We study possible values of the global dimension of endomorphism algebras of 2-term silting complexes. We show that for any algebra A whose global dimension gl.dim A ≤ 2 and any 2-term silting complex P in the bounded derived category D^b(A) of A, the global dimension of End_{D^b(A)}(P) is at most 7. We also show that for each n > 2, there is an algebra A with gl.dim A = n such that D^b(A) admits a 2-term silting complex P with gl.dim End_{D^b(A)}(P) infinite.

The mathematical picture language project that we began in 2016 has already yielded interesting results. We also point out areas of mathematics and physics where we hope that it will prove useful in the future.

Starting from the roots of the equation 3^x + 4^x = 5^x discussed in the Tenth Grade, we utilized the method, the algebraic extension of the rational number eld, to produce the ways to judge whether the roots of the basic exponential equation with a form as a^x+b^x = c^x are rational or not. For equations with more than two terms on the left side, as is the equation a_1^x+a_2^x+
···

+a_n^x = d^x, the determination of whether the root was irrational was comparatively dicult.Therefore, we provided a prevalent method for the examination of the root of a three-term equation as well as a conclusion that if the equation doesn't have integer roots, the roots won't be a rational number with a denominator of two. Finally, based on the method, the algebraic extension of the rational number eld, we concluded that under special occasions, the root of the equation can't be some rational numbers with certain denominators.

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