If all the blackboards in the world disappear overnight, the mathematicians and physicists may suffer the most. The blackboard has witnessed many highlight moments in the history of science, those magical scientific ideas or core calculus have been written on it, and many palace-level scientists have iconic "blackboard portraits" photos. Because of this, you should never give a scientist a blackboard without permission.
Written by | Du Baojie
In the long history of human civilization, those great scientists have a common "assistant" - the blackboard, on which miraculous scientific ideas or core calculus have been written. So scholars are calling for not erasing what scientists have left on the blackboard, because that could be a crucial equation and source of inspiration.
Legend has it that when Roman soldiers broke into the home of Archimedes, an ancient Greece mathematician, astronomer and physicist, and killed him, his last request was "don't touch my circle." Valerius ·Maximus, a writer active in the first century A.D., also described this in his book Deeds and sayings worth remembering: "Don't, please, don't destroy the sand", because Archimedes was immersed in calculating a geometric figure, probably for the first time a mathematician shouted "don't erase".
Picture: The Death of Archimedes conceived and created by the artist丨Source: National Trust Images
In ancient Greece and Rome, a "blackboard" was simply a wooden board covered with fine ash or fine sand on which the user could draw and calculate with a stick.
When was the world's first chalkboard born? There is no way to know for sure, but some scholars believe that the blackboard originated in United Kingdom before the 19th century, when students learned to carry a small piece of wood as a writing board on which letters or prayers could be written. Later, Scottish educator James · Pillans invented the first blackboard for classroom teaching, and he taught geography lessons with easy-to-write blackboards and colored chalks.
图:大卫·希尔伯特(David Hilbert)和爱因斯坦的黑板肖像。 丨来源:google、wikipedia
In the 70s of the 18th century, Leonhard Euler, a pioneer ·of modern mathematics, began to draft equations on a large blackboard to record and express mathematical ideas. At the end of the 19th century and the 20th century, the chalkboard saw more highlights. Many of the world's leading mathematicians and scientists have iconic "blackboard portraits" of Hilbert, Poincaré, Kolmogorov, Einstein, Faraday, Schrödinger, Feynman, and many more. For these academic sages, although the blackboard is primitive and simple, it has a unique charm in visualization and exchange of ideas, they are constantly calculating and writing on the blackboard, exploring the beauty of mathematical logic and the profundity of physics, and promoting the exchange and discussion of top academic ideas under the combination of abstract and empirical expression.
Left: Lee Tsung-do; Right: Yang Zhenning
With the advancement of science and technology, the blackboard in the classroom is now being crowded out by the whiteboard, PPT multimedia presentation and even interactive LED whiteboard. In the future, will this tool, which is essential for scientific success, be endangered until it disappears completely? This has attracted the attention and discussion of many scholars.
Scientists' preference for chalkboards
If chalkboards and chalk disappear overnight, mathematicians may be one of the most afflicted.
An interesting story occurred in March 2015, when the Hagar Stationery in Aichi Prefecture, Japan, announced its closure. This news made many mathematicians anxious at once. It turns out that mathematicians from all over the world, except for Japan, love to use the chalk of the feather coat brand, because it is called the Rolls-Royce of chalk, which is less dusty, difficult to break, silky and not dirty, and can make mathematicians feel quite comfortable when writing on the blackboard. Fortunately, the feather coat stationery was later acquired by other companies and was not really out of stock.
Math lessons taught on a blackboard tend to be more engaging. The lecturer starts with an empty blackboard and gradually fills it with symbols and charts in real time, and the audience who wants to listen carefully has no choice but to listen and take notes, paying close attention to every move on the stage, because at some point in the lecture, the handwriting will be erased and replaced by new character images, and it is easy to lose your thoughts if you are not careful.
Picture: United States mathematician David · Eisenbud (David Eisenbud) teaches through the blackboard丨Source: Alchetron
For many mathematicians, demonstrating on the blackboard how formulas are derived and how ideas unfold is like a unique subject performance art, this exciting scene has impressed many audiences. For the audience, the information conveyed and absorbed by the blackboard book is a gradual process, and the lecturer presents the steps and methods at a speed that the audience can keep up with, rather than showing all the pre-drawn content on the slide.
