The readings tickled Koch’s fondness for principles and order, and they steered him deep into a structured, almost numeric, view of how human society functions. But none of them shaped Koch, in his rise to personal fortune and political fame, as much as a 10-page tract from a relatively obscure British scientist named Michael Polanyi.

Polanyi’s “The Republic of Science: Its Political and Economic Theory,” published in 1962, is the text that best illustrates what Koch is trying to do with his massive personal fortune — and the contradictions and controversies that come with it.

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That paper argues that science should function like an economic market, with research dollars flowing to the very best scholars and ideas, as determined by scientific consensus. It has guided Koch’s effort to donate more than $200 million to colleges and universities, an effort that he plans to accelerate in the coming years and that will continue to shape academic research and student learning long after the effects of his political giving have faded.

It also raises the question of whether Koch has become, for university researchers, the sort of distorting force that Polanyi warns against.

Koch’s donations have fueled the expansion of a branch of economic research that aligns closely with his personal beliefs of how markets work best: with strong personal freedom and limited government intervention.

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They have seeded research centers, professors and graduate students devoted to the study of free enterprise, who often provide the intellectual foundation for legislation seeking to reduce regulations and taxes.

Long dwarfed by his prodigious support for conservative candidates, Koch’s academic giving has now landed him at the center of a white-hot debate over freedom and speech on campus.

His critics accuse Koch, 80, of corrupting the academy with his money, pushing students and faculty to embrace a small-government philosophy that they say benefits Koch financially.

Few charges rile Koch more than that. “The opposite is true,” he said recently, in a 100-minute interview in his offices here in Wichita. “They’re the ones campaigning to un-Koch our campuses and stuff. We’re not saying, ‘Un-Marxist our campuses.’ Fine, bring it all on. Let a hundred flowers bloom. We love it. That’s what we want.”

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Critics say Koch’s public embrace of academic freedom clashes with the practical effects of his donations. By accepting Koch’s money as offered, “What we sell, as an academy, is our credibility,” said Mohamed El-Hodiri, an economist at the University of Kansas who has criticized the Koch-funded research center in the university’s business school.

Koch laughed and smiled throughout the interview, but he bristled, momentarily, when pushed on the question of whether the research he funds helps him make more money.

“He views himself as taking a principled stand against government assistance to business, in a lot of ways,” said Tyler Cowen, an economist and blogger at George Mason University’s Mercatus Center, who has received grants and other financial assistance from Koch dating to his undergraduate studies. “And I think he is not perceived as having done that. He’s viewed as a crony capitalist, when he’s this opponent of crony capitalism. And I think that’s what bothers him.”

A Republic of Science

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In his youth Koch blew through eight schools, one of which kicked him out. He said he never felt good at anything until a third-grade teacher sketched math problems on a chalkboard and he realized he was the only student in class who could solve them. He would carry that facility to MIT and then the business world.

Koch left his consulting job in the 1960s, took over his father’s company, Koch Industries, and helped build a fortune for himself and his brothers. Sometime that decade he discovered Polanyi’s paper, which contends that “any authority which would undertake to direct the work of the scientist centrally” — even in the pursuit of a “public interest” — “would bring the progress of science virtually to a standstill.”

In the interview in his office tower, the longest and most detailed one he has granted to discuss his academic donations, Koch used the phrase “Republic of Science” at least 23 times.

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He also professed several beliefs that might surprise his critics. He expressed concern over middle-class stagnation and widening income inequality, which he said reflects rich people benefiting from government favoritism. He criticized business leaders, whom he cast as more interested in protecting profits than promoting competitive markets, and said the nation must cut back on “entitlements for the wealthy” before it considers any serious changes to Social Security or Medicare.

He said students should study Marx, and that he would be open to funding Marxist research, although there are no apparent examples of him doing so.

Koch has built, with his brother David, a network of conservative nonprofit groups that has set a goal of raising and spending $900 million during this election cycle. Their previous spending has helped to put Republicans in control of Congress, along with statehouses and governors’ mansions across the country, and has led Democrats to accuse the Kochs of buying elections.

