It turns out the math we use for all of modern physics has these 'infinitely small' numbers hiding in it that we thought were impossible.
March 25, 2026
Original Paper
Infinitesimals inside the Familiar Field of Complex Numbers
arXiv · 2603.22308
The Takeaway
For centuries, mathematicians tried to banish 'infinitesimals' because they were considered logically unsound, reinventing calculus to avoid them. This paper proves these ghost-like numbers have been hiding inside the standard number system all along, potentially simplifying how we model everything from quantum mechanics to fluid dynamics.
From the abstract
We show that the field of complex numbers $\mathbb C$ contains non-zero infinitesimals by observing that $\mathbb C$ contains non-Archimedean subfields. Our observation is based on an old theorem in algebra due to E. Steinitz, discussed in the article in detail. The presence of infinitesimals in $\mathbb C$ was surprise to the author and might be surprise to the readers as well, since $\mathbb C$ is commonly defined in terms of the field of reals $\mathbb R$, which is Archimedean. An additional