This is the one claim Christianity cannot survive without, so it should be argued like a historical question rather than a religious one. The best method is to start with the facts that even hostile scholars grant, and then ask what best explains them.

1. Work from the minimal facts. Gary Habermas's approach brackets the Bible's inspiration entirely and asks only what the majority of critical scholars — including atheists and agnostics — accept on ordinary historical grounds. The strict core is small: Jesus died by crucifixion, his followers believed they saw him alive, Paul and James were converted from opposition, and, by a strong majority though not unanimity, that the tomb was found empty. Everything else can be set aside for the sake of argument.

2. He died by crucifixion. This is as close to unanimous as ancient history gets. Tacitus records it, Josephus mentions it, Lucian mocks it, and the Gospels narrate it. Bart Ehrman and Gerd Lüdemann both accept it. And it is the one detail the early church had every motive to soften: Deuteronomy 21:23 says a hanged man is cursed by God, so a crucified Messiah was a scandal to Jews and folly to Gentiles (1 Corinthians 1:23). Nobody invents that.

3. The tomb was empty, and women found it first. All four Gospels name women as the first witnesses, in a culture where a woman's testimony was discounted in court. That is the criterion of embarrassment working in your favor: an inventor would have opened with Peter. And the proclamation began in Jerusalem weeks later, where the tomb was a short walk away and the body could have been produced (Acts 2:29-32 — Peter points out that David's tomb is still there, implying Jesus's is not).

4. They believed they saw him, and said so publicly. The creed in 1 Corinthians 15:3-8 is the earliest Christian text we have, and Paul says he received it — meaning it predates his letters, which date to the 50s. It lists Peter, the Twelve, James, five hundred at once, and Paul himself. "Most of whom are still alive" is an invitation to check, not a legend's hedge.

5. The disciples changed, and died. Before the resurrection they are hiding behind locked doors (John 20:19). Within weeks they are preaching in the temple courts and getting arrested for it. James is executed (Acts 12:2), and Peter and Paul are killed in Rome by early and widespread tradition. People die for what they believe is true; they do not sustain a fraud for decades and then die for a lie they know is false.

6. Two skeptics were converted. Paul was not a sympathizer; he was hunting Christians (Acts 8:1-3; Galatians 1:13-14). James, Jesus's own brother, did not believe during the ministry (John 7:5) and later led the Jerusalem church. What changes a hostile outsider and a skeptical sibling? Paul's own answer is an appearance of the risen Jesus (1 Corinthians 15:7-8), and he wrote it down within about twenty years, naming himself.

7. The alternatives are worse. Hallucination cannot explain repeated group appearances in different settings, or a skeptic and a hostile family member. The swoon theory requires a man to survive Roman flogging and crucifixion, move a stone, and convince everyone he had conquered death. The stolen-body theory requires the disciples to die for a theft they knew was a fraud. Legend requires decades, and the creed is too early. Wrong-tomb requires the authorities to end the movement by displaying a body, which they never did.

8. Turn: the skeptic has the same data to explain. You do not get to leave the facts unexplained. Whatever you propose has to account for the empty tomb, the appearances, the transformation of the disciples, the conversion of Paul and James, and the birth of a movement in the city where the execution happened. "Miracles are impossible" does not explain anything; it just rules out one candidate in advance. And that rule is not a finding of history — it is a philosophical commitment brought to it.

9. This claim is falsifiable, and Paul knew it. "If Christ has not been raised, then our preaching is in vain and your faith is in vain... we are misrepresenting God" (1 Corinthians 15:14-15). That is not the rhetoric of a religion designed to be unfalsifiable. Christianity staked everything on a public event in a known place at a known time, which is either very foolish or exactly what you would expect if it happened.

The resurrection is not proven the way a theorem is proven, and it does not need to be. It needs to be the best explanation of a set of facts that hostile scholars already accept, and on that question the case is stronger than most people expect.

Sources: Gary Habermas & Michael Licona, The Case for the Resurrection of Jesus; N.T. Wright, The Resurrection of the Son of God; William Lane Craig, Reasonable Faith; Bart Ehrman (for the skeptical case).