How to evaluate diverging sources and why it is important:
There is a widely held notion that Einstein was bad at math, or flunked math, or that “every boy in the streets of Gottingen understands more about four dimensional geometry than Einstein” (the great mathematician and contemporary of Einstein, David Hilbert). Yet we find sources claiming the following:
“Contrary to another myth, Einstein did not have difficulties in mathematics. Indeed, his preteen replacement of religious zeal with scientific fervor involved mathematics too. He was given a book on Euclidean geometry, which he devoured, even trying to prove theorems on his own before reading the solutions in the book. In his autobiography he referred to this math textbook as the ‘holy geometry book’– an extraordinary phrase for such a prosaic subject, but perhaps significantly it was an unconscious reference to his geometry book replacing the previous other “Holy Book” around the same time in his life. He went on to higher mathematical texts, teaching himself and mastering calculus by age sixteen. All of which explains the letter from his mathematics teacher that was in his pocket as he crossed into Italy.”
Topper, D. R. (2013) How Einstein Created Relativity out of Physics and Astronomy (Astrophysics and Space Science Library). Springer.
So did Einstein really have no difficulties with mathematics? Does the equivalence of “Einstein” and “genius” hold for mathematics as it is holds in general usage (i.e., “He’s no Einstein” or “She’s like an Einstein when it comes to problem solving”)? Well, the first problem is reading between the lines of the above. When I was in 2nd grade, I read Moby Dick cover-to-cover. I devoured it, mainly because I knew enough to know it was great literature. I understood almost nothing at that point of what I read. It was beyond me. In the introduction to a delightful math book I know of, the author notes how fascinated he was not just by a calculus text he read as a youngster, but a particular integral. Yet he didn’t really understand the integral or the text. And as for finding geometry sacred, the Greeks beat Einstein to this position on geometry by some ~2500 years, yet it was some ~1000 years until any culture was able to produce mathematicians able to make the jump of a pre-college student from geometry to algebra (actually, these days algebra tends to be introduced before geometry, but the jump is still possible to make in a year or less rather than a millennium). What we don’t find is why Einstein’s famous 1905 derivation E=mc2 was wrong (Ohanian, H. C. (2009). Did Einstein prove E= mc 2?. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 40(2), 167-173.), why so many of the mathematical developments in work began by Einstein like special and general relativity were developed by other physicists (Minkowski, Lorentz, etc.), or why Einstein relied on mathematicians or physicists better in mathematics than he:
“Einstein is generally recognized as the greatest physicist of the 20th century and perhaps the greatest physicist since Newton, though Faraday and Clerk Maxwell are close competitors… But unlike Newton, Einstein was not a mathematician. He used mathematics in an essential way but he did not create it and he relied on his colleagues for technical help.”
Atiyah, M. (2007). Einstein and Geometry. In S. R. Wadia (Ed.) The Legacy of Albert Einstein: A Collection of Essays in Celebration of the Year of Physics (pp. 15-23). World Scientific.
“If the air of Ulm [Einstein’s birthplace] carries some mathematical miasma, it did little good to Einstein. He always remained a rather mediocre mathematician. In his autobiography (or ‘obituary,’ as he liked to call it) written in his late years in Princeton, he confessed, ‘I had excellent teachers, so I really could have gotten a profound mathematical education…That I neglected mathematics to a certain extent had its cause not only in that my interest in natural sciences was stronger than in mathematics, but also in the following strange experience. I saw that mathematics was split up into many specialties, each of which could absorb the short lifespan granted to us. Thus I saw myself in the position of Buridan’s ass, which was unable to decide on a particular bundle of hay…’ Einstein preferred to leave any difficult mathematical labors to others, such as his mathematician friend Marcel Grossman, during his years in Zurich and the several other mathematical assistants he later employed during his years in Berlin and Princeton, whose job it was to grind out the mathematical details that Einstein found too troublesome. He called them his Rechenpferde, or his ‘calculating horses,’ a reference to Clever Hans the horse…”
Ohanian, H. C. (2008). Einstein’s mistakes: The Human Failings of Genius. WW Norton & Company.
Any significant reading in a given subject at an academic level will yield divergences as well as outright contradictions. It is thus important to be able to evaluate sources before one happens upon direct contradictions or divergences.