One widely held belief about Einstein is that he failed math as a student, an assertion that is made, often accompanied by the phrase “as everyone knows,” by scores of books and thousands of websites designed to reassure underachieving students. It even made it into the famous “Ripley’s Believe It or Not!” newspaper column.
Alas, Einstein’s childhood offers history many savory ironies, but this is not one of them. In 1935, a rabbi in Princeton showed him a clipping of the Ripley’s column with the headline “Greatest Living Mathematician Failed in Mathematics.” Einstein laughed. “I never failed in mathematics,” he replied, correctly. “Before I was fifteen I had mastered differential and integral calculus.”29
In fact, he was a wonderful student, at least intellectually. In primary school, he was at the top of his class. “Yesterday Albert got his grades,” his mother reported to an aunt when he was 7. “Once again he was ranked first.” At the gymnasium, he disliked the mechanical learning of languages such as Latin and Greek, a problem exacerbated by what he later said was his “bad memory for words and texts.” But even in these courses, Einstein consistently got top grades. Years later, when Einstein celebrated his fiftieth birthday and there were stories about how poorly the great genius had fared at the gymnasium, the school’s current principal made a point of publishing a letter revealing how good his grades actually were.30
As for math, far from being a failure, he was “far above the school requirements.” By age 12, his sister recalled, “he already had a predilection for solving complicated problems in applied arithmetic,” and he decided to see if he could jump ahead by learning geometry and algebra on his own. His parents bought him the textbooks in advance so that he could master them over summer vacation. Not only did he learn the proofs in the books, he tackled the new theories by trying to prove them on his own. “Play and playmates were forgotten,” she noted. “For days on end he sat alone, immersed in the search for a solution, not giving up before he had found it.”31
His uncle Jakob Einstein, the engineer, introduced him to the joys of algebra. “It’s a merry science,” he explained. “When the animal that we are hunting cannot be caught, we call it X temporarily and continue to hunt until it is bagged.” He went on to give the boy even more difficult challenges, Maja recalled, “with good-natured doubts about his ability to solve them.” When Einstein triumphed, as he invariably did, he “was overcome with great happiness and was already then aware of the direction in which his talents were leading him.”
Among the concepts that Uncle Jakob threw at him was the Pythagorean theorem (the square of the lengths of the legs of a right triangle add up to the square of the length of the hypotenuse). “After much effort I succeeded in ‘proving’ this theorem on the basis of the similarity of triangles,” Einstein recalled. Once again he was thinking in pictures. “It seemed to me ‘evident’ that the relations of the sides of the right-angled triangles would have to be completely determined by one of the acute angles.”32
Maja, with the pride of a younger sister, called Einstein’s Pythagorean proof “an entirely original new one.” Although perhaps new to him, it is hard to imagine that Einstein’s approach, which was surely similar to the standard ones based on the proportionality of the sides of similar triangles, was completely original. Nevertheless, it did show Einstein’s youthful appreciation that elegant theorems can be derived from simple axioms—and the fact that he was in little danger of failing math. “As a boy of 12, I was thrilled to see that it was possible to find out truth by reasoning alone, without the help of any outside experience,” he told a reporter from a high school newspaper in Princeton years later. “I became more and more convinced that nature could be understood as a relatively simple mathematical structure.”33
Einstein’s greatest intellectual stimulation came from a poor medical student who used to dine with his family once a week. It was an old Jewish custom to take in a needy religious scholar to share the Sabbath meal; the Einsteins modified the tradition by hosting instead a medical student on Thursdays. His name was Max Talmud (later changed to Talmey, when he immigrated to the United States), and he began his weekly visits when he was 21 and Einstein was 10. “He was a pretty, dark-haired boy,” remembered Talmud. “In all those years, I never saw him reading any light literature. Nor did I ever see him in the company of schoolmates or other boys his age.”34
Talmud brought him science books, including a popular illustrated series called People’s Books on Natural Science, “a work which I read with breathless attention,” said Einstein. The twenty-one little volumes were written by Aaron Bernstein, who stressed the interrelations between biology and physics, and he reported in great detail the scientific experiments being done at the time, especially in Germany.35
In the opening section of the first volume, Bernstein dealt with the speed of light, a topic that obviously fascinated him. Indeed, he returned to it repeatedly in his subsequent volumes, including eleven essays on the topic in volume 8. Judging from the thought experiments that Einstein later used in creating his theory of relativity, Bernstein’s books appear to have been influential.
For example, Bernstein asked readers to imagine being on a speeding train. If a bullet is shot through the window, it would seem that it was shot at an angle, because the train would have moved between the time the bullet entered one window and exited the window on the other side. Likewise, because of the speed of the earth through space, the same must be true of light going through a telescope. What was amazing, said Bernstein, was that experiments showed the same effect no matter how fast the source of the light was moving. In a sentence that, because of its relation to what Einstein would later famously conclude, seems to have made an impression, Bernstein declared, “Since each kind of light proves to be of exactly the same speed, the law of the speed of light can well be called the most general of all of nature’s laws.”