There are still some inherent shortcomings in modern tools, PPT cannot let the audience see the process of deriving, thinking, and writing a large number of advanced mathematical proofs, and the disadvantage of whiteboard markers is that it is easy to write and suddenly run out of ink, and electronic whiteboards are prone to delay jamming or power failure...... Therefore, when it comes to mathematics and other theoretical subjects, the reliability of the chalkboard and chalk combination is particularly outstanding. In addition, writing on the blackboard requires subtle sound and patience, which is a prerequisite for creative immersion.
Finland late mathematician, historian of science, and writer Osmo Pekonen visited · world's leading mathematical research institutes in Paris, Cambridge, Mumbai, Princeton, and Stockholm, and found the same thing in all of them whose main task was to cultivate the mind: blackboards and chalk were everywhere, not only in offices and lecture halls, but also in hallways, elevators, and bathrooms.
Jessica Wynne, a well-known ·United States art photographer, includes 110 stunning chalkboard photographs from mathematicians around the world in her photo collection, Do Not Erase: Mathematicians and Their Blackboards, each accompanied by an interpretation essay recalling their work on the blackboard at the time.
Jessica Wynne工作照。 来源:Jessica Wynne推特
These mathematicians range from pure to applied mathematicians, from prestigious award-winning professors to promising gifted students. The images on the blackboard represent different fields of mathematics, such as algebra, category theory, combinatorics, dynamical systems and ergodic theory, finance, geometry, group theory, knot theory, measure theory, noncommutative geometry, number theory, quantum computing, and statistics, among other fields, the blackboard photographs and words together provide an enlightening reflection on the unique relationship between mathematics, physics, art, and creativity, which are elusive but beautiful.
As can be seen from the accompanying texts of many mathematicians, there is a deep emotional and even intimate relationship between mathematicians and the blackboard, and there is a transcendent communication. Even though the chalkboard has its limitations, a good experience still prevails. For mathematicians who are accustomed to seeing mathematics as art, the formulas and drawings that leap onto the blackboard seem to have a life of their own.
Pictured: Photographer's blackboard photo of Dido's problem and mixed Gaussian distribution丨Source: Jessica Wynne
For many scholars, the blackboard is an important communication tool between teachers, students, and peers, and many people are still willing to continue to use this traditional way of teaching and discussion, and pass on what they have learned to their students in the world of the blackboard, so as to do a good job in the "inheritance of mathematics", which is a tradition that has lasted for hundreds of years.
In fact, not only mathematicians, but also scientists in various fields, represented by physicists, are also loyal users of blackboards. Most whiteboards are too small for writing modern physics long equations, but a good chalkboard is large enough that it is easier to write physics, math equations, and formulas accurately and clearly with chalk than with markers.
Many research institutes understand this and place high-quality blackboards in every possible room to provide the necessary space for work and thinking. To some extent, we can score institutions based on the amount of blackboard space they provide for each researcher, because many theoretical physics studies may not require expensive experimental equipment, but they definitely can't do without a blackboard that is good enough.
Erase the blackboard to erase regrets
图：理查德·费曼（Richard Phillips Feynman）在多层黑板前进行讲解丨来源：Science Photo Library
It's hard to imagine that cleaners can be a danger factor in mathematicians and physicists trying to solve difficult problems. If they accidentally do their job - erase the blackboard, they may destroy the work of art created by geniuses and erase regrets. As a result, scholars also have a call for "do not erase".
Theoretical astrophysicist Alan ·Lightman described a fortuitous incident at Caltech in the early 1970s, when theoretical physicist Richard Phillips Feynman ·United States solved an equation describing the radiation of a black hole on a blackboard, triggering a very different line of thought from the mainstream of physics at the time. Dr. Lightman came back the next day to copy down the equations so that he could explore them further, only to find that the blackboard had been wiped clean. Shortly thereafter, Stephen · Hawking made a similar calculation to form Hawking's radiation theory and became famous.
