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Talk about your mansion on a hill.

Several acres in Hastings-on-Hudson are being transformed into a dramatic, $75 million hillside home for the secretive and brilliant billionaire math whiz and hedge-fund titan David E. Shaw, his financial-writer wife, Beth Kobliner, and their three children.

The founder of Manhattan-based D.E. Shaw & Co., and his wife, both Democratic Party donors, have been plotting and tweaking what will be a stunning contemporary house of more than 38,000 square feet on land that overlooks the Hudson River and the Palisades.

According to public records, it took several years of local planning board meetings — where the buyers were never identified — to obtain approvals to demolish five previous estate homes, clearing the way for Shaw’s estate.

Even permits for the house are pricey — town officials say Shaw has ponied up $428,000 just for the paperwork.

The plans reviewed by The Post show a one-and-a-half-story, four-bedroom home with an elevator and a fully finished lower level. The home was designed by Stephen Holl Architects.

Three exercise rooms, a media room, children’s playrooms and even a babysitter room are notated on plans.

When completed, the driveway will end in a 3,179 square-foot underground garage. The basement will include additional bedrooms and multifunction rooms, possibly for staff.

The grounds, planned by Edmund D. Hollander Landscape Architect Design, will include a bluestone-paved 1.5 foot-deep reflecting pool in front.

A separate indoor swimming pool with changing rooms is also noted in the plans — as is a tennis court.

All the buildings will be heated, sources say, by more than 200 geothermal wells.

Ironically, a Tweet just last week by Kobliner stated: “. . . teach kids the value — fiscal and otherwise — of guarding personal info.”