Pioneer Baptist missionary, William Carey (17 August 1761 – 9 June 1834) is well known as the father of modern missions. As a missionary in the Danish colony, Serampore, India, he translated the Bible into Bengali, Sanskrit, and numerous other languages and dialects.
Though almost all churches in India and abroad, make appeals to follow Carey’s example in missionary labor, very few are interested in knowing the theological convictions of Carey behind his missionary zeal. Charles Spurgeon, preaching on August 19 1861 said, Carey was the living model of Edwards’ theology, or rather of pure Christianity. His was not a theology which left out the backbone and strength of religion—not a theology, on the other hand, all bones and skeleton, a lifeless thing without a soul: his theology was full-orbed-Calvinism, high as you please, but practical godliness so low that many called it legal.
Here is an excerpt from an article by Dr. Thomas Schirrmacher which investigates the reformed convictions of William Carey. Dr. Schirrmacher laments over the fact that though much has been written about Carey and his colleagues, their mission field in Serampore, and their achievements in printing, in Bible translation, in teaching and in many other areas, little attention has been paid in his numerous biographies to his theology.  He reasons, This failure is probably due to the fact that Carey's theology differs from that of the presently predominant, Post-Classical mission societies, which happily claim him as their father.
Carey was a Protestant by conviction, as the anti-Catholic and anti-Papist tenor of his history of the church clearly demonstrates. The turning point, he believed, was reached by the Reformers. He names especially Luther, Calvin, Melanchton, Bucer and Peter Martyr. He held the true Protestant dogma for essential to missions and to the missionary, for missionaries must, among other things, be "of undoubted orthodoxy in their sentiments."
Carey's theology is not only unusual for modern tastes in its Postmillennialism, but also in its Calvinist soteriology, for many now believe that the doctrine of presdestination extinguishes missionary effort rather than intensifying it. Carey, like most other Protestant missionaries and missionary leaders of his day, agreed with the Calvinist view.
Up into our century, the English Baptists were divided into two groups, the Arminian 'General Baptists' and the Calvinist 'Particular Baptists', to which John Bunyan and C. H. Spurgeon belonged. The designations indicate the extent of Jesus' atoning death: 'General Baptists' believe that Jesus died for all, 'Particular Baptists' believe that He died only for the Elect. Carey's Calvinist viewpoint is clearly demonstrated in various parts of his book.
Carey was not influenced by the Methodism of his day, as one might expect, but as a Calvinist, his significance lies in his reconciliation between the theology of the Reformation, particularly Reformed theology, and the Church's responsibility for missions. Frank Deauville Walker writes,
"He could not harmonize the views of the hyper-Calvinists with the duty of calling men to Christ. On the other hand, the opposite doctrine of Arminianism held by the Methodists seemed to him to strike at the roots of belief in the grace of God."
Hyper-Calvinism is the opinion that the Calvinist doctrine of Predestination refutes missions, because God would save those He wished without human aid, so that the Great Commission is already fulfilled. Although not typical of Calvinism, this viewpoint was popular, particularly among the Particular Baptists Carey knew.
Carey's significance lies therefore in his harmonization of the Calvinist doctrine of soteriology with Calvin and with the Reformed Protestants of the first and second generation. His precursor, according to Walker, was his friend, Andrew Fuller, who had been a Hyper-Calvinist, but had reconsidered his position and, in his printed sermon, "The Nature of Importance of Walking by Faith" of 1784 and in his book, The Gospel Worthy of All Acception, derived the responsibility for missions from the doctrine of predestination itself. Robert Hall's pamphlet, "Help to Zion's Travellers" of 1781, which deeply influenced Carey, also marks the transition from Hyper-Calvinism to missionary Calvinism. In short, "Anglican and Baptist pastors such as Thomas Scott, Andrew Fuller, Robert Hall,Sr. and John Sutcliffe ... " aided Carey in overcoming Hyper-Calvinism without surrendering the Calvinist view of salvation. A . Christopher Smith adds, "A neo-Puritan theology much indebted to Jonathan Edwards thus was mediated to Carey without his having to pore over theological tomes."
This demonstrates that not only Carey advocated Calvinist soteriology (and Reformed Postmillennialism), but that the leaders of his British mission society, Andrew Fuller, John Ryland and Thomas Scott, did as well. Scott wrote "The History of the Synode of Dort" and a history of the origin of the five points of Calvinism. Carey used these works in India and thanks Scott for them expressly.
The same is true of Carey's colleagues in India, according to their 'Form of Agreement' of 1805, which gave them a common basis: "we are sure that only those who are ordained to eternal life will believe, and that God alone can add to the church such as shall be saved."
Calvinism in Carey’s "An Enquiry into the Obligations of Christians to Use Means for the Conversion of the Heathens "
Carey derives the very possibility and the responsibility for missions from the doctrine of providence itself, while Hypercalvinism derived from the doctrine of predestination its belief that the heathen were lost unless God brought them the Gospel without human assistance. 'Providence' in Calvinist theology describes God's sovereignty. Carey uses this term six times in the "Enquiry" and often in other writings as well. As a Calvinist Baptist, he believed in Providence unreservedly and continually based his belief in the necessity of missions on this idea.
"It has been said that we ought not to force our way, but to wait for the openings, and leadings of Providence; but it might with equal propriety be answered in this case, neither ought we to neglect embracing those openings in providence which daily present themselves to us. What openings of providence do we wait for? ... Where a command exists nothing can be necessary to render it binding but a removal of those obstacles which render obedience impossible, and these are removed already. Natural impossibility can never be pleaded so long as facts exist to prove the contrary."
Even later, Carey never changed his view. James Beck adds,
"Carey never strayed far from his Calvinistic roots when reflecting on his God of providence. God was a God of order and control."
As we have already seen, Carey distinguishes in the "Enquiry" between God's sovereign will, Providence, and his moral will, duty. Not only here does he prove himself to be a pupil of Calvinist ethics. His arguments distinguish, for example between the moral and the ceremonial Law, and discusses the question, what factors revoke a Biblical commandment, with reasoning typical of Reformed ethics. In the churches he served prior to his departure for India, he exercised a strict church discipline typical of Calvinism, and followed Puritan ethics in many minor decisions, such as journeys on Sundays. 
 Gonzalez, Justo L. The Story of Christianity Vol. 2, pg. 306
 “C.H. Spurgeon’s tribute to William Carey”, Supplement to the Baptist Times, (16 April, 1992), pg.1
 Dr. Thomas Schirrmacher , William Carey, Postmillennialism and the Theology of World Missions