The Maths That Waited a Hundred Years for a Machine

The listener is a child; the reader is a parent. This page is here so you can answer the questions your child asks after the story. The story script is available through the script button during playback.

What this is about

One man built a piece of mathematics that was useless for a hundred years. Then, a century later, a twenty-two-year-old who was studying mathematics and electrical engineering at the same time read it and connected it to the switches inside a telephone exchange.

The heart of this episode is not invention but connection. Claude Shannon made nothing new. He recognised that two existing things were the same thing — the "and" written on paper, and the "and" made out of wires.

And George Boole never lived to see what his mathematics was for. His interest, our source notes, "was of course not related to the theory of computation — he was a century too early for that" (DOI: 10.23943/princeton/9780691176000.003.0006).

What actually happened

• George Boole (1815–1864), born in Lincoln, England, on 2 November 1815. His father John was a cobbler who had taught himself geometry and trigonometry because they helped with his optical studies — and he taught them to his son.
• Boole was essentially self-taught. His formal schooling "stopped at what today would be a junior in high school." He nonetheless became a master mathematician held in the highest esteem by men who had graduated from Cambridge and Oxford (DOI: 10.23943/princeton/9780691176000.003.0003).
• In 1854 he published An Investigation of the Laws of Thought, the basis of what we now call Boolean algebra. It is not classical Aristotelian logic; today it lives with electrical engineers and mathematicians rather than philosophers (DOI: 10.23943/princeton/9780691176000.003.0002).
• Claude Shannon was born on 30 April 1916 in Petoskey, Michigan. He enrolled at the University of Michigan and graduated in 1936 with double bachelor's degrees in mathematics and electrical engineering. It was in a class there that he was introduced to Boole's algebra of logic (DOI: 10.23943/princeton/9780691176000.003.0003).
• At the time, the first real digital technology took the form of electromagnetic relays in telephone switching exchanges — switches and the logical connectives, the relay logical AND and OR, the bi-stable relay latch. This is exactly the technology Shannon used in his switching analyses (DOI: 10.23943/princeton/9780691176000.003.0005).
• In 1938 Shannon published A symbolic analysis of relay and switching circuits. In the paper's own words: complex electrical systems frequently require intricate interconnections of relay contacts and switches (automatic telephone exchanges, industrial motor control), and the paper gives a mathematical analysis of such networks, with particular attention to network synthesis — given the characteristics you want, find a circuit that has them (DOI: 10.1109/t-aiee.1938.5057767).
• Ten years later, in 1948, the same man published A Mathematical Theory of Communication, extending the theory to include the effect of noise in the channel and the savings available from the statistical structure of a message (DOI: 10.1002/j.1538-7305.1948.tb01338.x).
• The technology kept changing — relays → vacuum tubes → discrete transistors → integrated circuits. But "the one thing that remains the same is the math," the Boolean algebra (DOI: 10.23943/princeton/9780691176000.003.0005).

Questions your child may ask

"How can maths be useless?" Because the use for it did not exist yet. Boole's interest had nothing to do with computing machines — he was a century too early. For a child: "Even the person who made it didn't know what it was for. He made it because it was interesting."

"So what did Shannon invent?" Nothing, and that is the point. Boole's maths already existed. The telephone switches already existed. What Shannon did was see that they were the same thing. The lesson here is not "a genius made something from nothing" but "putting two far-apart things together is real work too."

"How can a switch be an 'and'?" Better to build it than to explain it (see Things to try together). The short version: depending on how you connect them, you get a circuit where the light comes on only if both switches are on, and one where it comes on if either is. The first is "and," the second is "or."

"Why did he study two things at once?" The record does not say why. But it turned out to be decisive. Plenty of people knew logic on paper, and plenty knew wires — very few carried both in one head.

"Did Boole know?" No. He died in 1864, long before computers. That is where the story lands: he did not know, but he wrote it down, and so someone could read it a hundred years later.

Ideas inside the story

• True and false can be calculated — the starting point of Boolean algebra.
• Same structure, different material — relays, tubes, transistors: the logic is the same. Machines change; the maths stays.
• Connecting is worth something — discovery is not only making new things.

What is established and what is not

Well established Boole's birth (2 November 1815, Lincoln), the cobbler father who taught him geometry, his largely self-taught education, The Laws of Thought (1854); Shannon's birth (30 April 1916, Petoskey), his 1936 double degree at Michigan, meeting Boole's algebra in a class there; the 1938 and 1948 papers; and the fact that the hardware changed from relays to integrated circuits while Boolean algebra stayed.

What this piece was careful about The famous Shannon anecdotes — the Bell Labs summer, juggling, the unicycle, the mechanical mouse that solved a maze — are not included. They are charming but absent from the abstracts we actually collected. Likewise, the common explanation that "switches in series make AND and in parallel make OR" is not stated as fact, because our sources do not specify the arrangement; the story says only "depending on how you connect them." Better to find out with an experiment.

Deliberately left out The circumstances of Boole's death and Shannon's later years — not needed for a child's story, and thinly sourced here.

Sources and what followed

Source papers

• A symbolic analysis of relay and switching circuits. DOI: 10.1109/t-aiee.1938.5057767 (1938)
• A Mathematical Theory of Communication. DOI: 10.1002/j.1538-7305.1948.tb01338.x (1948)
• George Boole and Claude Shannon (biographical sketches). DOI: 10.23943/princeton/9780691176000.003.0003 (2017)
• Boolean Algebra (introductory chapter). DOI: 10.23943/princeton/9780691176000.003.0002 (2017)
• Logic Switching Circuits. DOI: 10.23943/princeton/9780691176000.003.0005 (2017)
• Boole, Shannon, and Probability. DOI: 10.23943/princeton/9780691176000.003.0006 (2017)
• Sequential-State Digital Circuits. DOI: 10.23943/princeton/9780691176000.003.0008 (2017)
• The Logician and the Engineer. DOI: 10.23943/princeton/9780691176000.001.0001 (2017)
• Claude Shannon: Father of The Information Age. DOI: 10.12968/s0013-7758(2590335-2 (2024)

What followed

• Logic gained memory. The relay latch was refined into the clocked, edge-triggered flip-flop; wire those together and you have a machine that moves from state to state. Every sequential circuit today sits on this (DOI: 10.23943/princeton/9780691176000.003.0008).
• Information itself became mathematics. The 1948 paper brought noise and the statistical structure of messages into one theory, and communication, compression and cryptography all followed (DOI: 10.1002/j.1538-7305.1948.tb01338.x).
• Physics sets the ceiling. Neither Boole nor Shannon studied the physics of computation. Today quantum uncertainty and thermodynamics bound what is possible — but present-day technology falls far short of those limits, which means there is a long way still to go (DOI: 10.23943/princeton/9780691176000.003.0010).

Things to try together

• Build "and" and "or" with two switches. With a battery, a small bulb and two switches (or clip leads), let your child wire them in a single line, and then side by side. Have them work out when the light comes on in each case. Do not give the answer first — that observation is exactly what Shannon did.
• Play "both" and "either." Make sentences like "I have an umbrella AND it is raining" versus "I have an umbrella OR it is raining" and decide together whether each is true. That is what Boole did on paper.
• Look for things whose use came later. If your child loves something that gets a "what's that even for?", this is the story to bring out. Boole's maths waited a hundred years.