Nothing changed

Martin Drohmann, former postdoc at the Sandia National Laboratories

Mathematics always was the story of humans searching for truth. Truth that is so compelling and universally verifiable that it is difficult to deny.

Not always easy to believe: Although the details are lost, it took Pythagoras and his followers some significant time and effort to accept the existence of irrational numbers.

Similarly, David Hilbert stated the challenge to prove that mathematics is logically complete. Most mathematicians believed it at the time, including Kurt Gödel: until he disproved it.

Whether LLMs or math problem solvers can prove logical facts doesn’t change anything about mathematics: it is a human story of finding truth that we can validate and believe in.

If a machine can find truth is an almost irrelevant question, because it also has to convince us of it. For that to happen, the machine needs some truth-seeking fanatics aka mathematicians to read and make sense of what the machine created. And the machine needs those mathematicians to tell a story that convinces the rest of the world that this truth can be trusted. Trusted enough to be taught in schools, or even to create weird concepts on top of it – something like a global financial system.

It was difficult when only humans were doing the thinking part: I remember, a couple decades ago, excitedly explaining to my parents how encryption and verification on the internet works. Maybe my educational skills aren’t the best, but it probably wasn’t my lack of clarity that I could not bring my parents to check their bank account balance over the internet$\ldots$ Until almost everyone else around them did it. Trust grows slowly!

Sustainability

I am pretty sure that mathematics is sustainable as long as there are humans who want to dedicate at least some of their lives to searching for undeniable truth. Probably, most of the readers of this blog would agree that this is a joyous purpose, so likely there is something inherently human about it.

LLMs are powered by machines. Machines that consume natural resources that don’t replenish as fast as they are used. And as someone who has witnessed the truth of Jevon’s paradox play out – several times, I believe that every effort to make the use of LLMs more “sustainable” will just speed up their resource usage.

So, for those of us worried that mathematics will never be the same, and that the hard work of problem solving might be entirely done by machines. Let’s all be realistic: Thinking machines are unsustainable. Those rare earth minerals just don’t replenish fast enough.  This too shall pass. We just don’t know how fast.

But chances are good that truth-seeking humans will outlive this episode of machine-assisted thinking.

Morale

LLMs are a reality now, and they won’t go away for the next few years. So, should we use them or avoid them? There definitely are plenty of reasonable answers. I saw the introduction of plastic “recycling” speed up the production of plastic, the development of more efficient combustion engines leading to bigger and more cars, and more efficient computers to ever more demanding applications, such as bitcoin mining and now LLMs.

With this experience in mind, I believe that it is out of my control to reduce energy usage through personal restrictions. But I want to be mindful as much as possible about when I use LLMs for mathematics, and ask myself if my usage is at least aligned with some basic values.

These questions serve as a good guide for me:

• Are my prompts leading to more truth?
• Do they help me learn? (It is so easy to explore adjacent topics to the knowledge I have acquired, because LLMs have ingested so much information. And I think that’s wonderful.)
• Would it bring me more joy to think for myself?

With care,

Martin

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Received 26 August 2026.