He earned a B.S. in mathematics from California Institute of Technology (1966), where he was a Putnam fellow in 1964, and a Ph.D. in mathematics from Harvard University (1970). He studied linguistics and Bible translation at the Summer Institute of Linguistics at the University of Oklahoma in 1971 and 1972, and he enrolled at Westminster Theological Seminary, earning an M.Div. (1974) and a Th.M. in apologetics (1974). He then received an M.Litt. in New Testament from University of Cambridge (1977) and a Th.D. in New Testament from the University of Stellenbosch, Stellenbosch, South Africa (1981).
He taught mathematics at Fresno State College (now California State University, Fresno) for a year after earning his Ph.D. in the subject, and he taught linguistics at the Summer Institute of Linguistics in the summers of 1974, 1975, and 1977. He has taught New Testament at Westminster Theological Seminary in Philadelphia since 1976.
As an evangelical Poythress advocates the complete, divine authority of Bible, and as a Calvinist he places an emphasis on the sovereignty of God and adopts the Neo-Calvinist notion that Jesus is Lord of every area of life, not just private, religious life. He makes use of Biblical Theology in the tradition of Geerhardus Vos, and builds on Meredith G. Kline's work in Images of the Spirit to argue that "imaging" is a pattern in the Bible beyond man and woman being made in the image of God. He has a decidedly positive view of the Old Testament Law, though he rejects theonomy, and he rejects the hermeneutics of dispensationalism. In Christian eschatology, he advocates an Amillennial view (compare the summary of Christian eschatological differences).
He is an advocate of Cornelius Van Til's presuppositional apologetics, particularly the ideas that epistemology and ontology must find their ultimate grounding in the Trinity. He has also sought to work out presuppositionalism's central claim that there is no neutrality in the area of science and mathematics. In a manner akin to Augustine's view that truth is divine, Poythress views scientific law as a form of the word of God. In 1976, Poythress broke new ground with an article on "A Biblical View of Mathematics," while in a 1983 article, he argued that mathematics is the rhyme of the universe.
A central idea in Poythress' thought has concerned the validity of multiple perspectives, or multiperspectivalism, a project that he shares with his teacher and collaborator John Frame. In Poythress's seminal work Philosophy, Science, and the Sovereignty of God, he explored how the scientific concepts of wave, particle and field can be used analogically to demonstrate different ways of looking at things. He argued that such a triadic structure is a "a means of avoiding unhealthy dualism", and he continued on this line of thought in Symphonic Theology, where he applied multiperspectivalism to theology.
He has been editor of the Westminster Theological Journal since 2005, and he has contributed to a number of other volumes such as The Foundations of Christian Scholarship, Hermeneutics, Inerrancy, and the Bible, The New Testament Student and His Field, Inerrancy and Hermeneutic: A Tradition, A Challenge, A Debate, Theonomy: A Reformed Critique, Recovering Biblical Manhood and Womanhood, New Geneva Study Bible, and The Spirit of the Reformation Study Bible. He was also a member of the Translation Oversight Committee for the English Standard Version.
Additionally, he has published a number of scholarly articles, including: