their own sites.
Instead of just showing 1000 links all at once, you could introduce:
a pagination feature - showing between 10 and 30 links per page, e.g. 50 pages of 20 links each, or 20 pages of 50 links each. For example:
|< < Page 3 of 20 > >|
a search box - enabling users to seach for a document using related keywords instead of scrolling through an enormous list.
accompanying content - for each document link, provide a title and short synopsis paragraph, details of author(s), date of publication, number of pages, file size, perhaps an image of the front cover/page etc.
organisation - try to split the links up into topical sub-categories or a hierarchical tree.
smart data - try to use structured data / rich snippets in your HTML - see schema.org for more information about this - perhaps the CreativeWork might be a good place to start.
link text - ensure the text used for your link represents a title for the destination page or document, i.e. try to avoid generic link text such as "Click here", "Open" or "Download".
Essentially, rather than just using the page as a list, try to give it some content of value to the end-user, something to look at, something to read etc so that users could spend a minute or two on that page instead of just being signposted to other pages/documents. To answer your question yes it would make a significant difference.
If your only link to these internal pages in one link each from your home page, the problem is that they don't each get enough Pagerank. Pagerank is a measure of the link juice passed to a page from its inbound links. Your home page only has so much Pagerank and it can only pass a very tiny amount when you divide it up between 1,000 links.
One of the best ways to get a large set of pages to rank is to interlink them. This site has a similar problem: there are thousands of questions, but only a handful can be listed on the home page. Each question here has a set of "Related" question in the right hand column. That allows Googlebot to find all the questions on the site from other questions. It also passes Pagerank around the site very efficiently. Other answers here suggest using tags and categories for organization, but introducing related papers would be more effective.