Two teenage girls cracked a mathematical code that has stood for thousands of years: Ne’Kiya Jackson and Calcea Johnson, ...

First, we present a division theorem for two matrices, which guarantees that the remainder matrix is either the zero matrix or a nonsingular matrix with a smaller absolute determinant than that of the ...

Euclid’s structured and methodical approach, starting with axioms and building up to complex theorems through logical deductions, was revolutionary for its time. This work not only consolidated ...

For Euclidean lattices, periodicity leads to the formulation of Bloch band theory (29), whereby energy levels and wave functions are characterized by a well-defined crystal momentum quantum number. It ...

In this paper, the notion of equitable partitions (EP) is used to study the eigenvalues of Euclidean distance matrices (EDMs). In particular, EP is used to obtain the characteristic polynomials of ...

How Trigonometry Shapes the World,” Matt Parker recounts, for instance, how computers were a “game-changer in the field of ...

AlphaProof showed its prowess on questions from this year’s Mathematical Olympiad — a step in the race to create substantial proofs with artificial intelligence.

Main theorem Let X X and Y Y be nonempty closed subsets of Euclidean space. Then X X and Y Y are magnitude homology equivalent if and only if their cores are isometric. This is part — the most ...

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In this regard, we show that the abilityto draw a geometric structure, as well as theorems and propositions related to these structures, can bereduced to the rules of the invariance of information ...

In this regard, we show that the abilityto draw a geometric structure, as well as theorems and propositions related to these structures, can bereduced to the rules of the invariance of information ...