Unsolved problems

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Every specialist field has unsolved problems. The kind of problems that people have wasted entire careers on. The kind that maybe don’t even have solutions. But despite having this in common, different fields have different kinds of unsolved problems.

Mathematics

Lists of unsolved problems in mathematics date back to Hilbert’s problems, published in 1900. Today, fewer than half of the 23 original problems have accepted solutions. For example, consider Goldbach’s conjecture (Wikipedia):

even natural number greater than 2 is the sum of two prime numbers

Mathematicians have tried to prove this ever since Goldbach posed it in a 1742 letter to Euler. So far, they have ‘only’ proved weaker versions, such as allowing a sum of four prime numbers.

Solving this kind of problem typically requires new techniques in number theory, not some insight that escaped Goldbach three-hundred years ago. And even though using computers has shown that the conjecture holds for numbers up to 4 × 10¹⁸, partial evidence doesn’t count in pure mathematics. It only makes a formal proof seem more elusive.

Astonomy

Unsolved problems in astronomy include the Fermi paradox. On the question of whether extraterrestrial intelligence exists, the Fermi paradox asks a meta-question: why haven’t we found any evidence of it? This leaves two unlikely alternatives:

1. despite the overwhelmingly large number of stars in the observable universe, aliens don’t exist
2. extraterrestrial civilisations do exist – perhaps even in large numbers, but we didn’t notice them.

The Fermi paradox intrigues me, because evidence of extraterrestrial intelligence could appear at any moment. And yet, even if tomorrow brings radio transmissions from space, another civilsation’s Voyager probe, or actual flying saucers, we still might not know why it took so long, leaving the Fermi paradox unsolved.

Linguistics

Unsolved problems in linguistics include the Voynich manuscript. This interesting Wikipedia page, describes a fifteenth-century manuscript written in an undeciphered writing system. This detail from one of its 240 pages shows unfamiliar but often repeated letters and words, in fluid calligraphy:

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Intriguingly, like the Fermi paradox, the Voynich manuscript poses two unlikely alternatives:

1. no other example exists of this unknown writing system, probably used in this case by multiple scribes, and extensive research has failed to identify the language used
2. an elaborate hoax somehow managed to produce text that linguistic analyses developed hundreds of years later now identify as natural language.

As with the Fermi paradox, new evidence could illuminate the Voynich paradox at any time. Also, as with the Goldback conjecture, new techniques in the field could reveal a solution.

Software development

Industrial software development (excluding academic computer science) seems less likely to have such weighty unsolved problems. This adds perspective to our ongoing failure to meaningfully measure productivity, or even to find a proxy better than lines of code or electric energy consumption.

Not only does our industry lack an accurate, measurable and meaningful concept of productivity, we don’t know if such a thing can ever exist. And I can’t even tell if better techniques or more evidence would get us there.