# Making your mark by age 30?

There is this old adage that says something like: if you have not made your mark in Physics by the age of 30 then you are not going to.

Of course, I presume that other areas of study could be substituted for "Physics". But, when I was an undergrad Physics major in the latter half of the 1960s, this was often heard among students thinking about their future in Physics and wondering if they will "make it by 30".

But, where did this come from? That is my question.

In looking at the major players of the first part of the 20th century physics scene who are known for major breakthroughs we have: Planck age 30 in 1900 when he published his work, Einstein age 26 in his miraculous year of 1905, Bohr was 28 when he published his atomic "Bohr Model" in 1913, de Broglie was 31 in 1923 when he published his work on particle-wave duality, Heisenberg was 24 when he published his "Matrix Mechanics" in 1925, Schrodinger was 39 during his 1926 publication of wave mechanics, Max Born was 45 when he published about "Probability Waves" in 1927 and Paul Dirac was 26 when he published his Electron Theory in 1928.

So, a list of 8 well known physicists who definitely made a mark for themselves in Physics but only half of them were 30 or under in age. And, two of them were in their 40s (old men!).

I am curious -- who says you need to be younger than 30. I am hoping there is still hope for this 69-year old.

• Typically the young are able to focus exclusively on their goals - before family and career have caught up with them. As Isaac Newton said: "All this was in the two plague years of 1665-1666. For in those days I was in the prime of my age for invention & minded Mathematicks & Philosophy more then than at any time since.” – Peter Diehr Apr 22 '16 at 18:27
• A song with this message is quoted in "The Strangest Man", a biography of Paul Dirac. There, it is presented as "traditional Cambridge" lore, if I recall correctly. – Danu Apr 22 '16 at 19:13
• @Danu: Isaac Newton's quotation is given in full here, with the mss source reference at the bottom. – Peter Diehr Apr 23 '16 at 1:45

## 1 Answer

This opinion is quite common, especially in physics and mathematics, though everyone knows that there are exceptions. As a mathematician, I give examples from mathematics. G. H. Hardy, in his Mathematician's Apology wrote that mathematics is a sport for young people. I. M. Gelfand, when a 3-d year undergraduate approached him asking for a research topic, replied that s/he is too old to begin research (Soviet 3-d year undergraduates usually were 20-21 years old).

Examples that you give show that usually the best achievement of top physicists are obtained before or around 30, and that there are exceptions. In mathematics, the picture is the same. Examples of mathematicians who wrote their best paper at much later age exist, of course. Roger Apery proved his most famous (by far) result (irrationality of $\zeta(3)$) at the age of 63. One can argue that Antoni Zygmund made his most important contribution after 50, though he also did very important work before. de Branges proved Bieberbach's conjecture at 52; this is his most famous result, but he had first rate results in his youth as well.

In these examples mathematicians made their top contributions at an advanced age, but they were established mathematicians. Examples when a mathematician BEGAN his career late, and achieved top results, are much more rare, though they also exist.

From my own experience I can tell that opinions of Hardy and Gelfand reflect general trend: most outstanding mathematicians obtain their best results between 30 and 40. But there are exceptions. Rare but very precious. For this reason I think that the attitude expressed in the legend about Gelfand is wrong.

• Don't forget the recent example of Zhang, on bounded gaps between primes. He was completely unknown :) – Danu Apr 22 '16 at 18:59
• @Danu: Again, this is a VERY exceptional case. – Alexandre Eremenko Apr 22 '16 at 20:13
• Sophus Lie began around 30. – Geremia Apr 22 '16 at 23:44