Peter Thiel is almost definitely behind this mysterious Heterodox Science course

But the archaic meaning is reflected in, e.g., Knuth's "The Art of Computer Programming" (the book is meticulously and rigorously mathematical, not a treatise on style or idiomatic programming patterns; today we categorize the field as a science--computer science--instead of an art), and in the Copyright & Patent Clause of the U.S. constitution, where copyright is meant to promote "Science" (because the product of science is principally literary works) and patents the "useful Arts" (i.e. creation of functional objects).

The course is clearly a course on the philosophy of science, which among other things explores and critiques methods of acquiring, identifying, and applying knowledge, including things scientific inquiry.

Today science has a more narrow meaning--pursuits of knowledge by way of the scientific method and other systematized empirical methodologies (e.g. statistical inferences). Although, some of what we call science today is purely mathematical, like string theory; and many of the criticisms and defenses of string theory are great examples of what the philosophy of science encompasses.

The philosophy of science is a big tent. And, yes, a lot of it is gobbledygook: are we really in a dream world? Oh noes, Roko's basilisk! But there's a lot of mediocre "science" occurring in labs all around the world, so I'd think twice before dismissing the domain altogether. Ultimately, both in the archaic and modern meaning, science is based on the application of logic (of which there are several kinds) and I think that's what matters most; it's not sufficient in itself but it's definitely the greater distinction.

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Peter Thiel strongly identifies as libertarian. An article[1] posted here recently, written by a well-published libertarian-anarchist, described libertarianism as suffering from "a bias toward contrarian narratives". It only makes sense that Peter Thiel would be strongly interested in examining and analyzing so-called mainstream assumptions in sociology, economics, and political theory. I don't think Peter Thiel is wrong in being critical of mainstream assumptions and ways of thinking, but libertarians today are too incredulous regarding mainstream theories and "facts", and insufficiently skeptical of contrarian narratives, particularly those that lead to seemingly counter-intuitive and even opposite policy recommendations.

It's no coincidence that some of the most prominent climate change deniers and their apologists are avowedly libertarian. Being skeptical of climate change (unreasonably skeptical, I should say), and having an abiding "faith" in free markets, fits the culture of modern libertarianism. No matter that the science of economics is fundamentally descriptive, not prescriptive; strictly speaking, it makes no more sense to be pro-free market than it does to be pro-gravity. And no matter that the scientific method does not affirm facts, but merely rejects null hypotheses; and so in some sense even the most rigorous science is inconclusive.

I used to identify as libertarian years ago. But for this and other reasons I identify as an anarchist, at least in terms of what I consider ideal. Libertarianism began as a more pragmatic political movement derived from anarchist thought. It was a rejection of many radical and absolutist ideas in the anarchist community, and grounded itself in the science of economics. But libertarianism has become more like a religion now, whereas anarchist thought has softened. Libertarians are committing the same errors anarchists once did, namely eliding the distinction between normative (what should be) and positive economics (immutable economic phenomena)), and not appreciating the limitations of their models and assumptions. Libertarians (including in academia) increasingly tend to discount and reject empirical evidence when it doesn't line up with their philosophy (e.g. free markets are optimal), rather than accepting and applying empirical evidence, qualifying it as necessary but nonetheless reassessing theory in light of the evidence. It's really disconcerting. Peter Thiel seems like a very smart guy, but he does seem to be suffering from this contrarian bias. The thing is, some people like being contrarian. It's the adult version of the rebellious teenager. It's not enough to recognize that mainstream theory is flawed and incomplete; they have to reject it in its totality in favor of radical counter-narratives. This is increasingly happening across the ideological spectrum, rather than being confined to the edges of scholarly discourse; but it's really pervasive in the libertarian community.

[1] http://romaninukraine.com/putins-libertarians/