In another volume, Bernstein took his young readers on an imaginary trip through space. The mode of transport was the wave of an electric signal. His books celebrated the joyful wonders of scientific investigation and included such exuberant passages as this one written about the successful prediction of the location of the new planet Uranus: “Praised be this science! Praised be the men who do it! And praised be the human mind, which sees more sharply than does the human eye.”36
Bernstein was, as Einstein would later be, eager to tie together all of nature’s forces. For example, after discussing how all electromagnetic phenomena, such as light, could be considered waves, he speculated that the same may be true for gravity. A unity and simplicity, Bernstein wrote, lay beneath all the concepts applied by our perceptions. Truth in science consisted in discovering theories that described this underlying reality. Einstein later recalled the revelation, and the realist attitude, that this instilled in him as a young boy: “Out yonder there was this huge world, which exists independently of us human beings and which stands before us like a great, eternal riddle.”37
Years later, when they met in New York during Einstein’s first visit there, Talmud asked what he thought, in retrospect, of Bernstein’s work. “A very good book,” he said. “It has exerted a great influence on my whole development.”38
Talmud also helped Einstein continue to explore the wonders of mathematics by giving him a textbook on geometry two years before he was scheduled to learn that subject in school. Later, Einstein would refer to it as “the sacred little geometry book” and speak of it with awe: “Here were assertions, as for example the intersection of the three altitudes of a triangle in one point, which—though by no means evident—could nevertheless be proved with such certainty that any doubt appeared to be out of the question. This lucidity and certainty made an indescribable impression upon me.” Years later, in a lecture at Oxford, Einstein noted, “If Euclid failed to kindle your youthful enthusiasm, then you were not born to be a scientific thinker.”39
When Talmud arrived each Thursday, Einstein delighted in showing him the pro
blems he had solved that week. Initially, Talmud was able to help him, but he was soon surpassed by his pupil. “After a short time, a few months, he had worked through the whole book,” Talmud recalled. “He thereupon devoted himself to higher mathematics . . . Soon the flight of his mathematical genius was so high that I could no longer follow.”40
So the awed medical student moved on to introducing Einstein to philosophy. “I recommended Kant to him,” he recalled. “At that time he was still a child, only thirteen years old, yet Kant’s works, incomprehensible to ordinary mortals, seemed to be clear to him.” Kant became, for a while, Einstein’s favorite philosopher, and his Critique of Pure Reason eventually led him to delve also into David Hume, Ernst Mach, and the issue of what can be known about reality.
Einstein’s exposure to science produced a sudden reaction against religion at age 12, just as he would have been readying for a bar mitzvah. Bernstein, in his popular science volumes, had reconciled science with religious inclination. As he put it, “The religious inclination lies in the dim consciousness that dwells in humans that all nature, including the humans in it, is in no way an accidental game, but a work of lawfulness, that there is a fundamental cause of all existence.”
Einstein would later come close to these sentiments. But at the time, his leap away from faith was a radical one. “Through the reading of popular scientific books, I soon reached the conviction that much in the stories of the Bible could not be true. The consequence was a positively fanatic orgy of freethinking coupled with the impression that youth is intentionally being deceived by the state through lies; it was a crushing impression.”41
As a result, Einstein avoided religious rituals for the rest of his life. “There arose in Einstein an aversion to the orthodox practice of the Jewish or any traditional religion, as well as to attendance at religious services, and this he has never lost,” his friend Philipp Frank later noted. He did, however, retain from his childhood religious phase a profound reverence for the harmony and beauty of what he called the mind of God as it was expressed in the creation of the universe and its laws.42
Einstein’s rebellion against religious dogma had a profound effect on his general outlook toward received wisdom. It inculcated an allergic reaction against all forms of dogma and authority, which was to affect both his politics and his science. “Suspicion against every kind of authority grew out of this experience, an attitude which has never again left me,” he later said. Indeed, it was this comfort with being a nonconformist that would define both his science and his social thinking for the rest of his life.
He would later be able to pull off this contrariness with a grace that was generally endearing, once he was accepted as a genius. But it did not play so well when he was merely a sassy student at a Munich gymnasium. “He was very uncomfortable in school,” according to his sister. He found the style of teaching—rote drills, impatience with questioning—to be repugnant. “The military tone of the school, the systematic training in the worship of authority that was supposed to accustom pupils at an early age to military discipline, was particularly unpleasant.”43
Even in Munich, where the Bavarian spirit engendered a less regimented approach to life, this Prussian glorification of the military had taken hold, and many of the children loved to play at being soldiers. When troops would come by, accompanied by fifes and drums, kids would pour into the streets to join the parade and march in lockstep. But not Einstein. Watching such a display once, he began to cry. “When I grow up, I don’t want to be one of those poor people,” he told his parents. As Einstein later explained, “When a person can take pleasure in marching in step to a piece of music it is enough to make me despise him. He has been given his big brain only by mistake.”44
The opposition he felt to all types of regimentation made his education at the Munich gymnasium increasingly irksome and contentious. The mechanical learning there, he complained, “seemed very much akin to the methods of the Prussian army, where a mechanical discipline was achieved by repeated execution of meaningless orders.” In later years, he would liken his teachers to members of the military. “The teachers at the elementary school seemed to me like drill sergeants,” he said, “and the teachers at the gymnasium like lieutenants.”
