p value

A glucose meter that doesn't prick your finger but just looks at your wrist: that's the dream for millions of people with diabetes. It's the promise of algorithms that extract glucose levels from the ordinary pulse signal, the photoplethysmogram (the same one that measures heart rate in smartwatches).

In 1998, mathematician David Boyd noticed something strange. He was studying the Mahler measure of polynomials, a quantity that gauges the "complexity" of their roots, and found that for a family of curves, it always equals a special rational number times the derivative of an L-function.

In 1953, mathematician Alexander Grothendieck proved a theorem that became a cornerstone in the theory of tensor products. It states that for ordinary function spaces, two natural norms, the projective and the injective, are equivalent up to a universal constant. In other words, two ways of measuring the 'size' of combinations of vectors give similar results.

The weak equivalence principle, silently tested since the time of Galileo and laid at the foundation of general relativity, states: all bodies fall equally, regardless of their internal composition.

Two coins are flipped in different cities, but they always land the same way. Physicists call this entanglement: particles behave as if an invisible thread connects them. But what if the thread isn't instantaneous, just very fast — still not faster than light? Then some signal could slip between measurements, and the coincidences would be explained without any magic.

Galileo, legend has it, dropped balls from the Tower of Pisa to prove that heavy and light objects fall equally. This law formed the foundation of Einstein's theory of gravity. Today, scientists have turned an entire space station into such a tower.

A coin toss seems random, but in reality, physics decides everything: the force of the throw, air resistance, the surface's elasticity. If you knew all the details, you could predict the outcome. True randomness lives deeper — in the quantum world.

Genetic diagnostics is like comparing two photos taken with different cameras. If one camera slightly shifts the colors, the image will show "defects" that don't exist in reality.

All bodies fall the same: this was first observed by Galileo. Einstein elevated the observation to the equivalence principle: gravity and acceleration are indistinguishable, giving birth to curved spacetime.

Measured dipole moment of tantalum-181: 3.39 × 10⁻³² e·cm — like spotting a one-atom shift across the entire Solar System. An ordinary atomic nucleus is perfectly balanced, like a spinning top. In tantalum, that balance is broken: the positive and negative charges are slightly offset from each other.