An exploration of political philosophy founded in mathematical principles

S2 E2 Politicking Mathematicians by Julius Knapp. Interviewed by Brian Smyers

It was an obsession. The pointless but worthwhile pursuit had taken a hold of my psyche. Appealing to my ego in a special way that many Mathematicians would recognize, but that few others could understand. At its core is the belief that every problem can be solved, given enough enthusiastic patience and arrogant humility. Of course, at the time, I thought I knew just enough, and was just gifted or lucky enough, to figure it out.

I don’t remember the exact year. It was probably somewhere between 2003 and 2004. The Clay Mathematics Institute had just released the Millennium Prize Problems, a collection of 7 unsolved problems, each with a $1 million bounty. I learned about the problems from Keith Devlin’s “popular” mathematics book, “The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles Of Our Time”, a bold and grandiose title designed to captivate the mathematically curious. I was one of those people, a Senior in the final year or so of a university mathematics program and looking to make a name for myself before entering the workforce. And I was going to solve The Riemann Hypothesis.

(hold for gasps, applause, or laughter)

The Riemann Hypothesis is deceptively simple, at least as advanced mathematical theory goes. Many third- or fourth-year Mathematics undergraduate students would immediately recognize its symbols and be able to start picking apart some basic corollaries. I dug in… about 2 feet. I spent some time studying different approaches to the problem, eventually reproduced Willans’s Formula (although I didn’t learn that it had a name for another 15 years at least), and tattooed Euler’s relation on my left forearm to commemorate the experience. Eventually, I correctly arrived at the conclusion: this was beyond me.

Spoiler: I didn’t solve the Riemann Hypothesis. The slow and disappointing realization was barely tempered by the fact that this was basically beyond everyone. Bernhard Riemann proposed his Hypothesis about 167 years ago (at the time of writing). Dozens, possibly hundreds or thousands, of Mathematicians over the years have tried and failed to solve the Riemann Hypothesis. And there’s still the possibility that it’s not even possible to solve given our current mathematical framework.

“First, 
sometimes 
digging in is hard, but it’s never 
not 
worthwhile.”

I learned many lessons from this experience. Lessons I still carry to this day and will likely carry with me for the rest of my life. First, sometimes digging in is hard, but it’s never not worthwhile. I only made it 2 feet into this problem that could very well cut a hole through the Earth, but I learned a lot about what it means to be a Professional Mathematician, working endlessly on a complex problem, evaluating the potential risk and reward of every approach to the problem, while also navigating the constant distractions of everyday life. Andrew WIles, famous for his proof of the then 358-year-old Fermat’s Last Theorem, spent nearly ten years working in seclusion to successfully complete his mission. What chance would I have as an undergrad near the end of his university career, months away from marriage and adult life? The lesson was that work is easy, life is hard. But there was also this second lesson: you have to try, and you have to trust that others are trying at least as hard as you to solve the problems. To use a sports analogy: you carry the baton as long and as far as you can. If you’re lucky, you’ll carry it for a long time and pass it on to someone else. But even if you drop the baton, you have to trust that someone else will pick it up.

There were other lessons too, like the lesson that not every problem even has a solution. In my studies of the Riemann Hypothesis, I learned of Godel’s Incompleteness Theorem. Roughly stated “No matter how clearly you state the rules or how rigorously you define the ‘truth’, there will always be rules or statements that are beyond any logical reasoning from them”. As it relates to the Riemann Hypothesis, it may, in fact, be the case that this statement exists outside our current mathematical framework (and oddly enough, it may be possible to use our current mathematical framework to prove that this statement is not provable within our framework). And if it is the case that the Riemann Hypothesis exists outside of our current framework, then we may extend our current framework to include both cases: the first where we accept the Hypothesis as true, but also the second where we accept the Hypothesis as false. This gave me my final lesson: sometimes two contradictions can both be true, from a certain point of view, and that’s okay.

“…you have to try, and you have to trust that others are trying at least as hard as you to solve the problems.”

Now, some may ask, “So what? Why do I care? What does this have to do with the state of our politics today?” To that I would say “This is a period of uncertainty and widespread political turmoil. It’s not our first and won’t be our last, but we must try to understand and resolve the problem.” To be more clear, I’m not suggesting that this problem even has a solution, at least not some ego satisfying “This is right and this is wrong”; it may be the case that the solution to this uncertainty and this turmoil will be to accept that our current framework cannot adequately address the problem.

To put this more practically, let’s review the current tariff situation. At the time of writing, the Supreme Court has ruled that the “reciprocal” tariffs instituted by President Trump using the authority granted to him under the International Emergency Economic Powers Act, more commonly called IEEPA, are unconstitutional. Briefly, it appeared that Americans would gain some financial relief and economic speculation soared. But just hours later, President Trump announced that he would instead pursue a global tariff under a different authority.

The issue raises many questions. What authority will President Trump use to institute that new global tariff? What will happen to the revenue previously collected? Will any financial relief reach the American people? Will I, as a business owner, receive any reimbursement for the tariffs I paid when I purchased equipment last year? Honestly, none of those questions are especially interesting to me. Important, but not interesting.

The larger question is much more interesting. The one that calls into question the very framework the Constitution established almost 250 years ago. Will Congress amend IEEPA or abdicate their own authority, granting “emergency” powers of the purse to the Executive? At first glance, the answer appears to be “no”. Only Congress has the power to levy taxes and tariffs. But the keen observer will recall that only Congress can wage war. However, Congress abdicated that authority also, granting the Executive “emergency” war powers. Under the War Powers Resolution, the Executive can “temporarily” deploy troops without congressional authorization. Congress may then authorize the use of force, allowing the Executive to continue armed conflict effectively indefinitely, one temporary authorization at a time. Perhaps a similar scheme could also allow Congress to abdicate the power of the purse to the Executive.

Whatever the case, it appears the baton has been passed to us. This, among many others, is our problem to solve and it’s important that we try. Every new approach to solving the problem, however small, becomes something we learn, and that’s worthwhile. Those things we learn then become the new ways we can build upon and improve our Constitutional Democratic Republic. We also have to trust that others are working towards the same goal, even if they adopt a different approach. And it may turn out that no one has the answer. We will have to return to our founding document and amend it, one way or another, for better or worse.

Julius Knapp Julius Knapp

Owner and CEO of Dirgible Systems

Biography

Corrections, Clarifications, Addendums and References in interview.

16:15 It was not Revolving Staircases by Salvador Dali. There is no such thing. Relativity by M.C. Escher is what Brian was thinking of.

27:38 Trump’s Press Conference in reaction to the SCOTUS ruling on tarriffs instituted using the International Emergency Economic Powers Act.

28:20 Donald Trump is 79 and will turn 80 on June 14th 2026

29:48 Rebecca yells at Roy Kent. But this is the scene that Julius references (heavily censored).

38:10 Brian’s dinks were a reference to Dueling Banjos in the movie Deliverance.

40:15 Games Without Frontiers by Peter Gabriel

41:45 The Iraq War had its own Authorization for the Use of Military Force. It passed in 2003 and was repealed on December 18th 2025.

42:39 The Authorization for the Use of Military Force Against the Government of Syria never made it out of committee.

49:30 A pentagram inside an apple. Image is from Silent Owl on Blogger.

51:13 A nice wiki article about the Celts and how far they had spread pre-Roman times. Visigoths were a Germanic Tribe, not Celtic.

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