Another blackboard story comes from Albert Einstein. Einstein's mass-energy equation E=mc^2 is well known, and although the original copy of the blackboard has long since been erased, it is conceivable how brilliant the blackboard became when he first wrote the formula on the blackboard.
In May 1931, Albert Einstein was invited from Berlin to Oxford University to give three lectures, but there was no translation for him, and despite Einstein's best efforts, the German language made it difficult for Oxford scholars to understand the complex theory of relativity. In his speech, Einstein not only wrote new equations, but also drew some diagrams, explained them by constantly comparing them on curves with chalk, and repeatedly turned to the audience and the blackboard.
Picture: Einstein's chalkboard from the collection of the Oxford Museum of the History of Science丨Source: historic Oxford
One of the "Einstein blackboards" was rescued by some professors and housed in the Oxford Museum of the History of Science, and is now a treasure trove of the museum, with visitors almost worshipping it as soon as they enter the museum, finding its place and longing to establish some kind of connection with the almost mythical grandmaster of physics.
The equations kept on the "Einstein Blackboard" are his new model of the universe proposed in May 1931, that is, the Friedman-Einstein universe, and the equations relate the age, density and size of the universe. It is said that another blackboard used by Einstein in his lecture was actually donated to the museum, but it was accidentally erased by the museum cleaners.
As a physicist's performance space, the blackboard is like an abstract painting in the eyes of outside artists, because it has great academic significance and depth under its surface, trying to reveal a universal truth, which has given the artist a lot of inspiration.
Spain contemporary artist Alejandro Guijarro has taken a series ·of blackboard photographs of physics professors at CERN, Cambridge, Oxford, Stanford, and the University of California, Berkeley, and has curated an exhibition. These blackboards, which have not yet been wiped clean, show the fragmentary thoughts, fantastic ideas or interpretations of physicists, and the public may not understand the content of the characters, but they can appreciate the sheer intellectual beauty.
Picture: Blackboard-themed work completed by artists and scientists丨Source: Alexa Meade
There are also artists who make secondary creations based on the blackboard books of scientists. United States installation artist Alex·a Meade uses a classic trompe l'oeil concept that allows scientists to merge with their own chalkboard content. In 2015, as an artist-in-residence at the Waterloo Institute for Circumferential Theoretical Physics in Waterloo, Canada, she created an installation inspired by the work of scientists, which became one of her most famous masterpieces.
On the Home of the official website of the London Institute for Mathematical Sciences (LIMS) in United Kingdom, it is not how good the environment of the institute is and how many honorary awards it has received, but wonderful blackboard book works, which show the outside world how scientists break classic barriers on the blackboard, perform exponential Kaufmann scaling and Mahler measure calculus, etc., these concise blackboard photos are beautiful. It has an inexplicable appeal.
Figure: Researchers are carrying a large blackboard丨Source: LIMS
In reality, too, each room of the LIMS Institute is dominated by a large blackboard, which is either fixed to the wall or placed on a stand like a religious painting, all covered in runes, geometric lines, and mathematical graffiti.
·Thomas Fink, director of LIMS, explains: "The chalkboard is the best tool to get out of a rut. Most of your calculations are made on paper. Then, when you hit a dead end, you can go to the blackboard and share the problem with your colleagues. But the funny thing is that in the process of writing a problem on the blackboard, you can often solve it yourself. ”
The blackboard, as if it had some kind of magic, gave the brain a clear range of thoughts, it did not have many distracting elements, and its limitations were its strengths, because it forced science to think deeply, and on this very pure medium, innovative ideas and inspirations would often emerge when calculating in chalk step by step.
"Don't erase" the chalkboard spirit
The scene of the teacher brushing and writing on the blackboard is engraved in the memories of many generations, and it is nostalgic every time I think of it. The image of Jiang Lifu, the pioneer of modern Chinese mathematics, is also engraved in the history of mathematics along with the blackboard.