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Only in recent years have Charles Koch’s charitable contributions begun to attract similar scrutiny — along with an organized opposition at many universities, from professors, liberal political groups and an organization known as UnKochMyCampus.

“We really see higher education as the first cog in their political machine,” said Kalin Jordan, a co-founder of UnKochMyCampus. “They see themselves as creating the next generation [of libertarian thinkers] and in creating a next generation, they’re really pushing out any other thought on campus. They’re not interested in creating diversity of thoughts.”

Even Koch’s aides cannot say for certain how much money he has given to colleges, think tanks and other academic researchers dating to the late 1960s. They peg the total at $200 million, at least, from 1980 forward.

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From 2012 through 2014 alone, his charitable arm, the Charles Koch Foundation, donated $64 million to university programs. A tax filing from 2013 lists more than 250 schools, departments or programs that received grants from the foundation, in amounts that ranged from a few thousand dollars to more than $10 million at George Mason University in Virginia Fairfax, Va. Recipients include obscure liberal arts colleges, flagship state universities and members of the Ivy League.

Some donations flow to research hubs within an institution, such as Mercatus at George Mason and the Ed Snider Center for Enterprise and Markets at the University of Maryland, which ground their research in the belief that economic freedom — and less government intervention — is the key to increased prosperity. Some support faculty positions at schools such as Clemson University and Florida State University, which have long specialized in that same sort of research.

Where the money goes

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Koch no longer personally reviews those applications — his foundation staff does. “Charles is engaged at a very, very, very high level” in who gets funding, said John Hardin, the Koch Foundation’s director of university relations.

Koch, though, has articulated a set of principles to determine who gets his money. He has prized researchers whose values, as he calls them, are rooted in an economic philosophy that aligns with his— the belief that economic and personal freedoms produce the fastest advancements in human well-being.

“What we look at is okay, first of all, does the person who requests support, do they have good values?” he said. “Do they have integrity? Do they have courage? Do they have courage to stick with whatever they believe and be committed to trying to find the truth of the matter rather than shade the evidence?”

In interviews with Koch and his staffers, and in audio recordings from gatherings of university officials who receive Koch money, a picture emerges of how a particular type of institution, driven by questions of how best to unleash free enterprise, has evolved to capture Koch’s grants.

“I was doing this research, and I had this vision and mission” before the Koch Foundation offered money, said Rajshree Agarwal, who directs the Snider Center at Maryland, which opened in 2014 and fits the mold of a Koch-funded free-enterprise center. “They don’t micromanage, and I wouldn’t be micromanaged.”

Foundation officials say they fund a majority of the proposals they receive (although they declined to back a researcher who was attempting to build a time machine).

On campus, grants have sparked protests and debates over academic freedom. At Florida State, for example, Koch gave $1.5 million over six years to fund two professorships with a focus in free enterprise. The contract that accompanied the grant allowed for the school to form a committee to consult on the hiring process, which would have included a Koch-affiliated member. Some Florida State faculty members objected.

The committee was never constituted. David Rasmussen, an economics professor and dean who oversaw the grant, says no Koch representatives were consulted on the two professors who were initially hired. One was hired away by Southern Methodist University in Dallas and replaced after three years. The other recently failed to secure tenure.

Tim Salmon was an economics professor at Florida State when the Koch funding was first discussed. He sat on a department hiring committee for the two positions that the foundation eventually underwrote. Salmon said the committee forwarded 40 names of potential candidates to department leaders, and that 25 of them were crossed off the list, because, he was told, those candidates would not be acceptable to the Kochs.

He also said that, at an annual economic conference where the department interviewed candidates, the Koch Foundation conducted its own interviews with the Florida State candidates — without telling the hiring committee it was doing so. Koch Foundation officials say their staffers met with only one such candidate at the conference, and that no one from the foundation ever struck names from a university candidate list.

Salmon, who has since left the school for SMU, said he supported both candidates who were eventually hired.

“The process was horrible, and it was bizarre, and it was something that should never happen at an academic institution,” he said. But, he added, “we actually, through a torturous process, got two very good academics.”

