Oliver Knill

Mathematician

[Oliver Knill @oliverknill]

Density of wave fronts by Emily Kang and myself: https://t.co/3gSvFfnSqr

[Oliver Knill @oliverknill]

Wiesen Bocksbart in Wallis #shorts #nature #math https://t.co/dRLx21TmSr via @YouTube

Mathematica of the graph:

K=20;L=100;
A=Flatten[Table[Union[{Rule[{0},{k}]},Table[Rule[{k},{k,l}],{l,L}]],{k,K}]];
GraphPlot3D[UndirectedGraph[Graph[Flatten[Union[A]]]]]

[Oliver Knill @oliverknill]

Graphs, Games and Groups. A math project from this spring. We look at one and two player games in a pure graph theoretical frame work. #maths https://t.co/VQGDmxNIcA via @YouTube

[Oliver Knill @oliverknill]

The Perron Frobenius Theorem has a nice application for Markov chains. There exists a unique equilibrium if the Markov chain is a positive matrix. #shorts #linearalgebra #probability https://t.co/wArHXgCNjp via @YouTube

[Oliver Knill @oliverknill]

Sarnak: "Proving that something is random is probably one of the hardest things in mathematics!"
He also considers the probabilistic statement as the most suitable RH explanation for "a person on the street Talk of April 15, 2026 at Harvard. See the clip
https://t.co/4doiTUc6eK

[Oliver Knill @oliverknill]

20 years math in movies.
https://t.co/C29GpdIrF5

https://t.co/rZeMC26oos via @YouTube

[Oliver Knill @oliverknill]

If the digits of pi were random, then by Borel Cantelli, pi would write every possible text infinitely often. For Piday 2026, we build "Pi Monkey" and see how long it takes to write "piday".
#shorts #piday https://t.co/JCP7lhzhtl via @YouTube

[Oliver Knill @oliverknill]

One minute Probability Review of the first half of the course. We tried to get the 10 most important focus points in 10 slides.
https://t.co/FCspRupzBV
#shorts #probability https://t.co/B2qYu7CBE8 via @YouTube

[Oliver Knill @oliverknill]

Characteristic Functions of Random Variables #shorts #probability https://t.co/Y4XxuOsqka via @YouTube

[Oliver Knill @oliverknill]

The Caratheodory Extension Theorem https://t.co/oGxmwAaMgc via @YouTube

[Oliver Knill @oliverknill]

The Lebesgue Integral. We also show the short 4 page paper of Lebesuge from 1901. No journal today would even consider publishing such a short note these days. The paper is almost comically simple but it is a fantastic frame work. #shorts https://t.co/7TxEG2yT4U via @YouTube

[Oliver Knill @oliverknill]

The Probability approach to the Riemann Hypothesis #shorts https://t.co/bOELzjjrrA via @YouTube

[Oliver Knill @oliverknill]

Volumes of higher dimensional spheres and balls in 58 seconds with proofs #shorts https://t.co/glMdcbpusG via @YouTube

[Oliver Knill @oliverknill]

Spherical Averages https://t.co/Zrl51Zmjwl via @YouTube

[Oliver Knill @oliverknill]

A neat trick on how to lie with statistics
https://t.co/cBdKF3SBE9
It is based on a famous paradoxon, but you can be almost certain that your manipulation will not be detected.

[Oliver Knill @oliverknill]

My bikeride to work this morning. https://t.co/wCgp6epPC6 via @YouTube

[Oliver Knill @oliverknill]

@rfleury Even if it would work, it is a bad idea to have an operating system do "random". Doing random might work at some point, and not later, maybe in a crucial moment of your workflow.Modern AI technology by nature is non-deterministic and does not belong into the operating system.

[Oliver Knill @oliverknill]

T[x_]:=Total[IntegerDigits[x]^2];
HappyQ[x_]:=Nest[T,x,x]==1;
Print["Happy 2026! ", HappyQ[2026]];

[Oliver Knill @oliverknill]

A bit more abou the Density of Wave front Conjectures treated here https://t.co/ZmjaH97HMB with Emily Kang (we currently revise the paper and make more experiments)
https://t.co/wJoXlr0Sij via @YouTube

[Oliver Knill @oliverknill]

Descartes Theorem on Polyhedra. One of the amazing theorems in geometry. It is astounding that Descartes already got the main point of the Gauss-Bonnet theorem. #shorts #geometry https://t.co/7IzQZ8htmO via @YouTube