He once asked C. P. Snow, the British writer and scientist, whether he was familiar with the German word Zwang. Snow allowed that he was; it meant constraint, compulsion, obligation, coercion. Why? In his Munich school, Einstein answered, he had made his first strike against Zwang, and it had helped define him ever since.45
Skepticism and a resistance to received wisdom became a hallmark of his life. As he proclaimed in a letter to a fatherly friend in 1901, “A foolish faith in authority is the worst enemy of truth.”46
Throughout the six decades of his scientific career, whether leading the quantum revolution or later resisting it, this attitude helped shape Einstein’s work. “His early suspicion of authority, which never wholly left him, was to prove of decisive importance,” said Banesh Hoffmann, who was a collaborator of Einstein’s in his later years. “Without it he would not have been able to develop the powerful independence of mind that gave him the courage to challenge established scientific beliefs and thereby revolutionize physics.”47
This contempt for authority did not endear him to the German “lieutenants” who taught him at his school. As a result, one of his teachers proclaimed that his insolence made him unwelcome in class. When Einstein insisted that he had committed no offense, the teacher replied, “Yes, that is true, but you sit there in the back row and smile, and your mere presence here spoils the respect of the class for me.”48
Einstein’s discomfort spiraled toward depression, perhaps even close to a nervous breakdown, when his father’s business suffered a sudden reversal of fortune. The collapse was a precipitous one. During most of Einstein’s school years, the Einstein brothers’ company had been a success. In 1885, it had two hundred employees and provided the first electrical lights for Munich’s Oktoberfest. Over the next few years, it won the contract to wire the community of Schwabing, a Munich suburb of ten thousand people, using gas motors to drive twin dynamos that the Einsteins had designed. Jakob Einstein received six patents for improvements in arc lamps, automatic circuit breakers, and electric meters. The company was poised to rival Siemens and other power companies then flourishing. To raise capital, the brothers mortgaged their homes, borrowed more than 60,000 marks at 10 percent interest, and went deeply in debt.49
But in 1894, when Einstein was 15, the company went bust after it lost competitions to light the central part of Munich and other locations. His parents and sister, along with Uncle Jakob, moved to northern Italy—first Milan and then the nearby town of Pavia—where the company’s Italian partners thought there would be more fertile territory for a smaller firm. Their elegant home was torn down by a developer to build an apartment block. Einstein was left behind in Munich, at the house of a distant relative, to finish his final three years of school.
It is not quite clear whether Einstein, in that sad autumn of 1894, was actually forced to leave the Luitpold Gymnasium or was merely politely encouraged to leave. Years later, he recalled that the teacher who had declared that his “presence spoils the respect of the class for me” had gone on to “express the wish that I leave the school.” An early book by a member of his family said that it was his own decision. “Albert increasingly resolved not to remain in Munich, and he worked out a plan.”
That plan involved getting a letter from the family doctor, Max Talmud’s older brother, who certified that he was suffering from nervous exhaustion. He used this to justify leaving the school at Christmas vacation in 1894 and not returning. Instead, he took a train across the Alps to Italy and informed his “alarmed” parents that he was never going back to Germany. Instead, he promised, he would study on his own and attempt to gain admission to a technical college in Zurich the following autumn.
There was perhaps one other factor in his decision to l
eave Germany. Had he remained there until he was 17, just over a year away, he would have been required to join the army, a prospect that his sister said “he contemplated with dread.” So, in addition to announcing that he would not go back to Munich, he would soon ask for his father’s help in renouncing his German citizenship.50
Aarau
Einstein spent the spring and summer of 1895 living with his parents in their Pavia apartment and helping at the family firm. In the process, he was able to get a good feel for the workings of magnets, coils, and generated electricity. Einstein’s work impressed his family. On one occasion, Uncle Jakob was having problems with some calculations for a new machine, so Einstein went to work on it. “After my assistant engineer and I had been racking our brain for days, that young sprig had got the whole thing in just fifteen minutes,” Jakob reported to a friend. “You will hear of him yet.”51
With his love of the sublime solitude found in the mountains, Einstein hiked for days in the Alps and Apennines, including an excursion from Pavia to Genoa to see his mother’s brother Julius Koch. Wherever he traveled in northern Italy, he was delighted by the non-Germanic grace and “delicacy” of the people. Their “naturalness” was a contrast to the “spiritually broken and mechanically obedient automatons” of Germany, his sister recalled.
Einstein had promised his family that he would study on his own to get into the local technical college, the Zurich Polytechnic.* So he bought all three volumes of Jules Violle’s advanced physics text and copiously noted his ideas in the margins. His work habits showed his ability to concentrate, his sister recalled. “Even in a large, quite noisy group, he could withdraw to the sofa, take pen and paper in hand, set the inkstand precariously on the armrest, and lose himself so completely in a problem that the conversation of many voices stimulated rather than disturbed him.”52
Einstein: His Life and Universe Page 4