Mathematical beauty

Mathematical beauty is the aesthetic pleasure derived from the abstractness, purity, simplicity, depth or orderliness of mathematics. Mathematicians may express this pleasure by describing mathematics (or, at least, some aspect of mathematics) as beautiful or describe mathematics as an art form, (a position taken by G. H. Hardy) or, at a minimum, as a creative activity. Comparisons are made with music and poetry. Mathematicians describe an especially pleasing method of proof as elegant. Depending on context, this may mean: A proof that uses a minimum of additional assumptions or previous results. A proof that is unusually succinct. A proof that derives a result in a surprising way (e.g., from an apparently unrelated theorem or a collection of theorems). A proof that is based on new and original insights. A method of proof that can be easily generalized to solve a family of similar problems. In the search for an elegant proof, mathematicians often look for different independent ways to prove a result—as the first proof that is found can often be improved. The theorem for which the greatest number of different proofs have been discovered is possibly the Pythagorean theorem, with hundreds of proofs being published up to date. Another theorem that has been proved in many different ways is the theorem of quadratic reciprocity. In fact, Carl Friedrich Gauss alone had eight different proofs of this theorem, six of which he published. Conversely, results that are logically correct but involve laborious calculations, over-elaborate methods, highly conventional approaches or a large number of powerful axioms or previous results are usually not considered to be elegant, and may be even referred to as ugly or clumsy. Some mathematicians see beauty in mathematical results that establish connections between two areas of mathematics that at first sight appear to be unrelated. These results are often described as deep. While it is difficult to find universal agreement on whether a result is deep, some examples are more commonly cited than others.

Arterial pulse wave modeling and analysis for vascular-age studies: a review from VascAgeNet

Vasiliki Bikia, Patrick Segers

Arterial pulse waves (PWs) such as blood pressure and photoplethysmogram (PPG) signals contain a wealth of information on the cardiovascular (CV) system that can be exploited to assess vascular age and identify individuals at elevated CV risk. We review th ...

AMER PHYSIOLOGICAL SOC2023

Seeking the new, learning from the unexpected: Computational models of surprise and novelty in the brain

Arterial pulse wave modeling and analysis for vascular-age studies: a review from VascAgeNet

Arterial pulse wave modeling and analysis for vascular-age studies: a review from VascAgeNet

Seeking the new, learning from the unexpected: Computational models of surprise and novelty in the brain