Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student
http://www.ams.org/profession/prizes-awards/pabrowse?purl=morgan-prize
Click the PDFs in link above to see the biographical sketches of the winners. The biographical sketches are quite informative if you are curious what the path looks like for of someone who goes on to do research in math. These are obviously highly gifted young mathematicians, yet the experiences they had in high school and undergraduate reflect what preparation for life as a research mathematician looks like.
First is winner. Next are honorable mentions, if any, that year. No info for 200 and 2001.
American Mathematical Society Morgan Award
2016 MIT, Harvard
2015 Harvard, Harvard
2014 Harvard
2013 MIT, Harvey Mudd
2012 Princeton, University of Chicago, Stanford
2011 MIT, Harvard, MIT
2010 Harvard, MIT
2009 Princeton, Princeton
2008 Princeton
2007 MIT
2006 MIT
2005 MIT, CalTech
2004 Duke, Univ of Waterloo
2003 Harvey Mudd
2002 Harvard, Harvard
1999 Indiana University, Harvey Mudd
1998 Washington University, Harvard
1996 Harvard
1995 University of Michigan, Harvard