How Close to the Sun in a Perfectly Reflective Suit?

An uncited 1871 account of a magnetic storm halting a train looked like the earliest case of space weather hitting technology. Railway history, observatory data and a handwritten annotation say the date is wrong.

Three independent routes to the same closed form, plus a sign slip in the contour step that is easy to copy without noticing.

As AI increasingly solves complex mathematical problems, the value and future of a PhD in Mathematics are being questioned. This article delves into the current landscape, the role of human insight, and the enduring significance of mathematical research in academia.