Rasmussen, who recently retired as dean, said the Koch funding allowed Florida State to add faculty positions “without any effect on university decision-making.”

He likens the Koch approach to a donor who tells a university department he would be interested in funding a faculty member to study Beethoven, but not Stravinsky. Hiring a Beethoven scholar doesn’t by itself stop a school from hiring a Stravinsky scholar. But if big dollars are available to study Beethoven, that could entice young scholars, in particular, to focus on his symphonies above all others.

Koch rejects that possibility.

“What does it mean to have too many Beethoven chairs and too few Stravinsky chairs?” he said. “I mean, that’s kind of a value judgment that isn’t really based on humility. We don’t know what the optimum number is, so let people figure this out on their own. People are more interested in Beethoven than Stravinsky? Great! Why would that bother me?”

Influencing policy

None of the largest recipients of Koch dollars appear on a list of the most influential academic economic departments in the United States, as calculated by the research arm of the Federal ­Reserve Bank of St. Louis. Only one professor who works at one of Koch’s most-supported centers cracks a similar list that calculates the top 5 percent of influential economists in the research community.

Koch-funded researchers make a larger impact in the public arena. They frequently testify before Republican-led committees in Congress. Their work often guides lawmakers, particularly conservatives, at the state level in drafting legislation, and they have provided the foundations for judicial opinions that affect the economy on issues such as whether the government should intervene to stop large companies from merging.

Researchers funded in part by Koch helped pave the way for a push in Washington to reduce mandatory minimum sentences for some criminal offenders, and also for efforts to scale back such federal regulations as carbon emissions limits and rules governing the financial sector.

The head of the nation’s foremost group of academic economists does not object to Koch’s support for researchers.

“As long as they don’t censor research, as long as they publish the results honestly, it’s okay to have a biased source” of money, said Robert Shiller, a Nobel Prize-winning economist at Yale University who is the president of the American Economic Association.

“You couldn’t get the government to support (Charles) Darwin, I’m thinking,” Shiller said, because Darwin’s theory of evolution was too controversial. “But somebody believed in him, some smart person, who made money.”

Koch insists he is promoting markets and competition, and not his own profits.

“Are you kidding me?” he says when asked about charges that the research he funds serves to boost Koch Industries’ business interests. “That’s why there’s so much corporate welfare, because they all want a free market? No.” As a counter example, Koch officials cite work they have funded that has criticized government subsidies for ethanol fuel — even though Koch Industries has ethanol holdings.

Cowen, the Mercatus economist, said Koch’s political image might undermine the impact of certain research, if it were linked to his donations.

“It’s probably not a good idea” for Mercatus to publish work on a carbon tax, he said, because of the center’s connection to Koch, who opposes one. Still, Cowen added, “I’ve written things promoting a carbon tax. I don’t get some little note in the mail or someone throwing an egg at my door at night. It’s never been a problem.”

No interference

No researcher interviewed for this article could recall any pressure applied by Koch or his foundation over a research finding. For example: Earlier this year, at the American Economic Association conference in San Francisco, the Mercatus economist Alex Tabarrok presented a paper on the relationship between government regulation and American entrepreneurship. He had expected to find that regulations chill entrepreneurship in highly regulated sectors. Instead, he found that they appear to have no effect at all.

Tabarrok said he never heard any criticism from Koch or his network about the results. Koch said in the interview that he welcomed them: “We’re trying to find the truth.” (A few months later, a separate Mercatus study found that increased regulations hurt economic growth.)

The questions of how government affects the performance of the U.S. economy are widely considered by economists to be important. It is unclear how much of the research into those questions would exist without funding from Koch and other donors who share his general economic philosophy.

It is also hard to say whether the research that is funded by other sources — such as grants from the National Science Foundation, university endowments or donations from other donors, many of whom have liberal political views — is biased toward particular political or economic philosophies, as opposed to simply supporting the “best” research, whatever that might be.

Polanyi wrestles with those issues in “Republic of Science” and eventually warns against any one person or government body playing too large a role in steering a society’s quest for truth.