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Already in school, he showed great ability for mathematics and passed the entrance examination to university with high distinction. But that was it for Hans Frederik, since he had no hope of ever attending any institute of higher learning. The family was far too poor to put their junior through college. To escape the bleak future in the Old World, the Blichfeldts emigrated to the United States in 1888. At first, the New World was not much better than the Old, and 15 year-old Hans Frederik had to start earning a living. He was a tall, strong youth and quickly found work as a farmhand and laborer in sawmills and lumber companies in Nebraska, Wyoming, Oregon and Washington. “I worked with my hands doing everything, East and West across the country” he recounted later.

But the New World did afford opportunities for the upwardly mobile and, after a while, Blichfeldt became a draftsman for the engineering department of the County of Whatcom, Washington. That was quite a step up from lumbering, but it wasn’t the end of the line for Blichfeldt. He became a surveyor. His new colleagues marveled at his skill to do arithmetic in his head. To laymen, such ability always seems a sure indication of mathematical genius, and they suggested he study at university. Blichfeldt would have liked to act on their advice but saw no possibility of doing so. As luck would have it, however, his skills came to the attention of the county superintendent of schools who wrote an enthusiastic letter of recommendation to Stanford University. Stanford University had been founded just three years earlier by the railway pioneer Leland Stanford and his wife, to commemorate their son, Leland Stanford Jr. who had died of typhoid fever at the age of fifteen. Within a few years of its founding, Stanford University had established itself as one of the foremost centers of learning in the United States. In 1894, the 21-year old Blichfeldt joined “the Farm”, as Stanford University was to became affectionately known, as a special student. It took him only two years to complete his B.A. After that it took him just one additional year to be awarded the Master’s degree. The question was, what to do now. A visit to Germany was a must for budding mathematicians, but Blichfeldt, again, was out of money. However, the young man had made a name for himself at Stanford. One of his professors, who recognized the student’s gifts, came to the rescue by loaning him the necessary funds. Blichfeldt was off to Leipzig.

Scandinavians abroad, like expats all over the world, tend to band together, and Blichfeldt was no exception. He became friendly with Sophus Lie from Norway, the erstwhile mentor of Axel Thue. But Blichfeldt did not waste the occasion as Thue had done five years earlier. He used his proximity to the great Lie to his advantage, and learnt a thing or two from his thesis supervisor. Nevertheless, he was in a great hurry to finish his doctorate and it took him again barely a year to complete his dissertation.

The year 1898 found him back at Stanford and stayed there until his retirement in 1938. The same year the King of Denmark made him a Knight of the Order of Dannebrog. He received the white and red-enameled cross in silver, with which the King rewards faithful servants for meritorious civil or military service, or for a particular contribution to the arts, sciences or business life. Blichfeldt died in Palo Alto in 1945.

Mozartkugeln:

I like to compare Blichfeldt’s spheres with my favorite Austrian sweets, the Mozartkugeln (Mozart balls). These delicious little balls have a core made of marzipan, surrounded by a layer of dark nougat crème, followed by a layer of light nougat crème, followed by a coat of chocolate. If we now assume – I don’t know if this is strictly true – that marzipan is heavier than dark nougat crème, that dark nougat crème is heavier than light nougat crème, and that light nougat crème is heavier than chocolate, we have nothing else but Blichfeldtkugeln. (The latter don’t have the same ring to their name, however.)

Paul Erdös:

How is it that papers with his name still keep appearing, even though Erdös is long dead? No, it is definitely not because he is writing to us from the beyond. The reason is that papers of which he is a co-author are still being revised.

C. A. Rogers:

If a picture is worth a thousand words then this learned professor obviously preferred a thousand words to a picture.

Lindsey:

Why is it that mathematicians are so talkative but so disapproving of illustrations? Are words more rigorous than figures? Or are mathematicians uncomfortable when they are too easily understood? Do pictures look too cute, like cartoons, thereby detracting from the seriousness of the subject? It is the same conduct that sociologists and representatives of other soft sciences are chided for: using jargon instead of plain language. Learned gibberish, and the lack of illustrations, holds the close-knit community of scholars together, and keeps outsiders were they belong: out. A more subtle reason may be that illustrations get fairly complicated for three dimensions. For higher dimensions they become impossible. Whatever the reason, a well-chosen picture here, or an illustration there, would make the subject of mathematics more accessible to everyone.

Doug Muder:

Doug and his wife Deb are active in the Unitarian Universalist church and are invited to give lay sermons about once a year. Muder has held forth from the pulpit on such highly interesting topics as spiritual healing, forgiveness, the shape of the next religion, happiness and the goodness of people whether to have children and why he and his wife decided against it. Even though his essays, sermons, fairy tales and poems can be found and read all over the Web, Doug Muder is a rather private person. He doesn’t like to be bothered and a colleague who once tried to track him down on the Internet considered hiring a private detective to find him.

We will not deal with his sermons here, even if they are a worthy read. It is the 1988 paper that captures our attention.

Fortunately, all the surgery occured only in the mathematician’s minds, because no human hand would be steady enough to perform such operations.[i]

Upper bound:

The upper bound inched downwards like the world record in the 100 meter dash. On July 6, 1912, the American sprinter Donald Lippincott covered the distance in 10.6 seconds. On June 16, 1999, in the Olympic city of Athens, the American athlete Maurice Greene lowered the world record to 9.79 seconds. The world record had improved by 7.6% over a period of 87 years. During about the same period, the upper bound for the packing density decreased from 0.883 by 14.2%.[ii]