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 ...

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

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 ...

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 ...

Harvard College Dean of Science Jeff W. Lichtman wants to reshape how undergraduates are solving problems. Lichtman — who was appointed as Dean of Science in July — said in an interview with The ...

It is impossible to imagine a master chef who doesn’t know how to cook, a cabinet maker who doesn’t know anything about carpentry, or a pianist who can’t read music. All three sound like ...

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 ...

Visit NAP.edu/10766 to get more information about this book, to buy it in print, or to download it as a free PDF. Cyber (computing and communication) technologies underpin every facet of the U.S.