What does the order of authors mean in a scientific paper?
It depends on the field. In life sciences and medicine, first author = lead worker, last = senior researcher, and everyone in between contributed but did not lead. In mathematics and economics, authors are usually listed alphabetically regardless of contribution. In physics, large collaborations list hundreds or thousands of authors alphabetically. There is no universal rule — assumptions from one field mislead in another.
En détail
The life sciences convention (most common in what people call 'science')
First author = person who did most of the practical work, often a PhD student or postdoc. Last author = principal investigator, lab head, or the one who conceived the study and secured funding. Middle authors = contributed but did not lead. This is the most common convention worldwide.
The alphabetical convention
Standard in mathematics, economics, and some physics. Author order reveals nothing about contribution. Under this convention, 'first author' means little for career credit — reviewers understand this. Do not compare a mathematician's 'second author' credit against a biologist's 'second author' credit.
Corresponding author
Often marked with an asterisk (*), can be any position in the list. In some conventions the corresponding author is the last (senior); in others the first (lead); occasionally in the middle. Always check the specific paper.
Equal contribution marker
When two or more authors led equally, they are often marked with a dagger (†) or double dagger (‡) and a footnote reads 'these authors contributed equally'. This signals to hiring committees that the second-listed author should be credited as if they were first.