Nearly a month had passed since I submitted my ideas for a new server design. Clarence thought I was joking, and when I assured him I wasn’t, he pointed out a dozen things he found wrong with my plans, most of which could be categorized as being because my design was different from what he was used to. When I didn’t hear back from Mr. Winters, I sent a follow-up email, to which he replied that he’d sent my designs up the chain through the usual channels. I knew what that meant: they’d likely die in engineering purgatory. Still, he thought I should sit tight and give it at least a few months before we followed up on them. In the meantime, I performed my job duties at Applazon’s data center, which were getting to be rather tedious. I’d been expecting to work on at least a little web design but had yet to be given a project, and so I’d taken it upon myself to work on the code that drove the web interface for server management. This time I wasn’t going to present any of it, however, until it was a finished product.
It was now mid-April, and Jerry, Henry and I finally managed to get an appointment to meet with the chair of the mathematics department at the University of Nebraska at Omaha. Of course, the appointment was for Henry to explore options for testing out of the high-school and college math courses he’d already mastered, which at this point amounted to just about everything short of a Ph.D. I didn’t see that there was any role for me in the meeting, but Jerry insisted I be there, so I arranged to trade my day off that week in return for Jerry’s wheels to get me there.
At least my voice had finally changed so I wouldn’t sound so much like a little kid when we met with the department chair. Just as importantly to me, I now had visible pubes and a few wisps of hair under my arms.
What I didn’t realize when we left the house that morning for our meeting, all three of us in coats and ties, was that the meeting was as much for me as for Henry. We arrived early, and the departmental secretary asked us if we’d like coffee. If I’d been at all nervous, I’d have passed, but since it was Henry that was interviewing, I accepted her offer. So did Jerry and Henry, all three of us drinking it black. The stuff was pretty vile, but I sipped mine anyway to be polite. We didn’t have to wait long before a very young-appearing man appeared and invited us inside. We all took advantage of the situation to leave our coffees behind.
I assumed the man who greeted us must be a graduate student, but he led us into a rather nondescript office with a desk with a computer on it, as well as a small conference table and chairs. A whiteboard dominated an entire wall while bookshelves dominated another. The remaining two walls consisted of floor-to-ceiling glass with sheer window curtains in front of them. Obviously, this was a corner office. The young man motioned for us to sit at the conference table, which we did, but rather than going to fetch Dr. Fletcher, the chairman of the mathematics department, he sat down across from us and said, “Good morning, gentlemen, I’m Dan Fletcher. My apologies for the cramped space, but mathematics doesn’t rank highly in the pecking order of departments. However, I’m not complaining. Not every department chair has a corner office. So, what can I do to help you today?” Holy fuck, this young guy was the chair of mathematics. Cool!
Before Jerry could open his mouth, Henry asked, “You’re the chairman of mathematics? That’s amazing. It gives me hope for my future. Can I ask how old you are?”
“I appreciate your honesty, young man,” Dr. Fletcher replied. “Most everyone meeting me thinks, ‘Holy Shit! This guy is just a kid,’ but they keep their thoughts to themselves rather than take a chance on offending me. I’m thirty years old and just became the chair not quite a year ago. I was what some call a prodigy, skipping high school and starting college when I was thirteen. I finished my Ph.D. when I was twenty and was a full professor by the time I was 27. Frankly, it’s not a career path I’d recommend to anyone.”
“I skipped middle school,” I responded, “and being an eleven-year-old high school freshman was probably worse than being in college as a young teenager. At least, Henry’s already in the seventh grade. I suggested he start high school next year, a year early. He already looks like he could be a freshman, anyway, and maybe he could finish high school in three years and start college as a sophomore or junior when he’s sixteen and better able to fit in.”
“I’m at a distinct disadvantage,” Dr. Fletcher said. “I have no idea who you are or why you asked to see me.”
“That was my idea,” I offered.
“Let me explain who we are,” Jerry began. “I’m Jerry Gonzalez, one of the deputy directors of the U.S. Strategic Command at Offutt Air Force Base. My son, Henry, is a seventh grader. He’s a straight-A student whom I thought was doing fine, until J.J. joined our family,” he said as he nodded in my direction. “It took J.J. to discover just how unhappy Henry really was. I’d no idea he was bored in school. I didn’t know he was a math whiz.”
“Let me explain,” I chimed in. “You’re probably wondering who this J.J. is. My story’s a bit more complicated ’cause I grew up in a small Midwestern town with an abusive father who ultimately threw me out for being gay. I eventually found my way to Kansas City, where I was taken in by the Rodriguez family and took the opportunity to get my GED. Like I said, I started high school at eleven and was close to finishing when I was forced to leave.
“I did a lot of college-level coursework online but didn’t have the means to get college credit for it, but when I saw Henry doing his math homework, I realized he was solving problems way too quickly for a seventh grader, so I showed him a little calculus as an alternative way to solve simultaneous polynomial equations, and he breezed through that. It didn’t take me long to realize how depressed he was, and it was because he didn’t see much of a future when nothing much challenged his intellect.
