Euler's identity displays a profound connection between fundamental numbers π, e (the base of natural logarithms), and i (the imaginary unit).

It is considered one of the most beautiful formulas in mathematics.

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Discovery of explicit solution formulas for Polynomial eq. a₀xʲ+a₁xʲ⁻¹+...+aⱼ=0
j=2 Pythagoras (500 BC)
j=3 Girolamo Cardano (1545)
j=4 Lodovico Ferrari (1540)
j≥5 No general formula exists, Niels Abel (1824)

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Erwin Schrödinger postulated his famous equation in 1925 - work that resulted in his Nobel Prize in Physics in 1933. The equation provides a way to calculate the state of a system and how it changes dynamically in time. |ψ> is the state of a system and H is its Hamiltonian.

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This is the only prime that is the average of 2 consecutive Fibonacci numbers

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Difference between Δ, 𝑑, 𝛿 and ∂
Δ - finite variation of a quantity (not infinitesimal)
𝑑 - infinitesimal variation of a quantity or differential operator
𝛿 - infinitesimal variation of a quantity or variation of a functional
∂ - partial derivative

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At the age of 19, Gauss was the first person to accomplish the ruler and compass construction of a 17-gon polygon. This proof represented the first progress in regular polygon construction in over 2000 years. While doing it, he also discovered this expression for cos(2π/17)

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This week’s paper is from 2019, and the authors find evidence that the bacteria Porphyromonas gingivalis, which is associated with chronic gum diseases, is involved in the pathology of Alzheimer's.

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Isaac Newton regarded all varying quantities as flowing quantities and he called fluxion the rate of flowing - he used the dotted notation to refer to it. Adopting his fluxional notation we can write simple mechanical equations considering x as a flowing quantity as follows.

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Every number greater than 55 is the sum of distinct primes of the form 4n+3

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Proof that √2 is irrational
If √2 is rational, √2=a/b (a,b>0 lowest terms)
Then a²=2b²=b²+b² - place 2 carpets bxb in an axa room

Since the sum of the overlap and uncovered areas is equal
(2b-a)²=2(a-b)²=>√2=(2a-b)/(a-b) a contradiction since a,b were the lowest terms!

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Werner Heisenberg developed the Uncertainty Principle in 1927. It states that the position and the velocity of an object cannot both be measured exactly at the same time. With high certainty on the position (Δx small) then you very high uncertainty on the momentum (Δp large)

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The Williams-Kilburn tube introduced in 1947 was the first entirely electronic memory used in early computers. It used a cathode tube to store bits as dots on the screen's surface. Each tube could store about 1024 bits of data.

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377 years ago Pierre Hérigone wrote a six-volume algebra text almost entirely in symbols, in which he first proposed the use of ⊥ (perpendicular) and ∠ (angle).

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Tree Mountain is an artificial mountain near Ylöjärvi in Finland. Over a period of 4 years 11,000 people planted 11,000 trees in a specifically designed mathematical pattern based on the golden section.

The project was conceived by the artist Agnes Denes in 1984.

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This is the largest known Fibonacci number that's also prime, which is 21925 digits long and was proved prime by Mathew Steine and Bouk de Water in 2015.

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Gustav Dirichlet (1805–1859) was a prodigy who at the age of 20 proved that Fermat’s Last Theorem has no solution when n=5

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"Truth... is much too complicated to allow for anything but approximations" - John von Neumann

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J.J. Thomson won the Nobel Prize for the discovery of the electron in 1906. He was a very gifted teacher. Six of his research assistants won Nobel Prizes in Physics and two in Chemistry. Thomson's son won the Nobel Prize in Physics for showing that electrons are waves.

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Choose 2 numbers at random - here's the probability they will have no common factor

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A visual proof why 1+3+5+...+(2n-1)=n²

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