Mathematics insights presented through animations, formulas, pictures, graphics, quotes, books, history, and memes. Open DM.
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"If you want to find the secrets of the universe, think in terms of energy, frequency and vibration."
- Nikola Tesla
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Viviani’s theorem demonstrates spatial conservation, showing that the three perpendicular lines behave like a zero-sum game: moving closer to one side requires corresponding movement away from the other two. Local changes maintain a global constant.
Visual proof of Viviani's theorem: pick any point inside an equilateral triangle. Its three distances to the sides always sum to the same "h" the triangle's height.
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Among two-digit numbers, excluding palindromes, only two pairs have the property where the number and its reverse both square to numbers that are also reverses of each other.
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Leonhard Euler (1707–1783) is among the most prolific mathematicians in history. He wrote more than 850 papers and books across analysis, number theory, mechanics and optics. Nearly blind in later life, he kept working, and his work remains central to mathematics today.
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Beauty in mathematics often reveals unexpected simplicity where none seemed to exist. The Gaussian integral stands as one of the cleanest examples.
The bell curve looks almost ordinary, yet its total area hides a remarkably exact result.
The most interesting about the Gaussian integral is that a function arising naturally in probability leads to a constant deeply connected with geometry. At first sight, there seems to be no obvious reason for a circle-related constant to appear in a problem about a bell-shaped curve.
Yet this is precisely where mathematics becomes beautiful. A curve associated with randomness leads to an exact geometric quantity, bringing probability, analysis, and geometry together in a single result.
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Matrix multiplication seems complex until you observe it step by step. Watch how each of the nine entries is formed: one row from matrix A, one column from matrix B, three products, and one sum.
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Just noticed that the spelling of the smallest two-digit odd number includes the word "even" at the end.
That seems "odd".
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He will remain the last human to solve a Millennium Prize problem without AI.
We’re sharing a solution to the Navier-Stokes Millennium Prize Problem, one of the deepest problems at the frontier of mathematics.
The proof was produced by a group of agents, using an OpenAI next-generation model significantly more capable than GPT-6 Astra.
The problem concerns whether the description of smooth three-dimensional fluid motion modeled by the Navier-Stokes equations can break down. It has remained unresolved for roughly 90 years.
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