Famous Mathematician by Theorem

Given a right triangle, then the sum of the squares of the short sides equals the square of the long side.

There exist no non-trivial integer solutions to the equation aⁿ + bⁿ = cⁿ for n>2.

Given a surjective group-homomorphism f: H → G, then the induced homomorphism f ' : H/Ker(f) → G is an isomorphism.

Let ω be a smooth (n-1)-form with compact support on an oriented, n-dimensional manifold-with-boundary M, where ∂ M is given the induced orientation. Then

Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete.

The integers are integrally closed.

Consider J an ideal in the polynomial ring in n variables over an algebraically closed field. Let V(J) be the vanishing locus of J in the affine n-space and I(M) the vanishing ideal of a algebraic set M in affine n-space. Then

Given and endomorphism f of a finite dimensional vectorspace and let P be its chracteristic polynomial. Then P(f) = 0, the zero endomorphism.

In any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.

The sum of the numbers of vertices and faces minus edges of a polyhedron equals 2.

Given a finite group G and a subgroup H, then the order of G is the product of the order of H and the index of H ind G.

Given a normal and separable field extension L/K, then any subgroup of the group of isomorphisms of L fixing K corresponds to a field extension L/F, where F is a field extension of K.

Every riemannian manifold can be isometrically embedded into real n-space for some natural number n.

There are infinitely many prime numbers.

When the sides meeting at each vertex of a triangle are extended by the length of the opposite side, the six endpoints of the three resulting line segments lie on a circle whose centre is the incentre of the triangle.