David Hilbert (1862-1943), shown in 1912. A German mathematician and one of the most influential mathematicians of the nineteenth and early twentieth centuries, he discovered and\/or developed a broad range of fundamental ideas in many areas, including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, mathematical logic, and foundations of mathematics (especially proof theory).
(Wikimedia Commons public domain image)<\/figcaption><\/figure>\n\u00a0<\/p>\n
A nice little interlude from Carlo Rovelli, Reality Is Not What It Seems: The Journey to Quantum Gravity<\/em>, translated by Simon Carnell and Erica Segre (Penguin, 2017), pages 74-77:<\/p>\n\u00a0<\/p>\n
Contrary to his popular image, Albert Einstein was not a great mathematician. \u00a0Indeed, he struggled<\/em> with mathematics. \u00a0In 1943, a nine-year-old girl named Barbara wrote to him about her own difficulties with math, and he responded \u201cDon\u2019t worry about experiencing difficulties with maths,*<\/strong><\/span> I can assure you that my own problems are even more serious!\u201d \u00a0And he wasn\u2019t entirely joking. \u00a0Others who were more mathematically gifted, such as his friend Marcel Grossman, often had to help him out.<\/p>\n\u00a0<\/p>\n
\u201cIt was his intuition as a physicist,\u201d says Carlo Rovelli, \u201cthat was prodigious\u201d (74).<\/p>\n
\u00a0<\/p>\n
During the last year of his thinking about what would become his general theory of relativity, Einstein found himself in competition with David Hilbert, who is generally reckoned among the greatest mathematicians of all time. \u00a0Having attended a lecture by Einstein in the north German university city of G\u00f6ttingen,<\/p>\n
\u00a0<\/p>\n
Hilbert immediately understood that Einstein was in the process of making a major discovery, grasped the idea and tried to overtake Einstein and be the first to write the correct equations of the new theory Einstein was slowly building. \u00a0The sprint to the finish line between the two giants was a nail-biting affair, eventually decided by a matter of just a few days. \u00a0Einstein, in Berlin, ended up giving a public lecture almost every week, each time presenting a different equation, anxious that Hilbert would not get to the solution before him. \u00a0The equation was incorrect every time. \u00a0Until, that is, by a hair\u2019s breadth \u2014 just marginally ahead of Hilbert \u2014 Einstein found the right one. \u00a0He had won the race.<\/span><\/p>\nHilbert, a gentleman, never questioned Einstein\u2019s victory, even though he was working on very similar equations at the time. \u00a0(75)**<\/strong><\/span><\/p>\n\u00a0<\/p>\n
At the time, the University of G\u00f6ttingen, where Hilbert was on the faculty (and a place that I first visited during my mission to Switzerland \u2014 thereby hangs a tale! \u2014 with all of the awe appropriate to its eminence in the history of physics and mathematics), was the seat of the most important school of geometry in the world. \u00a0And what Einstein needed in order to formulate his theory was a grasp of geometry in four dimensions. \u00a0Hilbert later reminisced that \u201cAny youngster on the streets of G\u00f6ttingen understands geometry in four dimensions better than Einstein. \u00a0And yet, it was Einstein who completed the task\u201d (cited on page 75). \u00a0Carlo Rovelli, himself a distinguished theoretical physicist, reflects on the reason for Einstein\u2019s victory, and for his scientific greatness:<\/p>\n
\u00a0<\/p>\n
Why? \u00a0Because Einstein had a unique capacity to imagine how the world might be constructed, to \u2018see\u2019 it in his mind. \u00a0The equations, for him, came afterwards; they were the language with which to make concrete his visions of reality. \u00a0For Einstein, the theory of general relativity is not a collection of equations; it is a mental image of the world arduously translated into equations. \u00a0(75-76)<\/span><\/p>\n\u00a0<\/p>\n
David Hilbert, too, placed a high value on imagination. \u00a0The Wikipedia entry on him reports that, when he was told that one of this students had dropped the study of mathematics in order to concentrate on writing poetry, Hilbert responded\u00a0\u201cGood. \u00a0He did not have enough imagination to become a mathematician.\u201d<\/p>\n
\u00a0<\/p>\n
*<\/strong><\/span>\u00a0 I\u2019m guessing that the translators are British. \u00a0The British say maths<\/em> (and trades unions<\/em> and drugs policy<\/em>) where Americans would say math<\/em> (and trade unions<\/em> and drug policy<\/em>). \u00a0How do people in Australia and New Zealand handle these terms? \u00a0I don\u2019t know. \u00a0Maybe they\u2019ll tell us.<\/p>\n**<\/strong><\/span>\u00a0 I\u2019m reminded of the \u201ccompetition\u201d between Charles Darwin and Alfred Russel Wallace, whom Darwin barely beat out with his publication of On the Origin of Species<\/em> in 1859. \u00a0Darwin is esteemed as one of the titans in human intellectual history; for most non-specialists, Wallace is barely a footnote.<\/p>\n\u00a0<\/p>\n
\u00a0<\/p>\n<\/body><\/html>\n","protected":false},"excerpt":{"rendered":"
\u00a0 \u00a0 A nice little interlude from Carlo Rovelli, Reality Is Not What It Seems: The Journey to Quantum Gravity, translated by Simon Carnell and Erica Segre (Penguin, 2017), pages 74-77: \u00a0 Contrary to his popular image, Albert Einstein was not a great mathematician. \u00a0Indeed, he struggled with mathematics. \u00a0In 1943, a nine-year-old girl named […]<\/p>\n","protected":false},"author":1019,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[10552,10219,10537,7914,10531,132,10528,10534,10525,10519,10522,10543,5730,10549,69,10540,9727,2195,10204,10216,10546,3901,2454],"class_list":["post-84587","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-carlo","tag-carlo-rovelli","tag-competition","tag-david","tag-dimensions","tag-einstein","tag-four","tag-general-relativity","tag-geometry","tag-gottingen","tag-hilbert","tag-imagination","tag-math","tag-mathematical-ability","tag-mathematics","tag-maths","tag-physicist","tag-physics","tag-relativity","tag-rovelli","tag-scientific-method","tag-theory","tag-university"],"yoast_head":"\n
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![\"Hilbert](\"https:\/\/wp-media.patheos.com\/blogs\/sites\/186\/2020\/04\/Hilbert.jpg\")
<\/a>