Mathematicians and cyclists have long been fascinated by Arthur Conan Doyle’s story “The Adventure of the Priory School,” featuring the well-known character Sherlock Holmes.

You can read the full text of the story — in fact, the full text of Arthur Conan Doyle’s works — on the Internet Archive.

Holmes and Watson are summoned to investigate the disappearance of a prominent student from a distinguished school. A teacher of German has also disappeared, along with his bicycle. How could they have escaped without being seen? Why hasn’t the kidnapper issued a ransom demand? Holmes and Watson search the area north of the school for answers.

Here is a relevant section:

[….]

The day was just breaking when I woke to find  the long, thin form of Holmes by my bedside.

He was fully dressed, and had apparently already been out.

“I have done the lawn and the bicycle shed,” said he. “I have also had a ramble through the Ragged Shaw. Now, Watson, there is cocoa ready in the next room. I must beg you to hurry, for we have a great day before us.”

His eyes shone, and his cheek was flushed with the exhilaration of the master workman who sees his work lie ready before him. A very different Holmes, this active, alert man, from the introspective and pallid dreamer of Baker Street. I felt, as I looked upon that supple figure, alive with nervous energy, that it was indeed a strenuous day that awaited us.

And yet it opened in the blackest disappointment. With high hopes we struck across the peaty, russet moor, intersected with a thousand sheep paths, until we came to the broad, light-green belt which marked the morass between us and Holdernesse. Certainly, if the lad had gone homewards, he must have passed this, and he could not pass it without leaving his traces. But no sign of him or the German could be seen. With a darkening face my friend strode along the margin, eagerly observant of every muddy stain upon the mossy surface. Sheep-marks there were in profusion, and at one place, some miles down, cows had left their tracks. Nothing more.

“Check number one,” said Holmes, looking gloomily over the rolling expanse of the moor. “There is another morass down yonder and a narrow neck between. Halloa! halloa! halloa! what have we here?”

We had come on a small black ribbon of pathway. In the middle of it, clearly marked on the sodden soil, was the track of a bicycle.

“Hurrah!” I cried. “We have it.”

But Holmes was shaking his head, and his face was puzzled and expectant rather than joyous. “A bicycle, certainly, but not the bicycle,” said he. “I am familiar with forty-two different impressions left by tyres. This, as you perceive, is a Dunlop, with a patch upon the outer cover. Heidegger’s tyres were Palmer’s, leaving longitudinal stripes. Aveling, the mathematical master, was sure upon the point. Therefore, it is not Heidegger’s track.”

“The boy’s, then?”

“Possibly, if we could prove a bicycle to have been in his possession. But this we have utterly failed to do. This track, as you perceive, was made by a rider who was going from the direction of the school.”

“Or towards it?”

“No, no, my dear Watson. The more deeply sunk impression is, of course, the hind wheel, upon which the weight rests. You perceive several places where it has passed across and obliterated the more shallow mark of the front one. It was undoubtedly heading away from the school. It may or may not be connected with our inquiry, but we will follow it backwards before we go any farther.”

We did so, and at the end of a few hundred yards lost the tracks as we emerged from the boggy portion of the moor. Following the path backwards, we picked out another spot, where a spring trickled across it. Here, once again, was the mark of the bicycle, though nearly obliterated by the hoofs of cows. After that there was no sign, but the path ran right on into Ragged Shaw, the wood which backed on to the school. From this wood the cycle must have emerged. Holmes sat down on a boulder and rested his chin in his hands. I had smoked two cigarettes before he moved.

“Well, well,” said he, at last. “It is, of course, possible that a cunning man might change the tyre of his bicycle in order to leave unfamiliar tracks. A criminal who was capable of such a thought is a man whom I should be proud to do business with. We will leave this question undecided and hark back to our morass again, for we have left a good deal unexplored.”

We continued our systematic survey of the edge of the sodden portion of the moor, and soon our perseverance was gloriously rewarded. Right across the lower part of the bog lay a miry path. Holmes gave a cry of delight as he approached it. An impression like a fine bundle of telegraph wires ran down the centre of it. It was the Palmer tyre.

“Here is Herr Heidegger, sure enough!” cried Holmes, exultantly. “My reasoning seems to have been pretty sound, Watson.”

“I congratulate you.”

“But we have a long way still to go. Kindly walk clear of the path. Now let us follow the trail. I fear that it will not lead very far.”

We found, however, as we advanced that this portion of the moor is intersected with soft patches, and, though we frequently lost sight of the track, we always succeeded in picking it up once more.

“Do you observe,” said Holmes, “that the rider is now undoubtedly forcing the pace? There can be no doubt of it. Look at this impression, where you get both tyres clear. The one is as deep as the other. That can only mean that the rider is throwing his weight on to the handle-bar, as a man does when he is sprinting. By Jove! he has had a fall.”

There was a broad, irregular smudge covering some yards of the track. Then there were a few footmarks, and the tyre reappeared once more. “A side-slip,” I suggested.

Holmes held up a crumpled branch of flowering gorse. To my horror I perceived that the yellow blossoms were all dabbled with crimson. On the path, too, and among the heather were dark stains of clotted blood.

“Bad!” said Holmes. “Bad! Stand clear, Watson! Not an unnecessary footstep! What do I read here? He fell wounded, he stood up, he remounted, he proceeded. But there is no other track. Cattle on this side path. He was surely not gored by a bull? Impossible! But I see no traces of anyone else. We must push on, Watson. Surely with stains as well as the track to guide us he cannot escape us now.”

Our search was not a very long one. The tracks of the tyre began to curve fantastically upon the wet and shining path. Suddenly, as I looked ahead, the gleam of metal caught my eye from amid the thick gorse bushes. Out of them we dragged a bicycle, Palmer-tyred, one pedal bent, and the whole front of it horribly smeared and slobbered with blood. On the other side of the bushes a shoe was projecting. We ran round, and there lay the unfortunate rider. He was a tall man, full bearded, with spectacles, one glass of which had been knocked out. The cause of his death was a frightful blow upon the head, which had crushed in part of his skull. That he could have gone on after receiving such an injury said much for the vitality and courage of the man. He wore shoes, but no socks, and his open coat disclosed a night-shirt beneath it. It was undoubtedly the German master.

Holmes turned the body over reverently, and examined it with great attention. He then sat in deep thought for a time, and I could see by his ruffled brow that this grim discovery had not, in his opinion, advanced us much in our inquiry.

“It is a little difficult to know what to do, Watson,” said he, at last. “My own inclinations are to push this inquiry on, for we have already lost so much time that we cannot afford to waste another hour. On the other hand, we are bound to inform the police of the discovery, and to see that this poor fellow’s body is looked after.”

“I could take a note back.”

 

“But I need your company and assistance. Wait a bit! There is a fellow cutting peat up yonder. Bring him over here, and he will guide the police.”

I brought the peasant across, and Holmes dispatched the frightened man with a note to Dr. Huxtable.

“Now, Watson,” said he, “we have picked up two clues this morning. One is the bicycle with the Palmer tyre, and we see what that has led to. The other is the bicycle with the patched Dunlop. Before we start to investigate that, let us try to realize what we do know so as to make the most of it, and to separate the essential from the accidental.”

[…]

Whoa! Read more (if you like) at the Internet Archive.

It turns out that someone made a TV version, available on YouTube. For the full experience, start at part one — the link below is to the beginning of the part that cyclists and mathematicians like: