Quick question on Albert Sidney Johnston

[Philip Leigh]

What were the two problems on Albert Sidney Johnston's senior math exam—and there were only two—that the cadet could not solve thereby causing his class ranking to drop from second to eighth (out of 41)?

 

[Jim in Wisconsin]

I sure don't know, but I hope someone does. It would be fun to see what sort of math problems they had to solve and if I (or someone else) could do it.

 

[JackADriscoll]

Great topic. I did some searching on this one and this is the best I could find on math at West point. I could not find any exams.

 

[gary]

Awesome question. Wish I knew the answer.

 

[35th MA InfRegt]

Great topic. I did some searching on this one and this is the best I could find on math at West point. I could not find any exams.

Johnston graduated from the Military Academy in 1826, four months shy of 200 years ago. I doubt the necessary evidence still exists after all that time. Good luck with finding Johnston's final mathematics examination.

 

[SWS]

One cadet wrote in a calculus textbook: "God **** all mathematics to the lowest depths of hell!! May it be made capable of bodily suffering & undergo such torments that the veriest fiend in hell shall shrink in horror at the sight."

 

[JackADriscoll]

Library lady can you find a text book scanned in from back then?

 

[Saruman]

Not sure if this particular example was used at West Point, but I found this early nineteenth century maths problem:

Required: From a station A, the angle of elevation of the summit of a hill C is observed to be 18° 24′. Advancing in a straight line toward the hill a distance of 500 yards to station B, the angle of elevation is found to be 26° 40′. Determine the height of the hill, and the distance from the first station A to the foot of the hill, neglecting the height of the observer's instrument.

 

[NH Civil War Gal]

One cadet wrote in a calculus textbook: "God **** all mathematics to the lowest depths of hell!! May it be made capable of bodily suffering & undergo such torments that the veriest fiend in hell shall shrink in horror at the sight."

Just read this to my husband, who is a mathematician, and he couldn't stop laughing!

 

[35th MA InfRegt]

Not sure if this particular example was used at West Point, but I found this early nineteenth century maths problem:

Required: From a station A, the angle of elevation of the summit of a hill C is observed to be 18° 24′. Advancing in a straight line toward the hill a distance of 500 yards to station B, the angle of elevation is found to be 26° 40′. Determine the height of the hill, and the distance from the first station A to the foot of the hill, neglecting the height of the observer's instrument.

That sounds like a problem in geometry. That was definitely not my cup of tea in school.

 

[gary]

Not sure if this particular example was used at West Point, but I found this early nineteenth century maths problem:

Required: From a station A, the angle of elevation of the summit of a hill C is observed to be 18° 24′. Advancing in a straight line toward the hill a distance of 500 yards to station B, the angle of elevation is found to be 26° 40′. Determine the height of the hill, and the distance from the first station A to the foot of the hill, neglecting the height of the observer's instrument.

I can see its relevance for map making and gunnery.

 

[Philip Leigh]

Not sure if this particular example was used at West Point, but I found this early nineteenth century maths problem:

Required: From a station A, the angle of elevation of the summit of a hill C is observed to be 18° 24′. Advancing in a straight line toward the hill a distance of 500 yards to station B, the angle of elevation is found to be 26° 40′. Determine the height of the hill, and the distance from the first station A to the foot of the hill, neglecting the height of the observer's instrument.

I think you, Gary, and 35th Mass are on the right track.

Here is what Grok had to say:

The exact wording or content of the two math problems is not specified in surviving historical records. However, given the West Point curriculum at the time (emphasizing advanced mathematics, including calculus and conic sections), the questions were likely from those areas. Johnston claimed he could answer every other question in the textbook and requested a re-examination on the entire course, which he passed with distinction, securing his commission.This anecdote is documented in sources like "The Father of West Point" article on HistoryNet, highlighting how Superintendent Sylvanus Thayer allowed the exception due to Johnston's overall abilities and soldierly qualities.

 

[gjpratt]

I still remember a college computer science final exam that I was unable to solve.. Write a Fortran based (punch cards) program that will sort in numerical order 1000 random numbers. I wrote a program that would have worked but it was so inefficient that it shut down the then state of the art IBM mainframe that was housed in a 3 story dedicated building. I never figured out the trick. As I recall, I created an infinite do loop.

When I bought my first home computer — a Compaq that looked like a sewing machine —I noticed that there was Basic macro that was a random number generator. So I generated 1000 numbers and wrote the same program to sort them. The PC purred a few seconds and printed out 1000 numbers in order. More a commentary on advances in computer technology between 1974 and 1985, but I still remember the math-like problem I could not solve.