“I think there’s still a value in him going through AP courses in English, Spanish, History and the like in high school, but math and science are another matter. I gave him some links to the same self-study math sites I’d used, and within days he was solving partial differential equations. Clearly, he should get at least one Ph.D. in math or engineering or both, but in the meantime, I saw no point in him suffering through a high school math curriculum he’s already mastered, even if it’s an advanced one. I suggested he either challenge the entire high-school math syllabus or seek college credits in math and use them for dual credit.”
“So, you’re meeting with me to explore your options for obtaining college credit by test for Henry?” Dr. Fletcher asked.
“And for J.J.,” Jerry added.
In shock I exclaimed, “What?”
“I’d like to see what you can do for both boys,” Jerry reiterated. “My son pursued a course of study, following a path already forged by J.J., who’s also seeking a college degree. Shouldn’t they both be rewarded for their efforts?”
“Of course. However, we only award college credit by test to our own students,” Dr. Fletcher interjected. “So, you’d need to enroll at the University of Nebraska before I could test you.”
“I’m working for Applazon,” I noted. “I have full tuition benefits from them.”
“That should be no problem,” Dr. Fletcher replied. “I don’t get into those specifics. That’s a matter between the Registrar and the Bursar and you. But first, let’s get an idea of exactly where each of you might be in your studies. J.J., how much have you done in your studies of math?”
“I’ve completed advanced calculus, vector analysis, complex numbers and partial differential equations,” I replied.
“So, in your case, we’re talking a traditional masters-level engineering curriculum,” Dr. Fletcher noted, and I nodded in the affirmative.
“And Henry, what have you done?” he continued.
Laughing, Henry said, “What J.J. did was just a warmup.” He then went on to list a series of additional areas of math study that would’ve made Einstein wince, but then I remembered that Einstein had flunked math.
“That’s an impressive course of study, even for our Ph.D. students,” Dr. Fletcher related. “Henry, there’s a whiteboard behind you. Would you try to prove the fundamental theorem of calculus?” The fundamental theorem of calculus was the bridge between the two branches of calculus, differential and integral. It was so basic to all of mathematics, it had never dawned on me before that it was presented as a given. I’d never seen it proven before and wasn’t sure how I’d even begin to prove it.
For his part, Henry’s eyes flew open wide as he said, “Oh, fuck!” and then sat frozen for at least a couple of minutes, hardly moving at all. At first, I thought that maybe he’d become catatonic or something, and Jerry started to get up, obviously worried about his son, when all of a sudden, Henry stood up and said, “Wow, who knew something so basic could be so difficult?” Did he just do the proof in his head?
Henry walked up to the whiteboard and picked up a marker and started writing a flurry of equations, explaining what he was doing as he went. It didn’t take him long to completely fill the board, and so he erased it, rewrote the last derivation and then continued to fill the board twice more. “This is where it really gets hairy,” he said as he went into a lengthy side derivation that involved a number of concepts I’d never heard of before. Finally, he came up with a conclusion that he plugged into his work on the fundamental theorem and proceeded in quick order to complete the proof.
“Well done, Henry,” Dr. Fletcher responded as Henry sat down. “Around here we call that a tank-top proof, because completing it works up quite a sweat in most of us. I should’ve told you to take off your suit coat before you started, but you just dove right in and didn’t stop. Two things. The side proof is the step that causes most people to come up short. It’s something not generally within the realm of all but an advanced math grad student, and you managed to get through it. I imagine that was what your ‘Oh, fuck!’ comment was about.” Henry grinned and nodded his head.
“Fortunately, there are a series of named theorems that few outside of math are familiar with,” the professor continued. “It might be worth your while to take a couple of advanced math courses or at least study the associated material. The courses are so esoteric that we only teach them every four years in cycle, and there are only two or three students taking them. I can arrange for you to take the courses in independent study if you prefer.
“The other thing is that in step six, you could’ve saved yourself about a page and a half of whiteboard if you’d made a simple substitution.”
“Oh, shit!” Henry suddenly exclaimed. “How’d I miss that?”
“Henry, most students fail to get through the proof at all on their first attempt, let alone make it through with nothing more than a missed opportunity for simplification,” Dr. Fletcher related. “Now as far as how to proceed is concerned, the simplest way to award you credit is to have you both take the qualifying exam for a mathematics Ph.D. Our students have to take this before they can go on to write their thesis proposal for their dissertation. The exam is in six parts, and it’s open book. You need to complete any three parts to proceed with your Ph.D., but I can only award credit for the parts completed. For any part completed, I’ll award credit for all of the course material covered, including all prerequisites. That includes the prerequisite courses that are available for dual credit in high school. I don’t expect you boys to get through all six parts, particularly you, J.J., but finish what you can.
