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Equation 3 · Part 2 · Mathematics, Proof, and Scientific Computation in 2035: Scenarios, Signals, and Falsifiable Predictions

Symbol n^omega

O(nω)O(n^{\omega})
nωn^{\omega}

What this part means

non^omega is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

non^omega is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

On the complexity side, progress has been real but almost entirely incremental and mostly orthogonal to the central P vs NP question itself. The matrix multiplication exponent ω\omega — the smallest number such that two n ×\times n matrices can be multiplied in O(nωn^{\omega}) arithmetic operations — sets an upper bound relevant to a huge range of numerical linear algebra, and it has been chipped downward repeatedly. A January 2024 paper identified a previously unrecognized inefficiency in the leading “laser method” approach and used the fix to bring the best known upper bound to approximately 2.371552 [ 5 ] , continuing a sequence of small improvements stretching back decades. No one working on…

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An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

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