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While the P vs NP problem is mainly approached form the point of view ofdiscrete mathematics, this paper proposes reformulations into the field ofabstract algebra, geometry, fourier analysis and of continuous globaloptimization - which advanced tools might bring new perspectives and approachesfor this question. The first one is equivalence of satisfaction of 3-SATproblem with the question of reaching zero of a nonnegative degree 4multivariate polynomial (sum of squares), what could be tested from theperspective of algebra by using discriminant. It could be also approached as acontinuous global optimization problem inside $[0,1]^n$, for example inphysical realizations like adiabatic quantum computers. However, the number oflocal minima usually grows exponentially. Reducing to degree 2 polynomial plusconstraints of being in $\{0,1\}^n$, we get geometric formulations as thequestion if plane or sphere intersects with $\{0,1\}^n$. There will be alsopresented some non-standard perspectives for the Subset-Sum, like throughconvergence of a series, or zeroing of $\int_0^{2\pi} \prod_i \cos(\varphi k_i)d\varphi $ fourier-type integral for some natural $k_i$. The last discussedapproach is using anti-commuting Grassmann numbers $\theta_i$, making $(A \cdot\textrm{diag}(\theta_i))^n$ nonzero only if $A$ has a Hamilton cycle. Hence,the P$\ne$NP assumption implies exponential growth of matrix representation ofGrassmann numbers. There will be also discussed a looking promisingalgebraic/geometric approach to the graph isomorphism problem -- tested tosuccessfully distinguish strongly regular graphs with up to 29 vertices.

P?=NP as minimization of degree 4 polynomial, integration or Grassmann number problem, and new graph isomorphism problem approaches