The Van Allen family hails back to the Netherlands. They were early settlers in New York, and were known for fur hunting and trading.
Biographies for James A. Van Allen are available online, as they often are for those who have achievements, so I learned through reading them that he was born in 1914 to parents Alma Olney and James Alfred Van Allen.
I found through tracking through the census that his father's parents were George Van Allen of Pillar Point, Jefferson County, married to Jennie Wright, and that George Van Allen's parents in turn are Cornelius Van Allen and Lory Ackerman, she of Saratoga County. Cornelius in turn has parents Cornelius Van Allen, born 1803 in Montgomery County, New York, and Catherine Martin, all eventually from northern New York where Van Allen families do seem to center in those early years. The feeling of finding one of these people, famous, or just related to us, is quite indescribably tremendous. If you do not have access to ancestry.com, try familysearch.org--it is free and will provide most census images.
It is possible to research a bit father back, and to follow the Ackerman line as well, but you get the picture. The most interesting part was seeing the family origins, and then reading about the amazing accomplishments of the man I started looking at, James A. Van Allen, for whom the Van Allen Radiation Belts in the atmosphere are named.