            By 1912, however, Einstein had reached an impasse  , realizing that he needed to go beyond the mathematics that he knew and was familiar with.
<meaning-changed>             By 1912, however, Einstein had reached an impasse  , realizing that he needed to go beyond the mathematics that he knew and was familiar with.
 Einstein's 1911 thought experiment to demonstrate that the energy of gravitational mass must equal the energy of inertial mass To further clarify that the energy of gravitational mass must equal the energy of inertial mass, Einstein proposed the following cyclic process: (a) A light source is situated a distance above a receiver in a uniform gravitational field. A movable mass can shuttle between and (b) A pulse of electromagnetic energy is sent from to The energy is absorbed by (c) Mass is lowered from to releasing an amount of work equal to (d) The energy absorbed by is transferred to This increases the gravitational mass of to a new value (e) The mass is lifted back to , requiring the input of work (e) The energy carried by the mass is then transferred to completing the cycle. By 1912, however, Einstein had reached an impasse , realizing that he needed to go beyond the mathematics that he knew and was familiar with.