Tech with Mak@techNmak
In 1933, a 30-year-old mathematician published a 62-page monograph that changed how mathematics understood uncertainty.
Before him, probability was powerful, but its foundations were still debated.
After him, probability had a modern axiomatic foundation.
The man was Andrey Kolmogorov. Born April 25, 1903.
Britannica describes him as a mathematician whose work influenced many branches of modern mathematics, especially probability, set theory, information theory, harmonic analysis, and number theory.
But three of his ideas still quietly shape modern AI, physics, and computer science.
1./ Modern probability theory
In 1933, Kolmogorov published Foundations of the Theory of Probability.
His key move was to ground probability in measure theory.
Today, his framework is usually summarized through three core axioms:
→ Probabilities are non-negative
→ The whole sample space has probability 1
→ Mutually exclusive events add up, even countably many of them
That sounds simple.
But this is the formal language behind Bayesian inference, stochastic processes, Markov chains, Monte Carlo methods, statistical learning, and uncertainty estimation.
Every probabilistic model in AI rests on this basic idea:
uncertainty can be reasoned about mathematically.
2./ Turbulence and the −5/3 law
In 1941, Kolmogorov turned to one of physics’ hardest problems:
turbulence.
His K41 theory described how energy in turbulent flow moves from large scales to smaller scales, until viscosity dissipates it as heat.
In the inertial range, this led to the famous Kolmogorov −5/3 scaling law:
E(k) ∝ k^(-5/3)
It is not a complete solution to turbulence.
Nothing is.
But it remains one of the most important reference points in turbulence theory, computational fluid dynamics, and modern simulation.
Even physics-informed ML models for fluid dynamics often use Kolmogorov scaling as a benchmark for whether they are capturing the right physics.
3./ Kolmogorov complexity
In 1965, Kolmogorov helped formalize a brutally elegant idea:
The complexity of an object is the length of the shortest program that can produce it.
A repeated string is simple because a short program can generate it.
A truly random string is complex because it has no shorter description than itself.
This became one of the foundations of algorithmic information theory.
Important caveat:
exact Kolmogorov complexity is uncomputable.
But the idea still shapes how we think about randomness, compression, information, and learning.
It also connects deeply to the Minimum Description Length principle:
the best model is not just the one that fits the data.
It is the one that explains the data with the shortest useful description.
That is Occam’s razor in mathematical form:
compress the pattern, not the noise.
Kolmogorov did not just solve problems.
He built frameworks inside which future problems could be solved.
