Who was the first to prove the fundamental theorem?

In summary, the fundamental theorem of calculus was first proven by Cauchy, but the discovery of the theorem is credited to Newton and Leibniz. The idea of finding tangent lines and areas using smaller sections dates back to Archimedes, but it was the fundamental theorem that showed the inverse relationship between these two problems. Wikipedia also claims that the theorem was known before Newton and Leibniz and was first proven by James Gregory and Isaac Barrow.
  • #1
armolinasf
196
0
Just curious who wrote the first proof of the fundamental theorem of calculus. Thanks.
 
Physics news on Phys.org
  • #2
Try google. The theorem was first proven rigorously by Cauchy.
 
  • #3
There were many people who found different ways of finding tangent lines, and, in particular, the slope of the tangent line (i.e. derivative) before Newton or Leibniz. And finding areas by dividing into smaller and smaller sections goes back to Archimedes. It is the discovery of the "fundamental theorem", that states that these two problems are, in an important sense, "inverse" that make Newton and Leibniz the "creators" of the Calculus. Cauchy may well have been the one to prove the theorem rigorously, using limits (Newton and Leibniz used nebulous appeals to "infinitesmals" rather than limits), but the theorem was "discovered" by Newton and Leibniz.
 
  • #4

Related to Who was the first to prove the fundamental theorem?

1. Who is credited with proving the fundamental theorem?

The French mathematician Pierre de Fermat is generally credited with proving the fundamental theorem of algebra.

2. When was the fundamental theorem first proven?

The fundamental theorem of algebra was first proven in the 17th century, but the exact date is unknown. Some sources suggest it was proved by Italian mathematician Lodovico Ferrari in 1540, while others credit it to Rafael Bombelli in 1572.

3. What is the fundamental theorem of algebra?

The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. In other words, every polynomial equation of the form ax^n + bx^(n-1) + ... + c = 0 has at least one solution in the complex numbers.

4. How did Fermat prove the fundamental theorem?

Fermat's proof of the fundamental theorem of algebra is not fully known, as he did not publish his proof. It is believed that he used a geometric argument involving the intersection of conic sections to prove the theorem.

5. Has the fundamental theorem of algebra been proven in other ways?

Yes, there have been many different proofs of the fundamental theorem of algebra since Fermat's time. These proofs use a variety of mathematical techniques such as complex analysis, topology, and algebraic geometry. The most famous and widely accepted proof is by German mathematician Carl Friedrich Gauss, who published his proof in 1799.

Similar threads

B Question about the fundamental theorem of calculus
    • Calculus
Replies
2
Views
506
B A proof of the fundamental theorem of calculus
    • Calculus
Replies
6
Views
2K
Insights A Numerical Insight for the Fundamental Theorem of Calculus - Comments
    • Calculus
Replies
8
Views
2K
I Why prove Taylor's theorem with p(x)=q(x)−((b−a)^n/(b−x)^n)q(a)?
    • Calculus
Replies
9
Views
1K
I Questions about the fundamental thoerem of calculus
    • Calculus
Replies
10
Views
2K
Fundamental theorem of calculus
    • Calculus
Replies
12
Views
2K
MHB Fundamental theorem of calculus and more....
    • Calculus
Replies
9
Views
2K
B Some help understanding integrals and calculus in general
    • Calculus
2
Replies
42
Views
4K
Fundamental Theorem of Calculus
    • Calculus
Replies
8
Views
1K
I Visual interpretation of Fundamental Theorem of Calculus
    • Calculus
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top