In revisiting past hard problems, it is also important to recount successes that helped us bolster our defense. Successes ...

In September 2019, news broke regarding progress on this 82-year-old question, thanks to prolific mathematician Terence Tao. And while the story of Tao's breakthrough is promising, the problem isn't ...

This blog was co-authored by Gregg Henriques, Ph.D., and John Vervaeke, Ph.D. Since the dawn of human consciousness, people have grappled with the problem of what it is and how it works. In academic ...

Chapter 2 explored key factors underpinning difficult cyber challenges. This chapter goes on to list and discuss the list of cyber hard problems—well-defined problems where progress toward their ...

The National Academies of Sciences, Engineering, and Medicine are private, nonprofit institutions that provide expert advice on some of the most pressing challenges facing the nation and world. Our ...

P vs. NP asks: are these two classes actually the same? If P = NP, then every “hard” problem is secretly fast to solve; we ...

The nation relies on cyber systems for commerce, critical infrastructure, national security, and most facets of daily life. However, the growing scale and complexity of cyber technologies–coupled with ...

I’m spotting a worrying trend among startup founders who seem to think that running a startup is effectively a get-rich-quick scheme. Apart from that mindset being wrong and naive, I suspect there’s ...

For all of the recent strides we’ve made in the math world—like a supercomputer finally solving the Sum of Three Cubes problem that puzzled mathematicians for 65 years—we’re forever crunching ...