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Illegal Maths?

As mathematicians, we often like dealing with absolute truths. There are 5 Platonic solids that’s never going to change. We can be certain that the angle in a semi circle is a right-angle. 1+1 =2 and that’s a fact*.

But what happens when people try to enshrine mathematical truths into law. Or worse, what happens when people try to enshrine mathematical falsehoods into law?

Well this is exactly what nearly happened in Indiana in 1897. An amateur mathematician proposed a bill (bill #246) which, if passed, would have made a whole number of things that we know to be mathematically false, legally true.

Edwin J. Goodwin was a physician and believed he had discovered a method by which he could square the circle. For those unfamiliar, this is problem posed by the ancient Greeks. It asks whether it is possible to construct in a finite number a square with the same area as a given circle using only a compass and straight edge. Spoiler alert: it’s not possible. But Edwin J. Goodwin believed it was. What’s more, he wanted legal recognition that it was possible. He approached his state representative who then introduced the bill to the house under the title (brace yourselves):

“A Bill for an act introducing a new mathematical truth and offered as a contribution to education to be used only by the State of Indiana free of cost by paying any royalties whatever on the same, provided it is accepted and adopted by the official action of the Legislature of 1897”

Catchy, isn’t it?

A square and a circle with equal areas

Goodwin backed up his claim with credentials though! His methods for trisecting the angle (which is impossible) and doubling the cub (also impossible), had been published in the American Mathematical Monthly! It doesn’t take much digging to find out though that these were published at Goodwin’s own request.

You may at this point be wondering what was so bad about this bill? Squaring the circle is a fun curiosity. Nothing more. Someone who is legally minded, writing for others who are similarly afflicted, would now start talking about the precedent it might set, but I am not that someone. I am a mathematician, writing for mathematicians and am about to write words that will strike fear into the bravest of you:

As a consequence of the bill, by law \sqrt{2} = \frac{10}{7} would be correct. Even worse, it would be legal fact that \pi = 3.2. The horror. This was neatly tucked away towards the end of section 2, in the following paragraph:

“Furthermore, it has revealed the ratio of the chord and arc of ninety degrees, which is as seven to eight, and also the ratio of the diagonal and one side of a square which is as ten to seven, disclosing the fourth important fact, that the ratio of the diameter and circumference is as five-fourths to four”

This sent shockwaves round the word. Due to this falsity, the bill was forevermore known as the “Indiana Pi Bill”. Such is the impact of this claim, that the bill has become famous with myth and lore surrounding it. Many people will tell you that the bill tried to legislate \pi=4 but this is not true (and by true, I mean the mathematical meaning of true – not Goodwin’s idea of truth). This misconception comes from the fact that on further examination Goodwin’s method for squaring the circle actually resulted in a square that was \frac{\pi}{4} times the size of the circle. So if \pi=4, his claim fo having squared the circle would be true. There’s no evidence that Goodwin intended to make this claim though.

Right. Back to 1897 Indiana. The bill was put before the Indiana House of Representatives, but the problem was that none of them knew what to do with it. One member suggested referring it to the Financial Committee, another proposed Committee on Swamplands (where it could “find a deserved grave”). Ultimately, it ended up with the Committee on Education, who passed the bill on February 6.

Disaster!! How did the United States of America survive such a threat to their nation? Thankfully a mathematician by the name of C. A. Waldo stepped in to save the day. The bill was debated by the Indiana Senate but fortunately Waldo spoke to the senators beforehand. On February 12, it was postponed indefinitely.

All’s well that ends well. And while Goodwin may not been able to square the circle, his efforts did result in a conclusive answer to another of the world’s greatest questions: Where’s Waldo?

Found Waldo! He’s chatting to some Indiana senators

*Indeed, Whitehead and Russell famously wrote hundred of pages in their Principia Mathematica to be certain of this, but that’s a story for another time.


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