PLANCK SOLVES A COMPLEX PROBLEM FOR HIS FORMER STUDENT. PLANCK, MAX. 1858-1947. Autograph Letter Signed ('M. Planck') to Dr. Ludwik Silberstein solving an equation for a special case that Silberstein had inquired about, 2 pp, 8vo (223 x 142 mm), single leaf, Berlin, October 5, 1897, small tear at upper margin. WITH: Photograph Signed and Inscribed in the mount ('M. Planck'), 90 x 67 mm gelatin silver print profile portrait, on a printed card celebrating his 80th birthday, Berlin May 3, 1938, his wistful note reads [translated], 'I also remember beautiful days in Vienna and still hear your wonderful voice. With best wishes, Yours truly, M. Planck.' AN INTRIGUING SCIENTIFIC LETTER WALKING HIS FORMER STUDENT, LUDWIK SILBERSTEIN, THROUGH A COMPLEX MATH PROBLEM INVOLVING A SINGULARITY. Likely following on from his 1896 paper on fluid dynamics, Silberstein had written to Planck for help with a particular equation in the special case where two variables c and ⍺ become equal, creating a singularity (a division by zero). Planck responds here in detail effortlessly instructing Silberstein in the resolution, before adding 'as you can easily verify later.' Silberstein, whose thesis advisors included both von Helmholtz and Planck, was known primarily for his contributions to Einsteinian relativity theory and somewhat infamously for his public disagreements with Einstein himself. But in his important 1896 paper on fluid dynamics, Silberstein studied the conditions under which eddies, or circular currents, develop in a frictionless fluid, laying some of the groundwork for the study of atmospheric turbulence and modern meteorology. These equations are likely an extension of that work, albeit with the more complex mathematics evinced here including second-order derivatives, complex numbers, and the concept of a singularity, which in terms of fluid dynamics may, for example, relate to a vortex. In 1897, Planck published his Vorlesungen Über Thermodynamik [trans, Theory of Thermodynamics]. Two years later, he would derive Planck's constant before changing our conception of physics with the Planck postulate that electromagnetic energy could be emitted only as quanta, essentially creating quantum physics in the process. Max Born called Planck's insight, '... the most revolutionary idea which ever has shaken physics' ('Max Planck,' Obituary, 1948). Planck and Silberstein continued their correspondence throughout their life, with much of that correspondence now held at the American Institute of Physics. While Planck was very helpful regarding Silberstein's equations, his post-script indicates his limits: 'The Verhandlungen der Physikalischen Gesellschaft are free only for dues paying members.' Sold with a fine photograph of Planck at 80 years old, signed and very warmly inscribed in the mount, this 1897 letter offers a rare look at one of the world's most important physicists performing complex mathematics at the height of his powers. With thanks to Distinguished Professor Jack Copeland for information about Ludwik Silberstein. For further information on this lot please visit Bonhams.com For further information about this lot please visit the lot listing