The AI Arms Race Will Be Won on Mathematical Proof

The Pentagon, National Security Agency, and Defense Advanced Research Projects Agency are racing to build AI-powered weapons and systems that will come with a significant vulnerability: our inability to determine how they will behave under real battlefield conditions. This is known as the "software understanding gap," where users do not understand the digital building blocks of their systems, leading to an inability to predict, verify, and secure their systems' actions.

Increasingly, users are facing a crisis in confidence in their most complex software, which will render the United States' world-class arsenal unreliable across modern battlefields. Adversaries may be emboldened to exploit those vulnerabilities, putting our national security at risk. So, how do we ensure these autonomous systems perform as needed? The answer lies in mathematical proof.

The Limitations of Testing

Traditional military hardware was designed to operate within clear and defined boundaries, but AI-driven systems employ automated decision-making that learns and adapts, making them susceptible to manipulation or error beyond human anticipation. Conventional testing methods that sufficed for deterministic systems with finite failure modes, such as a jet engine or a radar system, are woefully inadequate for the complexities of AI.

No amount of simulation or red-teaming can secure a system that is learning and adapting faster than any human can follow—especially in the face of an adversary intent on targeting its blind spots. Testing is akin to checking each link in a chain to make sure they're strong, but as the number of links increases, the likelihood that you miss a weakness increases as well.

The Power of Mathematical Proof

Mathematical proof takes a different approach. Instead of checking links one by one, proofs show that the entire chain is unbreakable—no matter how long it stretches. A proof starts by defining the fundamental rules: what the chain is made of, how much force it must withstand, and how it is connected.

Once these assumptions are established, the proof confirms the first link is strong, then follows a logical progression to ensure that every connected link must also hold. Whether the chain is ten links long or an infinite number of links, the proof guarantees that there are no weak points.

The Importance of Mathematical Proof in AI-Driven Military Systems

Testing can tell us if a system works under the conditions created in the test environment, but testing alone cannot cover every battlefield, cyberattack, or possible manipulation. A proof guarantees that no matter what conditions the system faces—even the ones not yet imagined—it will behave as intended.

Complete confidence in software systems is not theoretical—it has been proven. The Defense Advanced Research Projects Agency (DARPA) showed this in its High-Assurance Cyber Military Systems program, where researchers used mathematical proof to make a quadcopter's flight software unbreakable.

The Benefits of Mathematical Proof

DARPA's experience demonstrates that mathematically verified software does not just resist attacks, it eliminates entire classes of vulnerabilities. The private sector has reached the same conclusion. Amazon Web Services applies mathematical reasoning to its cloud infrastructure, not only to strengthen security, but to build better systems by ensuring faster deployment, fewer errors, and more reliable performance.

The takeaway is simple: proof does not just prevent failure, it drives innovation. Now we must bring this level of certainty to the AI-powered systems that are defining modern warfare.

The Stakes Are High

Consider the stakes: an autonomous air defense system in the Taiwan Strait detects an incoming missile. The system has mere seconds to classify and neutralize the threat. If China can surreptitiously corrupt sensor data by exploiting an undiscovered flaw, it could quickly neutralize one of the most important components of Taiwan's defense.

The same holds true for AI-driven cyber and electronic warfare. If adversaries can manipulate battlefield signals in ways our algorithms cannot recognize, entire operations will be compromised. Modern conflicts will not be won by those who simply build the most capable AI-powered systems, but by those who can definitively prove theirs will work when the stakes are highest.

A National Security Imperative

The U.S. and its allies cannot afford to deploy autonomous systems without mathematical rigor. This is not just a testing problem; it's a national security imperative. The defense community must act now to ensure that mathematical proof is powering every system we build.

Anything less is a bet we cannot afford to take. Our national security depends on it.