DARPA’s 23 Challenge Questions

The challenges were announced in 2007 from what I can find.

Here are some links about them:

https://www.hpe.com/us/en/insights/articles/the-toughest-mat...

http://www.math.utk.edu/~vasili/refs/darpa07.MathChallenges....

The first link talks about results for some of the challenges.

Some of these were hard. I wish the answer key had included the full solutions.

> Brain * Develop a mathematical theory to build a functional model of the brain that is mathematically consistent and predictive rather than merely biologically inspired.

My gut reaction to that was: that’s pie-in-the-sky outlandish.

However, with more thought, I agree it is possibly the most important in the list.

In the past year, Congress demanded a powerful general AI. (1)

Many have been and continue to be concerned that AIs will fail in the areas of ethics and morality.

An unethical and immoral AI could be chaotic and unpredictable. It could try to kill everyone (Skynet) or manipulate them for its amusement or quest for knowledge, or it could leave Earth in a spaceship never to be seen again, since it would have no obligation to us.

An ethical and moral AI on the other hand might decide that it should keep humans alive and happy in a virtual world to save us from ourselves or to better control disease, hunger, and other risks. But by doing so, would take away our actual physical freedom.

The problem with the human brain as a model is that it’s not necessarily going to be much better. For example, consider how humans treat other animal species: we let some roam free, we study some, we heal some, we feed some, we have pets, we have zoos, we milk some, we take their eggs, we eat them as food, some hunt them for sport, and some accidentally run them over with vehicles.

Perhaps if we only were to try to make AI purely just do some human jobs to save money or to act as a scalable collection of virtual human minds, that could in-theory be less risky than a hyper-intelligent general AI.

That’s not going to stop development of such a general AI. But, maybe it could help defend us better and could help those designing that AI to make dystopia less eminent.

(1) https://www.intelligence.senate.gov/publications/intelligenc...

Can someone please give us a better understanding in what's meant by this?

> Duality in mathematics has been a profound tool for theoretical understanding. Can it be extended to develop principled computational techniques where duality and geometry are the basis for novel algorithms?

There are certain problems that, if you solve, you earn a PhD as a byproduct.

>Mathematical Challenge Eight: Beyond Convex Optimization * Can linear algebra be replaced by algebraic geometry in a systematic way?

I think this is probably by far the most useful, practical and relevant challenge to be solved for science and engineering, and perhaps closely follows by the stochastic and duality challenges.

For computer science and engineering it is the popular "Gimbal lock" problem in 3-D environment in which linear algebra cannot comprehensively represent but easily represented by geometric algebra or quaternions.

Similarly in electromagnetics (EM) wave propagation, due to the prominent effect of polarization (other waves like sound does not has polarization), comprehensively modeling polarization with linear algebra is close to impossible. I kind of liken the geometric algebra unpopularity and conundrum similar to 18th mathematicians suspicious views when complex number was originally introduced and looks how far we have got now by embracing it [1]. Basically the discovery and utilization of complex number provide us with WiFi 6 and 5G. But if we want to move forward with robust and reliable wireless similar to wired (or close to wired connection reliability) we need to take control of EM polarization by embracing geometric algebra.

[1]https://en.m.wikipedia.org/wiki/Complex_number#History

DARPA isn't afraid to ask the easy questions I see /s

Too bad agency, DARPA included, wants to pay enough to have people work on these problems for extended time periods. It's good to see some funding for high-risk work but there just isn't enough anymore.

> Mathematical Challenge Three: Capture and Harness Stochasticity in Nature

> * Address Mumford’s call for new mathematics for the 21st century. Develop methods that capture persistence in stochastic environments.

This is interesting, what did Mumford asked for, and what does persistence in stochastic systems stands for?

I have a prototype solution to #20 and provided some runway it could, after validation by research, solve for #2. I am working a prototype distributed OS that (partially) executes in the browser. The prototype is far enough along that I can qualify some of my initial goals and assumptions.

But then those questions are for undergrads. I am just an old dumb soldier with my undergrad days long behind me.