Renaissance Technologies, a specialized hedge fund company based in East Seatauket, N.Y., is home to two of the biggest political donors in the 2012 elections — and they are on opposite sides.

James H. Simons, a theoretical mathematician who founded the $15 billion firm, has given at least $7.5 million to a variety of groups backing President Obama and other Democrats.

Renaissance co-chief executive Robert L. Mercer, meanwhile, has given more than $3.5 million to super PACs supporting Republicans and also has helped raise money for presidential nominee Mitt Romney.

The dueling donations at Renaissance provide a striking contrast to the broader finance and banking industry, which has largely rallied around Romney, a former private-equity manager who espouses lower regulations and taxes for Wall Street.

Romney has collected three times as much money from the finance, insurance and real estate sector as Obama, according to data from the Center for Responsive Politics. Mercer, hedge fund manager Paul Singer and other financiers have been among the top donors to conservative super PACs backing Romney and other Republicans.

Simons, with an estimated net worth of $11 billion, is known as the “Quant King” for pioneering the use of quantitative computer models to execute high-speed trading in securities markets. He has given $3.5 million to the pro-Obama Priorities USA Action super PAC; $3 million to Majority PAC helping Democrats in the Senate; and $1 million to House Majority PAC, which is spending to aid House Democrats.

The tally puts Simons just behind media executive Fred Eychaner as the biggest single Democratic donor to super PACs, which can collect unlimited checks from individuals and corporations, contribution data show.

But Republican mega-donors far surpass the other side, led by Las Vegas casino magnate Sheldon Adelson, whose family has funneled more than $36 million to GOP groups.

Mercer has given his money to an array of Republican groups, including $1 million each to the pro-Romney Restore Our Future super PAC and the Karl Rove-backed American Crossroads group.

Mercer also has given $240,000 to the Republican Super PAC, which so far has spent all of its money on ads opposing Rep. Peter A. DeFazio (D-Ore.), Federal Election Commission records show. Mercer gave money to a different super PAC in 2010 in an attempt to unseat DeFazio, who has proposed a financial transactions tax disliked by many Wall Street traders.

Both Simons and Mercer are press-shy and have largely stayed out of public view during the 2012 campaign season. Jonathan Gasthalter, a spokesman for Renaissance Technologies, said neither the firm nor the two executives would comment on the contributions.

The latest financial disclosures from the liberal Priorities USA Action super PAC contained one particularly surprising contribution: $300,000 from Samuel Rawlings Walton, grandson of the famously conservative founder of Wal-Mart.

The Sept. 10 gift stands in contrast to several other 2012 donations from Walton clan members, who have spent big in favor of conservative and Republican causes for years. An uncle and two aunts, for example, gave five- and six-figure donations to super PACs backing Republican nominee Mitt Romney and one of his GOP challengers, Jon Hunstman Jr.

One of the aunts, Alice Walton, was even more active in Republican politics in years past, doling out $2.6 million in 2004 to an independent group that ran ads in support of incumbent George W. Bush.

Sam Walton, 44 — grandson of the retail chain’s founder of the same name and son of chairman S. Robson Walton — has long leaned left compared with the rest of his family, sitting on the board of the Environmental Defense Fund and donating $30,000 to Obama’s campaign in 2008. (A family foundation also doles out healthy sums to environmental causes.)

But the $300,000 contribution marks a significant increase in Walton’s involvement and will help pay for anti-Romney ads aired by Priorities in key swing states over the final days of the campaign.

This isn’t the first wealthy family to show public disagreement over politics this year. TD Ameritrade founder and Chicago Cubs co-owner Joe Ricketts has spent more than $12 million on efforts to defeat Democrats this cycle; he was offered (and rejected) a proposal to run racially charged ads against Obama. His daughter Laura, meanwhile, is a top Obama bundler and prominent LGBT activist. Chicago’s wealthy Crown family is also divided between active Obama and Romney fundraisers, records show.