 

[Philip Leigh]

I still remember a college computer science final exam that I was unable to solve.. Write a Fortran based (punch cards) program that will sort in numerical order 1000 random numbers. I wrote a program that would have worked but it was so inefficient that it shut down the then state of the art IBM mainframe that was housed in a 3 story dedicated building. I never figured out the trick. As I recall, I created an infinite do loop.

When I bought my first home computer — a Compaq that looked like a sewing machine —I noticed that there was Basic macro that was a random number generator. So I generated 1000 numbers and wrote the same program to sort them. The PC purred a few seconds and printed out 1000 numbers in order. More a commentary on advances in computer technology between 1974 and 1985, but I still remember the math-like problem I could not solve.

I had a similar experience with a Radio Shack desktop in the early 80s for which I modeled a periodic function by using a Fourier Series in Basic. It was fun because the screen showed the realtime calculation of the series thereby revealing the underlying function better with each iteration. It was a simple Sawtooth function like the scanner in a Television.

 

[Rhea Cole]

About four by five feet & two feet deep, the winter of 1967 a computer arrived in our college math / physics classroom. Our teacher, the appropriately named Mr. Smart, left it for us to read the manual & figure out how to work the first computer to ever arrive in Watertown, South Dakota. I couldn't for the life of me describe exactly how it worked, but it did involve entering binary numbers by lighting the square switches exactly like those on Star Trek as Mr. Spok saved the crew from certain death.

It would work a quadratic equation, normally quite a laborious task for me, by winking back & forth rhythmically… it was really like watching the banks of twinkling lights on the bridge of the Star Ship Enterprise. As amazing as the quadratic equation was, the one thing I managed to master was extremely impressive & earned well deserved accolades that I seldom received in college math.

Watching the rows of lights wink on & off like some kind of electronic dance was an astonishing experience. Counting down from 100 to zero in binary was down right mesmerizing to watch… our mechanical adding machines were clacking antiques in comparison.

 

[Nathan Stuart]

William Preston Johnston in his biography of his father (see https://archive.org/details/lifegenalbertsi00johngoog/page/13/mode/1up @ pp. 12-13) refers to this subject incident at West Point, but without giving particulars.

Interestingly, William Johnston acknowledges (@ p. 13) in the context of referencing the examination that his father lacked skill in drawing. This might provide a hint as to what the type of the two problems were that his father failed.

Albert Sidney Johnston's mathematics teacher and examiner at the time may have been Charles Davies, who was professor of mathematics at West Point from May, 1823 to May, 1837. (See https://old.maa.org/press/periodica...ed-years-charles-davies-mathematics-professor ). Davies prescribed and used his own authored textbooks at the Academy where he taught. The first of his textbooks used at West Point in 1826 was 'Elements of Descriptive Geometry with their Application to Spherical Trigonometry, Spherical Projections and Warped Surfaces'.

Based on the above information. My best guess as to the type of problems Johnston failed involved tasks requiring the calculation and drawing of some sorts of geometrical shapes.

 

[nc native]

One cadet wrote in a calculus textbook: "God **** all mathematics to the lowest depths of hell!! May it be made capable of bodily suffering & undergo such torments that the veriest fiend in hell shall shrink in horror at the sight."

When I first encountered Algebra in school, I felt the same way although the language would have been toned down some. My feeble mind just couldn't grasp the fact that the letters in formulas were numbers and to this day my mathematical skills are very lacking. I survived the high school course I had to take with a grade below C level while my grades were good to excellent in the other courses I took. I took Business Math courses to fulfill my math requirements in high school after my first encounter with Algebra and did well in them.

When I got to college, I actually enjoyed taking Statistics and did average work in that course. Geometry and Calculus were deep water that I never even attempted to dive into.

 

[7th Texas Mounted Rifles]

One cadet wrote in a calculus textbook: "God **** all mathematics to the lowest depths of hell!! May it be made capable of bodily suffering & undergo such torments that the veriest fiend in hell shall shrink in horror at the sight."

Pretty sure I wrote something similar in my school algebra textbook as well.

 

[Jim in Wisconsin]

I'm the opposite I guess. I really liked math and I still like messing around with numbers. I had geometry as a freshman and advanced math the next year in high school. When there were maybe 15 problems at the back of the chapter and the assignment was to do the first 10, I sometimes would do the other 5 just for enjoyment. I wouldn't turn them in though because I didn't want to be a brown nose. That word problem in response 8 is a matter of drawing out and "solving" two triangles, one of which has a 90 degree angle. I wish I could remember a lot of it though. I'm 78 now - too much water over the dam since then. Too bad I was such a fizzle at most every other class.

 

[Jamieva]

One cadet wrote in a calculus textbook: "God **** all mathematics to the lowest depths of hell!! May it be made capable of bodily suffering & undergo such torments that the veriest fiend in hell shall shrink in horror at the sight."

I endorse this message.

I hated math