“The University will charge you full tuition for each course passed by exam. That’s a standard policy. I suggest you make application for summer admission as that will cut the cost per credit awarded in half. I’m sure Applazon will pick up the cost or pick up most of it, but you should clear it with your superiors before you apply. For Henry, there’s a math scholarship available that will pick up the cost of all of the graduate-level courses. If you pass three or more parts of the exam, I can guarantee you’ll be the next recipient and we’ll reimburse tuition retroactively. You’ll still be on the hook for your undergrad tuition, which is still far from trivial. You should check with student aid as it’s likely you would qualify for one or more scholarships based on academics. You may also qualify as the son of a military officer.”
Walking behind his desk and reaching into one of his desk drawers, he pulled out a thick document consisting of several hand-written pages. “We have so few Ph.D. students each year that it’s hardly worth our while to have anything printed up. The exam is graded based on your work, although we do expect you to get the right answers, especially since this is an open-book exam. I just have this one copy. Feel free to copy it if you wish or scan it into your computer. You can even work on it together as it doesn’t really matter so long as you each do your own work. When you finish, scan your work in and email it to me, and I’ll let you know how you did. If you pass, it’ll be up to the Registrar and Bursar to figure out what you owe, so do go ahead and apply for admission.
“I’m helping you out based on the assumption that you will continue degree studies at the University of Nebraska. In the case of Henry, I can come up with a plan of study that should cover much of his high-school curriculum as well. He’ll graduate high school in three or four years with a bachelor’s or possibly even a master’s in mathematics. We can then talk about admission to the Ph.D. program if that’s what you want, or you can go onto any top program in the country.”
“You seem so certain of my son’s ability to get a Ph.D. in mathematics,” Jerry asked. “Why?”
“Because anyone capable of doing that proof,” Dr. Fletcher said as he pointed at the whiteboard, “is capable of it.
“And J.J., if you complete three parts of the QE, I’ll be prepared to admit you directly to our master’s program. You won’t even need an undergraduate degree, but you might want to get one, and we can talk about a course of study for doing so. However, I suspect your interests lie more in engineering, so it might be best to have you meet with the chair of one of the engineering departments, or perhaps you’re interested in computer science, which is within my department. I’d be happy to discuss with you a degree path in computer science.”
“Is there a qualifying exam for computer science?” I asked.
“There is,” Dr. Fletcher confirmed. “It actually is an addendum to the one you already have, adding three additional parts to the exam. To pass the computer-science QE, you need to pass three parts, at least two of which are in computer science, which leaves you free to combine those with a math part or to do all three parts in comp sci.” Reaching into his desk, he pulled out another, much slimmer exam and handed this one directly to me.
This one was typewritten and involved a series of design projects. One of the parts was just a single question, but it was a doozy, to use an old expression. I was surprised, and I read it aloud. “Design a Java virtual machine to run on the HP35-S scientific calculator. Wasn’t the HP35 the very first scientific calculator back in the early seventies, with an operating stack of only four registers?”
Laughing, Dr. Fletcher replied. “Are you suggesting you couldn’t do it?”
“Not without augmenting the memory,” I explained. “Otherwise, there’d be no way to store executable code in the calculator, let alone run it.”
“Of course, you’re right,” he responded, “but the HP35-S is a completely different model, introduced in 2010. It looks a bit like the original HP35, but it’s a completely different calculator. You can pick one up from Applazon,” he added with a wink. “It’s a programmable, with 100 data registers and an 800-step nonvolatile memory.”
“That doesn’t leave a lot of room for error,” I replied. “At least it’s not a compiler, so I only need to map Java byte codes to executable codelets. There’s no way to protect memory, though.”
“Nor is that one of the requirements,” Dr. Fletcher pointed out. “The key is making it fit and figuring out how to reuse code for multiple instructions.”
“Kinda like DNA,” I replied, but then thought aloud to myself, “but that approach might actually work. It’d be like playing a song by telling a CD player where to start and stop playing.”
“Not an easy task,” Dr. Fletcher responded. “Many a student has tried and given up, choosing to substitute a part from the math exam instead.”
“I like challenges,” I countered. “Are we allowed to use computers to write and optimize the code?” I asked.
“Programmers have those tools available,” he replied. “The only thing that’s not allowed is to copy a solution if you find one on the internet.”
“Then, I’ll use a hash table and Bayesian statistics,” I replied.
“Just remember, there may be more than one way to execute an instruction,” Dr. Fletcher noted.
“Of course, but that you’re bringing it up is probably highly significant,” I replied. I was definitely obsessed with that one assignment. I doubted I’d be able to give it up until I had a solution, even if it took more time than the entire rest of the math and comp-sci QE.
Disclaimer: This story is purely fictional and any resemblance of characters to real individuals is unintentional. Although it takes place in actual locations, in no way are any official policies, opinions or events inferred. Some characters may be underage and at times engage in homosexual acts. Anyone uncomfortable with this should not be reading the story, and the reader assumes responsibility for the legality of reading this type of material where they live. The author retains full copyright and permission must be obtained prior to duplication in any form.