1960s F&SF short story - Insane Professor

"The Master's Thesis", a short story by David Madden, first published in The Magazine of Fantasy and Science Fiction, July 1967, available at the Internet Archive.

A strange young man named Philip Hockaday Fonville has signed up as Prof. Swinnard's Master's student and is already writing his thesis:

"Now, young man," he said, turning Current History right side up and looking for something, anything that he might have misplaced, "suppose we get this whole affair in perspective."

"I'm having it typed up now, sir."

"What's that?"

"The first chapter."

"Come now," Swinnard said, grinning, trying to find some way to attack the problem. "We must be serious."

"Sir, how much seriouser can I get? Up all night gnawing on candy bars to keep up my strength while I struggle with this thing."

"You are actually in the writing phase of — "

"Oh, it's going to be ready before the deadline — way before. Typed up in three neat copies, bound and everything. Neat and crisp."

Fonville gives Prof. Swinnard the first chapter to read, which he loses:

That night he realized he had forgotten to read the chapter, that he had, in fact, left it on the table in the Chinese restaurant. He telephoned, and the dishwasher answered. Yes, he had. It was in the garbage, and the garbage was on the truck. Yes, he could read a little English. One word on the second page, "Death," followed by a name in three parts. Swinnard thanked him and tried to sleep.

A peculiar odor:

Fonville pulled a chair close to the desk until their knees almost touched. Swinnard noticed what tremendous feet the boy had. His galoshes made his own feet look large, but they were small alongside the boy's. Fonville settled himself, but first, Swinnard wanted to know what that odor was.

"Smell, sir?" The boy got up and looked all around the room, sniffing in each corner, sticking his head out the door into the hall, and peeping over the window sill into the yard under the bushes. When the boy sat down, Swinnard realized that the odor was stronger.

The ending:

Standing on the peaceful lawn under the full moon, he knew that, despite the chill in the air, this was what he wanted to do. He ducked under the clothes line. The summer sound of the screen door was still in his ears. He bent over toward the curving grass and reached to grip the backs of his legs. Strands of his thin grey hair brushed the grass. His glasses slid down over the bridge of his nose and dangled from one ear as he peered between his legs, upside-down. The earth turned black, the moon melted, making the sky one white radiance, and in the soles of his feet, Swinnard felt the distant beat of hoofs.