Math Is Eating the World—And Software Is the Accelerant

In this post, I’d like to make a case that math will increasingly permeate the world, that the software we write will become ever more mathematical, and that software itself is a unique accelerant in the same way calculus revolutionized math.

But first, a quick detour into theoretical physics. I think it’s an early template for how math will continue to shape so many other fields.

The Surprising Role of Math in 20th-Century Physics

It’s no secret that the fundamental laws of physics are expressed in mathematical terms, but the relationship is deeper than just that. Over the last century, there’s been a pattern in physics where new ideas emerge directly from math and only later find experimental backing. This flips the expected script of “experiment first, theory second.”

• Special Relativity is derived from the postulate that the speed of light in a vacuum is the same in all reference frames. Though there was experimental motivation, Einstein’s key insights came from thought experiments about moving observers and the invariance of the speed of light.
• General Relativity extended that approach by proposing the equivalence between being in an accelerated frame and experiencing gravity, again sparked by thought experiments long before final empirical confirmation.
• Quantum Mechanics can, in a simplified sense, be viewed as a new approach to probability—the familiar 1-norm for probabilities morphs into a 2-norm for wavefunctions in a Hilbert space, with the math of complex vector spaces playing a key role.

In the latter half of the 20th century, the examples became even more striking:

• Quantum Field Theory (QFT) elegantly uses Lagrangian mechanics, an 18th-century mathematical framework, to describe fields and particles.
• Group Theory, which studies symmetry in its most abstract form, turned out to be crucial in QFT. It led to the prediction of new particles (like the W and Z bosons) purely by insisting on certain symmetries—predictions that experiments confirmed years later.

Math doesn’t just describe physical reality—it often predicts it.

Computation as the Next Big Vector for Math

My thesis is that this incredible power of mathematical insight won’t stay locked inside theoretical physics. I believe computation is the tool that will carry math to nearly every domain, making it indispensable in ways we’re only starting to see.

Just like calculus revolutionized math by showing how allowing local spatial arguments to lead to global deductions about geometric objects [2], computation allows decisions to be made rapidly based on local information (in a spatial or temporal sense), which can allow a system to behave much more optimally on larger scales. Computation translates local mathematical insight to more optimal global behavior.

Large Language Models (LLMs) are a great illustration. They’re based around using gradient descent, which is a local operation, to optimize a large model with respect to a loss function. I don’t think anyone predicted the degree to which such a relatively simple operation, applied using computation on a large scale has led to models that almost exhibit aspects of general intelligence.

Whenever mathematical models struggle to account for complexities or chaotic behavior in the real world, fast computation swoops in. Self-driving cars, for example, depend heavily on control theory, which essentially involves making locally optimal decisions many times a second to keep a car safely on the road. Finite Element Analysis (FEA) in mechanical engineering uses discretized math plus high-performance computing to simulate everything from bridges to jet engines. Fields like computational fluid dynamics and climate modeling are all based on software that apply foundational equations iteratively on a large scale.

What This Means for Software Engineers

I believe that this has key implications for the software industry. Roles that combine software development expertise with mathematical insight will become increasingly lucrative, while the rest of the industry faces commodification pressure. This is already reflected in the outsized demand for roles that require both math and software knowledge.

Those who can code and handle advanced math tend to earn outsized compensation—Wall Street “quants,” machine learning researchers, top-tier data scientists, etc. What used to be “business intelligence” or “analytics” is now sophisticated machine learning, Bayesian modeling, and data engineering. Management consultants pioneered the idea of using analytical frameworks for big decisions - modern data science is, in a way, a continuation of that principle leveraging increasingly sophisticated math and computation.

Put simply, mathematical knowledge is becoming increasingly valuable, and software is the force multiplier. It takes abstract mathematical models—sometimes centuries old—and breathes them into real products and systems. Whether it’s a neural network sifting through text, a feedback loop keeping a car on the road, or an elaborate model guiding corporate strategy, the blend of math + software is becoming increasingly common and “unreasonably effective”.

Notes

[1] See https://scottaaronson.blog/?p=6244

[2] General Relativity, built on Riemannian geometry, is a pinnacle example of using local differential geometry to derive far-reaching conclusions about the cosmos.