The first university in modern China, the Department of Advanced Mathematics, is thought to have originated at Peking University. In the autumn of 1913, the Department of Mathematics of Peking University (then known as the Department of Mathematics) welcomed new students, and Cai Yuanpei, then president of Peking University, made the mathematics series the first department of Peking University, paving the way for modern mathematics education and scientific research in China.
By the 20s of the 20th century, universities all over China had established mathematics departments, and mathematics research ushered in an unprecedented prosperity, such as the mathematics department of Nankai University.
Picture: In 1955, Jiang Lifu stood in front of the blackboard to teach students丨Source: Men of Mathematics
In 1920, Jiang Lifu returned from Harvard and founded the Department of Mathematics at Nankai University, the second mathematics department in China. At that time, he took charge of a department by himself, while dealing with daily administrative affairs, while opening several courses at the same time, including advanced calculus, spatial analytic geometry, projective geometry, complex variable function theory, advanced algebra, differential geometry, non-Euclidean geometry, etc., his students Chern Shiingshen, Jiang Zehan, Wu Daren, Liu Jinnian, Sun Benwang, etc., later became outstanding mathematicians in China and even in the world.
Picture: In the 70s of the last century, Yang Zhenning visited Jiang Lifu in his later years, and during the Southwest Associated University, Jiang Lifu's student Chen Shiingshen was Yang Zhenning's mathematics teacher. 丨Source: cnxw
When many mathematicians recall Mr. Jiang Lifu, he always remembers the appearance of his lectures in front of the blackboard. The light in the classroom comes from the left, Jiang Lifu is used to standing in front of the left side of the classroom to teach, generally drawing with chalk with bare hands, only using a ruler when special needs, the board book and drawing are neat and capable, and he pays great attention to saving blackboard space, and the chalk system of different colors is not flooded, a major feature is that he often does not use teaching materials when teaching, he just writes down the outline points of the day on a few pieces of waste calendar paper, and then unhurriedly and gradually unfolds on the blackboard.
This kind of teaching method of completely getting rid of the textbook on the blackboard seems simple, but it often requires the teacher to fully grasp the content before it can be controlled, and it requires a high degree of concentration of thinking and solid logical reasoning ability, and then drives students to follow their own pace to achieve the best teaching effect.
Mathematician Wu Daren wrote when recalling Mr. Jiang Lifu: "He is like a guide who is familiar with geography, guiding students to explore the hidden world, so that sometimes you seem to be in the middle of the peaks and loops, and sometimes you feel suddenly enlightened, and you do not feel the fatigue of climbing." Listening to Mr. Jiang's lectures is a rare enjoyment. I think you can only do it if you stand at a considerable height. ”
In a sense, the scholars' call for "not erasing" the blackboard is also a reminder to future generations not to erase the fine learning tradition and research ability left by their predecessors, and to preserve and continue the spirit of the pioneers, the wisdom of governing people, and the academic feelings of lifelong dedication.
Resources
[1] https://link.springer.com/article/10.1007/s00283-023-10321-2
[2] https://wuli.iphy.ac.cn/en/article/pdf/preview/74400.pdf
[3] https://hr.edu.cn/xueshu/202209/t20220908_2244759.shtml
[4] https://moocun.com/Home/News/detail/info_id/5561.html
[5] http://www.banyuetan.org/chcontent/wh/pd/2014829/110567.shtml
[6] https://lims.ac.uk/about/
[7] https://www.math.pku.edu.cn/xygk/xssys/index.htm
[8] https://www.sohu.com/a/149128824_642678
[9] https://www.tsinghua.org.cn/info/1952/37666.htm
[10] https://blog.sciencenet.cn/blog-528739-1220822.html
[11] https://pansci.asia/archives/123298
[12] https://news.nankai.edu.cn/nkrw/system/2023/09/01/030057658.shtml
[13] https://www.global-sci.org/v1/mc/issues/9/no2/freepdf/3s.pdf
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