Van Amringe taught at Columbia while an undergraduate but not, as one might expect, in the Department of Mathematics but rather in the Department of Greek. He received his A.B. in 1860 and his A.M. in 1863. Keyser writes :-
So brilliant and many-sided were his native powers and his attainments that even before graduation he had been tendered an instructorship in no fewer than five widely diverse departments: Greek, Latin, history, chemistry, mathematics. He might with equal propriety have been invited into the department of English, had there been such a department at that time, for his extant writings, including many published addresses, show that he had a remarkable control over the resources of English speech.Van Am, as he was known, spent his entire career at Columbia College. He was appointed as a tutor in mathematics in 1860 being promoted to adjunct professor of mathematics in 1863. He was a lecturer in the School of Mines in 1864-5 and full professor in 1865, holding this chair until 1873 when he was appointed professor of mathematics in the School of Arts. He was head of mathematics from 1892 until he retired in 1910. He served as dean of the School of Arts from 1894 to 1896 when he became dean of Columbia College. As dean he served on the University Council and for the year 1899 he served as President of the University. He held the position of dean for fourteen years until June 1910 when he resigned from his duties. At this time he was made Emeritus Professor of Mathematics.
Van Amringe was a good teacher of mathematics, Thomas  writes:-
... probably no other teacher of his day was so loved and revered...Keyser writes :-
Van Amringe was a great teacher, especially of undergraduate men. He was never converted to a belief in coeducation. He did not believe in, and he did not employ, the lecture method with undergraduates. He was convinced that one of the great desiderata is to teach students to read solid books understandingly, and so he assigned them daily definite lessons in a chosen book and required them to report, usually in the form of classroom recitations. Idleness was not tolerated; industry and achievement were praised generously and discriminatingly. If a student, having tried, failed to understand, he was not overwhelmed by explanations, but led, by the too rare art of skilful questioning and suggestion, into the presence of the truth.He was not, however, a research mathematician of any quality. He did not publish any research papers on mathematics but he is important in his role in the founding of the New York Mathematical Society which quickly changed its name to the American Mathematical Society. He was the first president of the Society appointed at the first meeting on 24 November 1888. He held this post until the meeting on 5 December 1890 when Emory McClintock, an actuary with the Mutual Life Insurance Company in New York, became the second president. At the meeting on 5 December 1890, Van Amringe proposed that the Society should publish a Bulletin. The Society accepted his proposal to publish a journal named The Bulletin of New York Mathematical Society.
Burgess  describes Van Amringe in colourful terms:-
He was ... the ideal college patriot, and consequently the idol of the students and alumni of the college, although he was quite a disciplinarian in the classroom. ... He was always having some accident, such as breaking an arm or a leg. ... he was a great smoker and frequenter of clubs. He was also something of a politician .. he was a good, staunch, reliable friend and very agreeable in social intercourse. No one could know the man and not love him.Raymond Archibald writes about the American Mathematical Society in :-
... it was only natural that one of [Van Amringe's] prominence, occupying the position that he did, should have become our Society's first president.He was also a member of the New York Historical Society and the American Society for the Advancement of Science. But there was another area in which he was extremely active in the community which was his involvement in many religious organisations. He served on the Vestry of Trinity Church, and was a Trustee of the New York Protestant Episcopal Public School, of the Society for Promoting Religion and Learning in the State of New York, of the Common Prayer Book Society, and of the General Theological Seminary of the Protestant Episcopal Church.
Van Amringe was married to Cornelia Bucknor, daughter of William G Bucknor, in New York City on 20 June 1865 by the Revd George Jarvis Geer. Howard and Cornelia Van Amringe, who lived at 48 West Fifty-ninth Street, New York, had a daughter Emily and a son Guy who became a New York lawyer. Cornelia was born in New York in 1837 and died in that city on 10 May 1914. Howard Van Amringe's death is described in :-
He had been suffering from a weak heart for the last three days and had remained in his room. At 1 o'clock luncheon was served in his room, and when he rose he was stricken with apoplexy and collapsed in his chair. His daughter, Miss Emily Van Amringe, rushed to his assistance, and he begged her to send for a physician, saying, "I think that I am suffering from a stroke." Then he lapsed into unconsciousness and died within an hour.Among many honours given to Van Amringe let us mention in particular the bust of the Dean Van Amringe that the alumni of Columbia University donated in March 1913 to the Columbia University Club. At this time the Chairman, Charles Halstead Maples, gave this tribute :-
Van Am has become more than a mere man to us; he's a sentiment. He was right, always right. What the Yale fence is to Yale, the ivy to Princeton, Van Am is to Columbia - a tangible, concrete expression of sentiment to which our members lovingly cling. He has been the friend of our youth, of our young manhood and now of our prime. This then, is the bust of the friend of each one of us - a friend like the Douglas of old, tender and true. It has come, as I know Van Am would have it come, by popular subscription, a gift from many loving Columbia hearts.We end this biography by quoting a song written by the students of Columbia University:
D'ye ken Van Am with his snowy hair,
D'ye ken Van Am with his whiskers rare,
D'ye ken Van Am with his martial air,
As he crosses the quad in the morning?
The sight of Van Am raised my hat from my head.
And the sound of his voice often filled me with dread.
Oh, I shook in my boots at the things that he said
When he asked me to call in the morning.
Yes, I ken'd Van Am, to my sorrow, too,
When I was a freshman of verdant hue.
First a cut, then a bar, then an interview
With the Dean in his den in the morning.
But we love Van Am from our heart and soul,
Let's drink to his health! Let's finish the bowl!
We'll swear by Van Am through fair and through foul,
And wish him the top o' the morning.
D'ye ken Van Am with his fine old way.
The Dean of Columbia for many a day?
Long may he live and long may he stay
Where his voice may be heard in the morning.
Article by: J J O'Connor and E F Robertson