From The Atlantic Monthly, since 9/11, the United States has spent $1 trillion to defend against al-Qaeda and ISIL, dirty bombs and lone wolves, bioterror and cyberterror — has it worked? Wendy Lynne Lee reviews The United States and Terrorism: An Ironic Perspective by Ron Hirschbein. Has ISIS learned to weaponize America’s homegrown spree killers? How ISIS weaponized the media after Orlando: In the space of minutes, Omar Mateen transformed from an “ordinary” mass shooter into a global terrorist. Islamic State is successfully radicalizing Americans — how do we stop them? Karen Yourish and Jasmine C. Lee on what the Americans drawn to ISIS had in common. “I am fed up with this evil”: How an American went from Ivy League student to disillusioned ISIS fighter. The Islamic State likes America’s “dumb” gun laws, defector says. Anne Speckhard and Ahmet S. Yayla on how ISIS defectors can help us beat terror.

Brendan O’Connor on how ISIS, Trump, and the Alt-Right have more in common than either would ever be likely to admit. Bethany Albertson and Shana Kushner Gadarian on how anxiety about terrorism advantages Hillary Clinton over Donald Trump. John Mueller on how Democrats seriously underestimate voter fear of ISIS.

Andrew Chongseh Kim (Concordia): When the Apocalypse Comes, Will Anything Change? Gay Marriage, Black Lives Matter, and the Rule of Law (“This essay, part of the Savannah Law Review’s symposium on The Walking Dead, argues that modern American society already operates in the same way, minus the zombies”.) Patriarchy’s full circle: The Mayor of Cannes was wrong to ban the “burkini”. Ivanka and Jared’s power play: Lizzie Widdicombe on how the patrician couple came to have an outsized influence on a populist presidential campaign. Eric Boehlert on how Clinton emails became the new Whitewater: A “scandal” in search of a crime. Has the American military fallen behind? Bear F. Braumoeller investigates. Is cyberwar turning out to be very different from what we thought? The future might look much more like Russia’s DNC hack than physical attacks on nuclear power plants. Why does Wikileaks have a reputation for anti-Semitism?

From the Journal of Humanistic Mathematics, Marcus Giaquinto (UCL): Mathematical Proofs: The Beautiful and The Explanatory. World’s largest math proof takes up 200 terabytes. Bizarre proof to torment mathematicians for years to come: A rare appearance by enigmatic Shinichi Mochizuki brings faint optimism about his famously impenetrable work. A surprising new proof is helping to connect the mathematics of infinity to the physical world. The physicist-mathematician Miranda Cheng is working to harness a mysterious connection between string theory, algebra and number theory. A new breakthrough that bridges number theory and geometry is just the latest triumph for a close-knit group of mathematicians. David Neil Corfield (Kent): Reviving the Philosophy of Geometry. A previously unnoticed property of prime numbers seems to violate a longstanding assumption about how they behave.

Gabrielle Emanuel on a history lesson: When math was taboo. How a mathematical superstition stultified algebra for over a thousand years. The introduction to Leonhard Euler: Mathematical Genius in the Enlightenment by Ronald S. Calinger. The first chapter from Mathematical Knowledge and the Interplay of Practices by Jose Ferreiros. Ayalur Krishnan on how a hypothesis can be neither true nor false. The great mystery of mathematics is its lack of mystery. The introduction to Summing It Up: From One Plus One to Modern Number Theory by Avner Ash and Robert Gross.

How math secretly affects your life: Bill Gates reviews How Not to Be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg. Chaos theory, the prisoner’s dilemma, and why math isn’t really boring: Elena Holodny interviews Steven Strogatz, Joy of X: A Guided Tour of Math, from One to Infinity.

Stop ruining math: Rachel M. Steinig on reasons and remedies for the maladies of mathematics education. The man who will save math: Dan Meyer, the most famous math teacher in America, wants to radically change the way we learn math. Andrew Hacker on the wrong way to teach math. Down with Algebra II: It drives dropout rates and is mostly useless in real life — Andrew Hacker has a plan for getting rid of it. Andrew Hacker, an outspoken critic of mandatory algebra education, is asked to defend his contentions at the National Museum of Mathematics.

Shoba Sivaprasad Wadhia (Penn State): Is Immigration Law National Security Law? Donald Trump argues that no one like him should be allowed into the United States. Alex Griswold on how Donald Trump’s newest Muslim ban is political correctness gone mad. What is extremist belief? An answer from medieval Islamic philosophy. The great natural experiment of this election cycle: Across a variety of dimensions, Donald Trump is an extreme candidate — this is awesome for political science. Bad news, ladies: The “pink tax” starts at birth. Romantic bureaucracy: Boris Groys on Alexander Kojeve’s post-historical wisdom. Tools of modern terror: C.J. Chivers on how the AK-47 and AR-15 evolved into rifles of choice for mass killers. Euphemisms are like underwear, best changed frequently — what work are they doing in our language and why do they expire?

From National Review, why wasn't there widespread, principled conservative opposition to Trump? Tim Alberta goes inside Trump’s conquest of America’s most conservative districts. People like Bret Stephens can condemn Sean Hannity and Donald Trump all they want — but if they want to understand what went wrong, they need to take a very hard look at themselves. If Donald Trump loses, will the Republican Party sink with him? Brian Beutler on conservatives’ laughable effort to blame liberals for Trump. It doesn’t make sense to attribute Trump’s support to economic anxiety. Felix Salmon on the subtle, dangerous way Donald Trump has changed American political discourse. Populist, frustrating, naive, wise, forever on the make: An excerpt from Trump Revealed: An American Journey of Ambition, Ego, Money, and Power by Michael Kranish and Marc Fisher.

Of psychopaths and presidential candidates: An analysis shows where some of this year’s aspirants rank on a standard assessment of psychopathic traits — and the results are interesting, to say the least.